Keywords: Control Design
Abstract: In this talk by ”using delays” I understand either Time-Delay Approaches to control problems (that originally may be free of delays) or intentional inserting delays to the feedback. I will start with an old Time-Delay approach – to sampled-data control. In application to network-based control with communication constraints, this is the only approach that allows treating transmission delays larger than the sampling intervals. I will continue with ”using artificial delays” via simple Lyapunov functionals that lead to feasible LMIs for small delays and to simple sampled-data implementation. Finally I will present a New Time-Delay approach – this time to Averaging. The existing results on averaging (that have been developed for about 60 years starting from the works of Bogoliubov and Mitropolsky) are qualitative: the original system is stable for small enough values of the parameter if the averaged system is stable. Our approach provides the first Quantitative bounds on the small parameter making averaging-based control (including Vibrational Control and Extremum Seeking) reliable.

Keywords: Frequency-domain Methods, Observation and Observer Design, Predictor-based Control
Abstract: We propose a predictor tuning method for a class of uniformly observable nonlinear time-delay systems. This method is based on the multiplicity-induced-dominancy property of quasipolynomials. The predictor gains are chosen in such a way that a dominant root is located in the left half-plane, thus the prediction error converges exponentially to zero. For illustration purposes, a state prediction for the feedback control of a simple pendulum is designed and simulation results are presented.

Keywords: Stabilization, Low-complexity Controllers
Abstract: The minimization of the spectral abscissa function of linear time-invariant time-delay systems, an established approach to compute stabilizing controllers with a fixed structure or dimension, often gives rise to minima, characterized by active characteristic roots with multiplicity higher than one. At the same time, recent theoretical result reveal situations where the so-called multiplicity induced dominancy (MID) property holds, i.e., the higher multiplicity implies that the root is dominant, leading to design approaches based on assigning multiple roots. Using an integrated approach, combining analytical characterizations, computation of characteristic roots and numerical optimization, a complete characterization of the stabilizability of second order systems with input delays is provided, for both state feedback and delayed output feedback, including two terms in the control. Level sets of the minimal achievable spectral abscissa are also characterized. These results shed light on the complex relations between (configurations involving) multiple roots, the property of being dominant roots, and of corresponding to global minimizers of the spectral abscissa function.

Keywords: Distributed Delays, Stabilization, Other Applications of Time Delay Systems
Abstract: This paper considers the stabilization of a rolling balance board by means of the multiplicity-induced- dominancy property. A two degree-of-freedom mechanical model of a human balancing on a rolling balance board is analyzed in the sagittal plane. The human body is modeled by an inverted pendulum which connects to the balance board through the ankle joint. The system is stabilized by the ankle torque managed by the central nervous system (CNS). The action of the CNS is modeled by a delayed full state feedback: a pointwise delay stands for all latencies in the neuromechanical system (reaction time, neuromechanical lag, etc.). The aim of the paper is to achieve a good occurrence in terms of the decay rate, it shows the links with dominancy and with the exponential stability property of the solution.

Keywords: Delays in Power Systems, Robust Control, Control Design
Abstract: In this paper, we consider the problem of regulating the output voltage of a Direct-Current-to-Direct-Current (DC-DC) buck converter when the input source is partially known, and the parameters of the converter are uncertain. Our objectives are: (i) to render the system with improved speed of response in spite of high-frequency measurement noise and, (ii) to guarantee robustness against uncertainties and disturbance attenuation in the face of unknown input signals. To fulfill objective (i), we utilize a Proportional-Integral-Retarded (PIR) controller to mitigate high-frequency measurement noise without compromising the system’s bandwidth. This is accomplished by placing the rightmost poles of the closed-loop system at an appropriate locus in the complex plane. To fulfill objective (ii), we first keep the controller design in (i) and then, we derive sufficient stability conditions via a rigorous L2-gain analysis. To our knowledge, these results are novel and further equip PIR controllers with much-needed, but previously missing, robust and H-infinity properties. Numerical examples testify to the feasibility of the proposed approach on a low-power DC-DC buck converter.

