Keywords: Passivity
Abstract: Both passivity based control and sliding mode control are well established useful techniques for nonlinear systems. Although they have been considered to be completely incompatible methods, there are actually some points of contact between them. This presentation shows recent results on their integration based on the port-Hamiltonian framework. Passivity based control is a method to find energy based Lyapunov function candidates for physical systems. It can generate Lyapunov functions for several objectives such as trajectory tracking control and/or those for output feedback control by a similar way to the standard artificial potential function method. On the other hand, sliding mode control is a technique to design a closed loop system with fast convergence by employing discontinuous high gain feedback without constructing any explicit Lyapunov function for the closed loop system. This presentation gives a brief summary on the author's developments on passivity based control with a recent attempt to integrate the two different techniques by employing a special class of non-smooth Lyapunov functions. This idea allows for highly flexible controller design that smoothly complements passivity based control and sliding mode control.

Keywords: Passivity, Lyapunov Methods, Bilinear Systems
Abstract: Climate change and geopolitics have led to the conception of plans for reducing greenhouse gas emissions and improving the sustainability of existing fossil-based energy systems. In this respect, district heating has been identified as an indispensable player for its potential to integrate seamlessly environmentally-friendly heat sources. To improve the efficiency of these district heating systems, optimal operation schemes can be devised and enforced through control systems. To this end, we present a control-oriented nonlinear ODE-based model of temperature dynamics in a multi-producer district heating system. The model features a modular design and comprises the thermal dynamics of heat exchangers of producers and consumers interconnected by a distribution network of meshed topology. Then, we establish passivity properties and zero-state detectability for the modeled temperature dynamics that could be exploited for controller design and solving constrained optimization problems.

Keywords: Bifurcation and Chaos, Dynamical Systems Techniques, Mechatronic Systems
Abstract: The dynamics of an artificial hair cell is analyzed by considering the bifurcation behavior of a dominant mode model. It is shown that this model undergoes an Andronov-Hopf bifurcation similar to its biological counterpart, i.e., the hair cell in the mammalian cochlea. Consequently, this dynamical behavior is exploited to control the amplitude of the deflection of the artificial hair cell. In particular feedforward control with disturbance injection is designed based on an approximation of the oscillation using an envelope model to achieve a constant deflection amplitude. The approach is evaluated in numerical simulations.

Keywords: Dynamical Systems Techniques, Geometric Methods, Nonlinear Cooperative Control
Abstract: The recent research on nonlinear control systems tends to prioritize safety beyond stability, and control barrier functions (CBFs) have been gaining popularity as a CBF-based controller can theoretically ensure safety of control systems with the notion of set invariance. In this paper, we define a time-varying CBF (Tv-CBF) for a nonautonomous control-affine system with a human operator input to address a time-dependent safety constraint problem. Then, we propose a human assist control law using a Tv-CBF that satisfies time-dependent safety constraints. We also prove that solutions to an ordinary differential equation denoting control systems are forward complete by employing the proposed human assist controller. Lastly, the effectiveness of the proposed method is confirmed through computer simulation.

Keywords: Passivity, Disturbance Atténuation, Lyapunov Methods
Abstract: In this paper the application of PID control to passive systems via passive interconnection is explored. The stability properties of PID control applied to linear systems is well understood, but the application to nonlinear system is more complex. In this work we exploit the passive structure of a PID controller by interconnecting with passive plants to ensure closed-loop stability. In many cases, however, the regulation output does not coincide with the passive output of the plant and the integral of the passive output is the regulation output of interest. Two methods for applying PID to the integral of the passive output via passive interconnection are introduced.

Keywords: Bifurcation and Chaos, Dynamical Systems Techniques, Lyapunov Methods
Abstract: In the present paper, a new model describing neutron star dynamics is analysed. The system under consideration can be described as a modified vortex creep model. Two component model and the vortex creep model have been used successfully to describe post glitch relaxation phase. However, glitch behaviour is yet to be explained. There can be a possible stochastic mechanism that trigger glitches in neutron stars. To this aim, we propose a modification in the nonlinear vortex creep model. The significance of the modification is twofold, the dynamics of the system is able to generate intermittency, imitating the glitch behaviour of pulsars, and the system also show chaotic motion when the system parameters are set accordingly. The chaotic dynamics is verified by using nonlinear tools such as numerical phase portraits, Lyapunov exponents and bifurcation diagrams.

Keywords: Model Based Control
Abstract: This paper deals with stochastic model predictive control (SMPC) based on polynomial chaos expansion (PCE) for linear systems with time-invariant stochastic parametric uncertainties and time-varying stochastic additive disturbances subject to chance constraints on states and inputs. Exploiting terminal ingredients in the SMPC problem and a hybrid update strategy, a recursively feasible optimization problem is formulated. Moreover, stability of the system of PCE coefficients can be shown. Furthermore, in the paper the performance and computational complexity of SMPC based on PCE is compared to tube-based SMPC and robust model predictive control (RMPC) and benefits are demonstrated in simulation.

Keywords: Nonlinear Model Predictive Control Theory and Applications, Feasibility and Stability Issues, Stability
Abstract: Model Predictive Control (MPC) is a successful control strategy, with solid theoretical and practical backgrounds. Currently, several stabilizing MPC formulations are available to deal with tracking of piecewise constant references. In particular, it is well understood that, in many cases, the use of artificial reference variables in the optimisation problem allows to sensibly extend the region of attraction of the controller. This work proposes a modified MPC for tracking formulation which is able to guarantee nominal stability also in presence of positive semidefinite stage cost. This can be particularly useful when dealing with high order and/or black-box models, as it allows penalizing the outputs or a subset of states of the system without compromising stability. The algorithm design is based on terminal ingredients and a cost detectability assumption which is explicitly accounted for in the algorithm formulation. Such assumption can be verified by means of input-output-to-state stability arguments, as well as dissipativity ones, thus exploiting techniques already available in the literature.

Keywords: Optimal Control, Necessary Conditions, Dynamical Systems Techniques
Abstract: We consider the fractional optimal control problem with state constraints. The fractional calculus of derivatives and integrals can be viewed as generalizations of their classical ones to any arbitrary real order. In our problem setup, the dynamic constraint is captured by the Caputo fractional differential equation with order alpha in (0,1), and the objective functional is formulated by the left Riemann-Liouville fractional integral with order beta geq 1. In addition, there are terminal and running state constraints; while the former is described by initial and final states within a convex set, the latter is given by an explicit instantaneous inequality state constraint. We obtain the maximum principle, the first-order necessary optimality condition, for the problem of this paper. Due to the inherent complex nature of the fractional control problem, the presence of the terminal and running state constraints, and the generalized standing assumptions, the maximum principle of this paper is new in the optimal control problem context, and its proof requires to develop new variational and duality analysis using fractional calculus and functional analysis, together with the Ekeland variational principle and the spike variation.

Keywords: Geometric Methods, Control of Sampled Data Systems, Control of Mechanical, Electrical and Process Systems
Abstract: We show that the Euler-discretization of the nonlinear continuous-time model of a single mast stacker crane is flat. The construction of the flat output is based on a transformation of a subsystem into the linear time-variant discrete-time controller canonical form. Based on the derived flat output, which is also a function of backward-shifts of the system variables, we discuss the planning of trajectories to achieve a transition between two rest positions and compute the corresponding discrete-time feedforward control.

Keywords: Optimization and Scheduling
Abstract: This talk focuses on the way robots interact with the world around us, interacting with humans to achieve certain tasks. Taking inspiration from nature leads to algorithm design for robots and design of functional networks that work together with humans to achieve more efficient and robust outcomes. Australia is an ideal location for autonomous technology, as robotic swarms can work collectively to assist humans in covering large areas or entering dangerous environments. These human-swarm interactions can provide an array of benefits from emergency surveillance, agriculture monitoring or military applications, in our vast ‘borderless’ country.

Keywords: Robotics
Abstract: Control of complex non-linear robots and devices can be challenging, and engineers are often constrained by the performance and structure of the plant they are given. However, judicious constitutive hardware design allow the empowered control engineer to reframe some problems from ones where the plant is fiendishly difficult to stabilise, to ones where the system devolves into a tractable tuning problem. This talk will consider two examples: grasping from a hovering drone and bipedal locomotion. Both of these systems involve strongly coupled non-linear dynamics, and both commonly involve complex (and expensive) sensing and control. By rethinking the constraints of these tasks and judiciously employing simply hardware solutions, each can be solved using only basic control techniques.

Keywords: Aerospace and Marine Applications, Parameter Estimation, System Structure Identification
Abstract: Conventional physics-based modeling is a time-consuming bottleneck in control design for complex nonlinear systems like autonomous underwater vehicles (AUVs). In contrast, purely data-driven models require a large number of observations and lack operational guarantees for safety-critical systems. Data-driven models leveraging available partially characterized dynamics have potential to provide reliable systems models in a typical data-limited scenario for high value complex systems, thereby avoiding months of expensive expert modeling time. In this work we explore this middle-ground between expert-modeled and pure data-driven modeling. We present control-oriented parametric models with varying levels of domain-awareness that exploit known system structure and prior physics knowledge to create constrained deep neural dynamical system models. We employ universal differential equations to construct data-driven blackbox and graybox representations of the AUV dynamics. In addition, we explore a hybrid formulation that explicitly models the residual error related to imperfect graybox models. We compare the prediction performance of the learned models for different distributions of initial conditions and control inputs to assess their suitability for control.