Keywords: Control Design, Frequency-domain Methods, Mechatronics and Mechanical Systems
Abstract: Designing controllers using intentional delays offers many new opportunities (Zhong and Li, 2002; Ramirez et al., 2013, 2015; Mazanti et al., 2021). However, in the presence of unintentional delays, these controllers may not perform as desired. Here, we design a Proportional Retarded (PR) controller at the face of an unintentional delay. The design is performed for first-order plants with a time constant. We present the controller formulation and explain its limitations against larger unintentional delays or smaller time constants.

Keywords: Infinite-dimensional Systems and Delays, PID Control, Filtering and observation
Abstract: The paper is focused on control design for time delay systems which can be described by delay differential equations of up to the third order. In spite of higher-order plant dynamics it can be reduced but there are cases where such a reduction would lead to losing significant dynamics feature. Typically, the plants of the third order are thermal, water or wind power plants, and also plants described by the second-order model dynamics but with additional, not negligible actuator dynamics. From application point of view the crucial problem is to reject loads or disturbances of plants providing energy conversion. The third-order plants with delays are apparently present in practice and therefore any other order reduction means inappropriate approximation.

Keywords: Parameter-based Methods, Infinite-dimensional Systems and Delays, Other Applications of Time Delay Systems
Abstract: We theoretically study the Atlantic Meridional Overturning Circulation (AMOC) by means of a mathematical model with two time delays. The time delays are associated with the positive temperature feedback between the Equator and the North Pole and the salinity exchange between the surface and deep water at the Pole. Studying the interplay between these delayed feedback mechanisms conceptually can improve our understanding of the long-term dynamics and possible responses of the Atlantic Ocean. Specifically, we consider a scalar delay differential equation with these two feedback loops, and we perform its numerical bifurcation analysis with the software package DDE-Biftool for Matlab. Our analysis shows rich behaviour organized by homoclinic orbits, as well as resonance phenomena between the delays.

Keywords: Other Applications of Time Delay Systems, State-dependent Delays
Abstract: We use analytical constructions and numerical continuation to study the dynamics of conceptual climate models of the El Nino-Southern Oscillation (ENSO) system. The models consist of scalar delay differential equations (DDEs) where the state variable portrays the deviation of the thermocline depth from its mean value in the eastern tropical Pacific Ocean, and also acts as an approximation to the sea surface temperature there. Delays arise due to the finite velocities of the oceanic waves. Seasonal variation is included through periodic forcing, which makes the DDEs nonautonomous which complicates both analysis and numerical computations.

Keywords: Parameter-based Methods, Other Applications of Time Delay Systems, Infinite-dimensional Systems and Delays
Abstract: The model of Suarez and Schopf is one of the earliest delay differential equation (DDE) models of the El Ni ̃no-Southern Oscillation (ENSO). It showed that a delayed action is able to generate an oscillation that can be interpreted as ENSO-like behaviour (with a warmer and a cooler Pacific Ocean during parts of the period). We perform a bifurcation analysis of this DDE model in the feedback strength and the feedback delay. We find the model dynamics to be significantly influenced by the presence of a double-zero bifurcation. We then extended the model to include annual periodic forcing and consider the effects this has had on the observed behaviour.

Keywords: Stabilization, Other Applications of Time Delay Systems, Delays in Biological Systems
Abstract: Postural sway is investigated in terms of the center of pressure location feedback in the sagittal plane. The human body is modeled by a single inverted pendulum subject to a delayed controller involving feedback of the human body angle, the angular velocity and the center of pressure location. The saturation of the ankle torque is included in the model. The effect of the gain, KCOP, for the feedback of the center of pressure is analyzed. Small value of KCOP is associated with reduced sensory information about the center or pressure location, which is typical for people living with peripheral neuropathy. The method of multiple time scales is used to investigate the nonlinear dynamics of the postural sway. The results show that the system undergoes supercritical Hopf-bifurcation in case of small values of KCOP, which may explain the arising larger postural sway of people diagnosed by peripheral neuropathy.

Keywords: Delays in Biological Systems, Modeling and Identification
Abstract: Collective motion is a common phenomenum in nature, and needs to be well-understood. In this paper, we try to understand this phenomenum by using the generalized Couzin model with heterogenous time delays. Simulation is carried out by using LAMMPS secondary development. It is found that when the homogeneous delay time increases, patterns of the collective motion change from highly parallel to vortex motion. While for heterogenous time delays, the individuals with short delays tend to distribute at the front part of the cluster when the delays are approximately normally distributed. If the cluster is divided into two sub-clusters, the distribution of individuals with short delays changes from favouring the front of the cluster to back, as the delay difference between two sub-clusters increases.

Keywords: Filtering and observation, Observation and Observer Design, Delay Compensation
Abstract: The demand for Unmanned Underwater Vehicles (UUVs) for various operations has increased. Automating these operations requires good knowledge of the location of the UUV. This study investigates the filter lag in the commercial low-cost Underwater GPS Explorer Kit, a short baseline (SBL) from Water Linked. Furthermore, different filters are designed in an attempt to minimize the filter lag. Minimizing the lag is beneficial for real-time navigation, as delays have a negative impact on stability. Three different filters are designed; a model-free simple moving average (SMA) filter, a Kalman filter (KF) based on a constant velocity motion model, and lastly, an unscented Kalman filter (UKF) based on the non-linear model derived from the robot's dynamics. A large filter lag is found in the original filter; however, it can be concluded that a model-based filter with knowledge of the system dynamics can be used for minimizing the filter lag.

Keywords: Fault Tolerant Control, Predictive Control, Energy and Nuclear
Abstract: In this paper, we formalise a fault-tolerant control and mitigation strategy for the energy management of renewable microgrids. The scheme is composed of a Model Predictive Control (MPC) algorithm based on a Linear Parameter Varying (LPV) model for the microgrid energy dispatch. The MPC uses fault diagnosis information in order to correctly update the LPV microgrid model, while adapting the process constraints in consonance with the level and location of faults. We show how closed-loop stability is ensured with simple quadratic terminal ingredients, provided through LMI-solvable remedies. Nonlinear simulation results of a real microgrid benchmark are included to demonstrate the effectiveness of the approach.

Keywords: Network Controlled Systems, Optimal Control, Other Applications of LPV Systems
Abstract: This paper studies the problem of optimal deception attacks against remote state estimation, where the measurement data is transmitted through an unreliable wireless channel. A malicious agent is capable of intercepting and modifying raw data, with the goal to cause the maximum estimation quality degradation and deceive chi-square anomaly detectors. Contrary to existing studies that focused on greedy attack performance, we consider a more general scenario that the attacker aims to maximize the summation of estimation errors in a fixed interval. It is shown that the information-based optimal attack is a linear combination of the minimum mean-square error estimates of all historical prediction errors. The combination coefficients can be obtained by solving a convex optimization problem. Moreover, the proposed attack can be generalized to deceive interval chi-square detectors with different lengths by slightly modifying the stealthiness constraint. The effectiveness of the proposed method is verified with numerical examples and comparative studies.

Keywords: Nonlinear Systems, Stability and Stabilization, Other Applications of LPV Systems
Abstract: This paper considers the problem of designing a shifting output-feedback controller for polytopic linear parameter-varying (LPV) systems subject to time-varying saturations. By means of the LPV framework and the use of the Lyapunov theory, the shifting paradigm concept, and the ellipsoidal invariant theory, a linear matrix inequality (LMI)-based methodology for the controller's design is proposed. The resulting gain-scheduled controller holds the control action in the linearity region of the actuators and regulates online the closed-loop convergence taking into account the instantaneous saturation limit values. The proposed approach is validated by means of an illustrative example.

Keywords: Switching Systems, Hinf Control, Other Applications of LPV Systems
Abstract: This paper presents a smooth switching between a set of Linear Parameter-Varying (LPV) controllers that have been designed separately. The switching control strategy is based on Youla-Kucera (YK) parameterization. A generalized interpolation scheme of various LPV controllers is shown and proved for the LPV-YK concept. Such kind of parameterization is beneficial to switch or interpolate between multiple controllers without adding any constraints to the design of the local controllers and the switching signals. The proposed method is applied to an Active Magnetic Bearing (AMB) system and compared to a switched LPV controller.