Keywords: Parameter Estimation, System Structure Identification, Numerical Methods
Abstract: We propose a method based on the combination of computed-aided nonlinear frequency response analysis with the Loewner framework, for identification and characterization of nonlinear dynamical processes with application in electrochemistry. The method is data-driven, i.e., requiring only samples of the first two generalized transfer functions of the underlying system, given as values of the nonlinear frequency response. Then, the purely data-driven approach, known as the Loewner framework, is used to extract the system’s invariant quantities. In this preliminary analysis, we have used a nonlinear electrical circuit model as a test case. The results of our approach are in accordance with the predicted ground truth.

Keywords: System Structure Identification, Input-To-State Stability, Parameter Estimation
Abstract: We present a physics-informed neural ordinary differential equation (ODE) based model to determine the temperature in electric motor permanent magnets. The input-to-state stability (ISS) property is ensured by the model's architecture independently of the model's parameters. This improves the model's safety and contributes to easy deployment as a virtual sensor. We train this model on a real-world data set and demonstrate its advantages over a nonlinear autoregressive exogenous (NARX) neural network.

Keywords: Control of Mechanical, Electrical and Process Systems, Robotics, Stability
Abstract: This paper proposes a novel legged locomotion robot model formed by four parallelogram links and equipped with a wobbling mass and a reaction wheel, and investigates the method for generating a strict stealth walking gait on the frictionless road surface. First, we describe the robot equation of motion, and develop an output-following control system for generating a walking motion by ignoring the condition of the vertical ground reaction forces. Second, we redesign the control system taking into consideration the distribution of the vertical reaction forces or the zero-moment point. Furthermore, the improvement of energy efficiency in terms of specific resistance using elastic elements is discussed.

Keywords: Applications of Observer Design, State Estimation and Applications, Robotics
Abstract: This paper addresses the problem of on-line consistent estimation of gyro bias using the measurements of a single vector and the biased angular velocity – both in the body-fixed frame. We propose two globally convergent gyro bias observers using new regression models, which are capable to deal with the cases of constant and time-varying reference vectors, respectively. Indeed, there are quite a few works discussing the latter case. To address this, we derive a nonlinear regression model, based on which a convexified gradient descent observer is designed, being able to provide globally asymptotically convergent estimates to the gyro bias under some sufficient excitation conditions. The proposed schemes are illustrated by some numerical simulations.

Keywords: Stability, Lyapunov Methods, Nonlinear Modeling of Lumped And/Or Distributed Parameter Systems
Abstract: This paper develops a constructive time-delay approach to averaging for gradient-based extremum seeking (ES) control of nonlinear static maps of non-quadratic form. Under the assumption that some prior knowledge of the nonlinear map with its derivatives is available, for the first time, we derive a quantitative analysis for ES close-loop systems with upper bounds on the tuning parameter that preserves the exponential stability and on the convergence error of extremum seeking. By transforming the ES system into a time-delay neutral type system with distributed delays, the developed method gives an accurate perturbed system of ES without employing any approximate calculation, and suggests a direct Lyapunov-Krasovskii approach in the form of linear matrix inequalities (LMIs), for the transformed time-delay plant to derive efficient stability conditions.

Keywords: Parameter Estimation, Stabilization, Lyapunov Methods
Abstract: This paper proposes an adaptation redesign approach of the immersion and invariance (I&I) adaptive control to achieve asymptotic stability of the controlled plant and the parameter estimator at the desired equilibrium. The key idea is to employ the technique of generalized parameter estimation-based observer on the parameter estimation error dynamics by applying the indirect I&I adaptive control scheme, yielding a linear regression equation, from which the adaptive law can be redesigned. As a result, it is shown that globally exponential parameter convergence can be guaranteed under an interval excitation (IE) condition, which is much weaker than the conventionally required persistent excitation. Under a stabilizability assumption, an adaptation-redesigned feedback control law can be designed to achieve global asymptotic stability at the desired equilibrium point under the IE condition. The proposed adaptive control approach is applied to a class of parameteric strict-feedback systems without overparameterization, which is needed by the standard I&I adaptive control.

Keywords: Lyapunov Stability Methods, Parameter Estimation, Stabilization
Abstract: In this paper, an adaptive control scheme is established for nonlinear systems with sinusoidal uncertainties from the perspective of internal model principle. We propose to embed the controller with a dynamic compensator which plays the role of an internal model for reproducing the unknown sinusoidal parameter. For linearly parameterized systems, under some full-information stabilizability assumptions, internal-model based controllers are developed, rendering the closed-loop system trajectories to be bounded and the plant states to be asymptotically convergent to zero. Further, we extend the proposed internal-model-based control scheme to nonlinearly parameterized systems with a (strictly) monotonic assumption. Two simulation examples are given to verify the effectiveness of the proposed schemes.