Keywords: Stability and Stabilization, Optimal Control, Nonlinear Systems
Abstract: This work proposes an alternative technique to design an incremental stabilizing output-feedback control law for constrained discrete-time linear parameter-varying (LPV) systems. We use an extended state space composed of the system's state and control variables and use the control variations as the control inputs. We employ polyhedral sets' Positive-Invariance and Contractivity properties to achieve local stability while satisfying the constraints. This work's main contribution is proposing a novel structure of the positively invariant polyhedron whose design can be achieved by means of a bilinear optimization problem. Comparative results are shown to highlight the benefits of the new approach.

Keywords: Uncertain Systems - LPVS, Positive Systems - LPVS
Abstract: For one class of uncertain Metzler MIMO systems the concepts of matching conditions, structural parametric constraints and system positiveness is noted in this paper when solving the problem of PID control design. In particular, exploiting the supported structure of the measurement, the design task is formulated as a linear matrix inequality problem if the constraint set consistent with the controller parameter representation is found to be feasible. Covering given assumptions, action consequence of the derivative parameter of the control law is stated separate to highlight desired positiveness of the closed-loop system matrix.

Keywords: Low-complexity Controllers, Control Design, Delays and Vibration Control
Abstract: In order to achieve a partial pole placement for linear time-invariant systems including time-delays in their models' representation, a method for the design of quasipolynomial-based controllers has been proposed in recent works. The ensuing controllers correspond to some output feedback control laws with constant parameters. It appears that such a controller has a limited number of degrees of freedom, limiting the potential performances in closed loop. To overcome this issue, we propose to modify the previous quasipolynomial-based controller by using dynamical parameters in their design. It turns out that the use of dynamical parameters corresponds to linear filtered terms in the control law of the original one. Such a controller is applied to the active vibration damping problem for a piezo-actuated flexible structure.

Keywords: Control Design, Infinite-dimensional Systems and Delays
Abstract: The scope of this work is to present the theoretical background for the safety-critical control of time delay systems with state delay. We extend the theory of control barrier functions by introducing control barrier functionals.

Keywords: Time-varying Delays, Predictor-based Control
Abstract: Control barrier functions (CBFs) have been recently considered for ensuring safety of nonlinear input-affine systems by means of appropriately designed controllers rendering a desired superlevel set of the CBF function forward invariant. In this work, we consider the safety control problem for nonlinear input-affine systems with multiple time-varying input delays. In order to ensure safety, we first design a set of predictors that estimate the state of the system at different future times by utilizing the control laws designed to ensure safety of the delay-free system. Under the assumption of perfect estimation of the future states, we show that under the designed controller the closed-loop performance of the systems with and without the input delays is the same by the time the input with the largest delay acts on the system with delays for the first time.

Keywords: Predictor-based Control, Control Design, Other Applications of Time Delay Systems
Abstract: This paper studies a control structure based on generalized predictive control (GPC) able to deal with SISO/MIMO dead-time processes. An equivalent dead-time compensator structure is presented in order to analyze the controller properties, such as set-point tracking, robustness and disturbance rejection. From the equivalent structure, a set of simple tuning rules are derived. Such rules employ a reduced number of parameters which facilitates the tuning of the controller, especially for the case of MIMO processes. A simulation result shows the enhanced performance of the proposed strategy when compared with other MIMO literature example. Furthermore, an experiment was performed to show the effectiveness of the proposed tuning strategy on the temperature and humidity control of an in-house thermal chamber.

Keywords: Infinite-dimensional Systems and Delays, Delay Compensation, Delays in Biological Systems
Abstract: Neurological studies show that injured neurons can regain their functionality with therapeutics such as Chondroitinase ABC (ChABC). These therapeutics promote axon elongation by manipulating the injured neuron and its intercellular space to modify tubulin protein concentration. This work introduces an input delay compensation with state-feedback control law for axon elongation by regulating tubulin concentration. Axon growth dynamics with input delay is modeled as coupled parabolic diffusion-reaction-advection Partial Differential Equations (PDE) with a boundary governed by a nonlinear Ordinary Differential Equations (ODE), associated with a transport PDE. A novel feedback law is proposed by using backstepping method for PDE and input-delay compensation. The gain kernels are provided after transforming the interconnected PDE-ODE-PDE system to a target system. The stability analysis is presented by applying Lyapunov analysis to the target system in the spatial H1- norm, thereby the local exponential stability of the original error system is proved.

Keywords: Delays in Biological Systems, Distributed Delays, Time-domain Methods
Abstract: We consider a multi-group epidemiological model in a heterogeneous population to describe infectious disease (e.g. COVID-19) outbreaks in a long-term care facility. Age-based heterogeneity reflects higher transmission with enhanced interactions, and higher fatality rates in the elderly. We analyse a SEIR model in the form of a system of integro-differential equations with general distribution function for the infectious period. Lyapunov functions and graph- theoretical methods are employed to establish the role played by the basic reproduction ratio R_0 : global asymptotic stability of the disease-free equilibrium and no sustained outbreak when R_0 < 1, in contrast to persistent outbreak and globally asymptotic endemic equilibrium when R_0 > 1.

Keywords: Infinite-dimensional Systems and Delays, Delays in Biological Systems, Approximation Methods
Abstract: For structured epidemic models, the basic reproduction number measures the number of new individuals generated by one average individual (in epidemiology, it is the number of new infected individuals generated by one average infected individual in a fully suscpetible population), and it is rigorously defined as the spectral radius of the next-generation operator (NGO), which is an infinite-dimensional positive and linear operator. We present a numerical method to approximate R_0, which first constructs the pseudospectral discretization matrices of the operators involved in the definition of the NGO, and second computes the spectral radius with standard techniques for finite-dimensional eigenvalue problems. We show the potentiality and the effectiveness of the approach through the analysis of some instances of tan epidemic model with two structures.

Keywords: Delays in Biological Systems
Abstract: The incubation period of Plasmodium vivax (P. vivax) malaria can vary depending on the strains or the geographic regions. In particular, its strains from temperate regions have extended incubation periods. This is considered to be an adaptation strategy to the seasonal environment. In this paper, I introduce a modeling study that models the long-term incubation period using delay differential equations. With the model, we investigate the role of incubation time in malaria dynamics and study its impact on the transmission risk in a seasonal environment.

Keywords: Delays in Biological Systems
Abstract: We consider a two-patch tick dynamics model where we take into account host mobility and local environmental factors through a coupled system of four delay differential equations with two delays. We study equilibria and stability for the isolated and interconnected patch models using monotone dynamical systems theory. In case of no host mobility, it is possible to provide explicitly a closed form solution for the coexistence equilibrium. The addition of host mobility complicates this, therefore we use perturbation analysis to determine the properties and the asymptotic expansion of the coexistence equilibrium. We then focus on periodic solutions and analyse Hopf bifurcations. In the isolated case, it is possible to provide analytically the Hopf bifurcation point; in the interconnected case, we will show some bifurcation diagrams to describe the model behaviour and the effect of mobility parameters on the model dynamics.

Keywords: Delays in Biological Systems
Abstract: Based on the well-studied Nicholson's blowfly equation, we propose a new mathematical model to address the evolution of maturation period. The model is a system of two delay differential equations with two discrete delays, which can be used either for populations of two species or the populations of two different strains of the same species. After analyzing the dynamics of the model in terms of four combined parameters, we discuss the issue of evolution of maturation. We identify an optimal maturation delay for each species/strain, depending on model parameters reflecting the quality and suitability of the habitat for each species. In the case of two strains (phenotypes) of a single species, we find that the common optimal maturation period is both a globally evolutionary stable strategy and a convergence stable strategy. These results help to explain the impact of the habitat on the evolution of the maturation period. We also discuss some open problems regarding the invasibility of oscillatory insect populations.

Keywords: Networks and Networked Systems, Frequency-domain Methods, Delays in Biological Systems
Abstract: The problem of synchronization in heterogeneous networks of linear systems with nonlinear delayed diffusive coupling is considered. The network is presented in new coordinates mean-field dynamics and synchronization errors. Thus the problem of network synchronization is reduced to the studying of synchronization-error system stability. The circle criterion for time-delay systems is used to derive the stability conditions of synchronization-error system. Obtained results are applied to a network of neural mass model populations, and the synchronization conditions are established. Simulation results are provided to illustrate the obtained analytical results.

Keywords: Structural Properties, Time-varying Systems, Symbolic Computation and Control
Abstract: In this paper, the algebraic analysis approach to linear state-space systems is further developed using rings of integro-differential operators. The module structure of linear state-space systems is investigated over these rings. The module associated with a linear state-space system is shown to be the direct sum of the stably free module defined by the linear system without inputs and the free module defined by the inputs of the system.

Keywords: Functional Systems, Structural Properties
Abstract: We develop an efficient algorithm for computing polynomial solutions of linear integro-differential equations. Considering a linear integro-differential operator written in normal form, we compute the possible degrees of its polynomial solutions. Then, we prove that the so-called {em monomial-by-monomial} method can be adapted to the integro-differential case. The difference compared to the well-studied case of linear differential equations merely comes from the presence of an ``evaluation term" in the normal form. Our algorithm is implemented in Maple and many examples are provided to illustrate the different results.

Keywords: Structural Properties, Functional Systems, Symbolic Computation and Control
Abstract: In this paper, we further develop the study of rings of integro-differential-delay operators considered as noncommutative polynomial algebras satisfying standard calculus identities. Within the algebraic analysis approach, we show that transformations and reductions of linear differential time-delay systems can be interpreted as homomorphisms and isomorphisms of finitely presented left modules over an algebra of integro-differential-delay operators. In particular, we show how Fiagbedzi-Pearson's transformation can be found again and generalized. This transformation maps the solutions of a first-order differential linear system with state and input delays to the solutions of a purely state-space linear system. Fiagbedzi-Pearson's transformation reduces to the well-known Artstein's reduction when the system has no state delay and yields an isomorphism of the solution spaces.

Keywords: Symbolic Computation and Control, Structural Properties, Multidimensional Systems
Abstract: The formal integrability of systems of partial differential equations plays a fundamental role in different analysis and synthesis problems for both linear and nonlinear differential control systems. Following Spencer’s theory, to test the formal integrability of a system of partial differential equations, we must study when the symbol of the system, namely, the top-order part of the linearization of the system, is 2-acyclic or involutive, i.e., when certain Spencer cohomology groups vanish. Using the well-known fact that Spencer cohomology is dual to Koszul homology and symbolic computation methods, we show how to effectively compute the homology modules defined by the so-called Koszul complex of a finitely presented module over a commutative polynomial ring. These results are implemented using the OreMorphisms package. We then use these results to effectively characterize 2-acyclicity and involutivity of the symbol of a system of partial differential equations. Finally, we show explicit computations on different examples.

Keywords: Structural Properties, Multivariable Systems, Symbolic Computation and Control
Abstract: We present several recent results and generalizations that have been obtained in the theory of collision-freeness studied in Zerz and Herty (2019). A nonlinear ODE system x'(t)=f(x(t)) is called collision-free if the solution to the initial value problem with x(0)=x^0 has distinct components for all times t whenever the initial state x^0 has distinct components. This is an important structural property of particle systems. Here, we address the case where the state of the i-th particle has d components x_{i1},...,x_{id}, and a collision occurs if there exist some time t and distinct i, j such that x_{ik}(t)=x_{jk}(t) for all k in {1,...,d}. Thus, the already known case corresponds to d=1. In this paper, we characterize d-collision-freeness for linear, polynomially nonlinear, and general C^1-systems. Moreover, we show that d-collision-freeness implies D-collision-freeness for all multiples D of d that divide the overall state space dimension. In particular, 1-collision-freeness implies d-collision-freeness. Finally, we address the connection between permutation symmetry and d-collision-freeness.

Keywords: Delays and Vibration Control, Control Design, Frequency-domain Methods
Abstract: This paper contains a review of very recent progress on the concepts of “Non-collocated vibration absorption”, and reiterates on a relevant benchmark problem which was recently published [20,21]. The key highlight is to actively tune a dynamically resonant absorber for spatial and spectral variations of the target suppression. Although not exclusive, our contributions to date have been using the broadly-studied Delayed Resonator approach to achieve the needed real-time tuning. This document summarizes the progress made up to now, and the major challenges remaining. This effort appears to offer very rich domain for vibration control specialists, and as such we believe some intense work will follow in the near future. Along with the conceptual descriptors we will include some surprising results from the ongoing studies.

Keywords: Delays and Vibration Control, Control Design, Frequency-domain Methods
Abstract: A generally applicable spectral design of non-collocated vibration suppression performed primarily by a delayed resonator is presented. The vibration suppression is achieved by direct assignment of imaginary axis zeros of the transfer function between the periodic disturbance force and the target's displacement. In order to increase the stability margin and to widen the range of frequencies which can be suppressed, the non-collocated vibration absorption by a delayed resonator is supplemented by a stabilizing controller tuned by spectral optimization. A unifying aspect of the resonator and the controller is that both use time-delay feedback of analogous structure. Another important aspect of the proposed method is that it can be applied to a system of general structure, where there possibly exist parallel paths for the disturbance force which go around the suppression target to the non-collocated absorber. Next to the theoretical design, experimental validation will be presented on a laboratory set-up.

Keywords: Delays and Vibration Control, Mechatronics and Mechanical Systems, Control Design
Abstract: The classical delayed resonator, proposed in nineties of the last century by N. Olgac and his co-workers, is traditionally used to fully absorb vibration of mechanical system in one direction. Once the multi-directional vibration absorption is targeted, it can be done by multiple deployment of one-directional delayed resonators. Though, the task is not straightforward as it is turned from SISO to MIMO problem. As a practical solution, two-dimensional delayed resonator for planar vibration absorption has recently been proposed and analysed. It has been shown that the resonation cannot be achieved only by controller tuning of the active vibration absorber with three degrees of freedom, but the absorber needs to satisfy relatively strict mechanical design characteristics. Currently, the concept of delayed resonator is being further extended towards spatial vibration absorption, which requires an absorber with six degrees of freedom. Also here, the absorber needs to fit within strict mechanical constraints. Besides, an additional correcting actuation needs to be included to achieve the required uni-frequency feature. In the presentation, next to outlining the novel delayed resonator concepts, the particular attention will be paid to the delayed feedback used to actuate the active absorber and its impact to the overall system stability.

Keywords: Delays and Vibration Control, Control Design, Robust Control
Abstract: This paper focuses on the development of a global sensitivity based design of robust input shapers. The Derivative-based Global Sensitivity Measure (DGSM) which consists of the expected value of the absolute value of the gradient of the terminal residual energy with respect to the uncertain parameters, is used to tradeoff performance to robustness. A multi-objective cost function which is a convex combination of the terminal residual energy for rest-to-rest maneuvers and the DGSM, is used to design robust input shapers. The proposed approach is illustrated on a single spring-mass-dashpot system and the benchmark floating oscillator. As compared to the traditional Zero Vibration Derivative Input Shaper, the proposed approach is demonstrated to reduce the average residual energy over the domain of uncertainty.

Keywords: Control Design, Mechatronics and Mechanical Systems
Abstract: The contribution aims in analysis of implementation aspects of nonlinear and time-delay controllers developed for damping oscillations of suspended payload under the motion constraints of the pivot. In particular, two configurations of the pendulum set-ups for damping the pendulum oscillations are considered here: with fixed and with vertically movable pivot. In the first case, the payload damping is performed via adjusting the suspension length, i.e. the pendulum string is shorten or extended. Whereas in the second case, the payload damping is performed via up and down movement of the pivot preserving fixed pendulum length. Unlike the classical problem of pendulum damping via moving the pivot in the horizontal direction, implemented e.g. in cranes, a direct solution based on control feedback theory for linear systems is not possible due to the fact that the linearization of both systems is uncontrollable in their equilibrium points. Thus, a derivation of a nonlinear controller or a time-delay based algorithm is necessary to solve the task.

Keywords: Delays and Vibration Control, Time-varying Delays, Delay Estimation
Abstract: As in the case of the Smith predictor, when applied to dynamical systems with delay in the input, the stability of the internal model control (IMC) system can be very sensitive to the mismatch that can occur between the plant delay and the identified delay. In this paper, we propose an online identification technique for the plant with input delay, which is used to adapt an IMC controller designed to reject periodic disturbances consisting of two harmonics. The proposed method is based on wavelet analysis and cross-correlation of the measured output. Moreover, the proposed controller structure introduces a novel analytical approach which makes it suitable for the adaptive application. The practical motivation of the study is to address the delay mismatch that can be caused by approximating time-varying high-order systems by first-order models with input delay. The approach is numerically validated.

Keywords: Time-varying Systems, Biological Systems
Abstract: We explore a matrix logarithm on time scales and show how it connects to systems of dynamic equations by solving a matrix Gompertz dynamic equation.

Keywords: Time-varying Systems, Uncertain Systems - SSSC
Abstract: This discussion paper compares deterministic and Markovian measures of stability for continuous-time linear switched systems. More precisely, we compare the maximal Lyapunov exponent of the system with its probabilistic counterpart when the switching signal is assumed to be determined by a Markov process. We report on recent results showing that equality of such measures of stability only occur in particular cases and hence, in general, Markovian measures of stability are less conservative than the corresponding deterministic ones.

Keywords: Uncertain Systems - SSSC, Observers, Networking and Network Controlled Systems
Abstract: Distributed estimation is a fundamental task performed by sensor networks, often achieved through the Kalman consensus filter. However, it requires exact models, which is seldom possible in practice since parametric uncertainties are usually unavoidable. We address in this paper the robust distributed filtering problem regarding linear discrete-time systems subject to polytopic uncertainties. We consider uncertainties in all parameter matrices of the target system and sensing models. First, we introduce a centralized filter, obtained as the solution to a min-max optimization problem whose cost function collectively weights all the underlying polytope vertices. Then, we derive a fully distributed version of this filter by applying the hybrid consensus on measurements and information approach. The estimators are recursive and do not rely on numerical solvers, appealing features for real-time applications. We validate our approach and assess its performance with a numerical example, comparing it with other robust distributed strategies.

Keywords: Robust Analysis and Control, Feedback Control, Numerical Issues in Control
Abstract: This paper deals with the problem of designing a sampled-data state feedback control law for continuous-time linear control systems subject to uniform input quantization. The sampled-data state feedback is designed to ensure the uniform global asymptotic stability (UGAS) of an attractor surrounding the origin. The closed-loop system is rewritten as a hybrid dynamical system. To do this, an auxiliary clock variable triggering the occurrence of sampling events is introduced. A numerically tractable algorithm with feasibility guarantees, based on concave-convex decomposition, is then proposed allowing to minimize the size of the attractor. Theoretical results are illustrated in a numerical example.

Keywords: Networking and Network Controlled Systems
Abstract: This paper studies fair dynamic rate allocation in a CDMA network. An optimization-based fair reverse-link rate assignment strategy is proposed. The network is modeled in a star topology, where the nodes represent either the base station (BS) or access terminals (ATs). The BS at every time instant computes the fair rate for each AT by minimizing the maximum disparity in user rates. Then, the BS sends a single bit to all ATs at every time instant. It is shown that if each AT could compute a specific variable, called the coordinating variable, it can find its fair rate, which means the decision-making strategy is distributed. The proposed method is computationally efficient, and simulations confirm its efficacy in different scenarios.