Keywords: Observability and Observer Design
Abstract: We start by reviewing the main techniques of state observer design for continuous-time dynamical systems. Starting from necessary conditions for the existence of such asymptotic observers, we classify the available methods depending on the detectability/observability assumptions they require. We show that each class of observer relies on transforming the system dynamics into a particular normal form which allows the design of an observer, and how each observability condition guarantees the invertibility of its associated transformation and the convergence of the observer. Then, we give a particular focus to the theory of KKL or nonlinear Luenberger observers. This design consists in looking for a change of coordinates changing the system dynamics into a contracting filter of the output. A state estimate is then obtained by implementing this filter from any initial condition and left-inverting the transformation, which is shown to be possible under a very weak backward-distinguishability property. We show how, unlike other methods, this idea is universal and can be extended to any type of dynamical systems (continuous or discrete time, autonomous or discrete, observable or non-observable, etc), thus offering a promising road towards a unified paradigm for observer design.

Keywords: Aerospace, Robotics
Abstract: Airplanes, helicopters, and other Vertical Take-Off and Landing (VTOL) vehicles, blimps, rockets, hydroplanes, marine ships, and submarines are generally under-actuated. They are essentially composed of a rigid body immersed in a fluid medium (air or water). They are commonly controlled via a propulsive thrust force directed along a body-fixed privileged axis and a torque vector with one (in the case of a marine ship) and either two or three (in the case of airships and submarines) independent components in charge of modifying the body’s orientation on a 2D-plane or in 3D-space. These vehicles are under-actuated because, apart from the direction associated with the thrust force, the other direction(s) of displacement is (are) not directly actuated. Yet, until some recent works, the above-mentioned structural similitude between all these vehicles has never been exploited to develop a general control framework. Several reasons can be pointed out to explain this. For instance, marine ships are (partly) immersed in water and essentially move on a 2D plane, whereas airships and submarines evolve in 3D space. Moreover, the ambient fluid is not the same, producing hydrodynamic or aerodynamic reaction forces with different properties and magnitudes. Gravity is not compensated by buoyancy in the case of an airplane, in contrast to the case of marine vehicles and blimps. Added-mass effects mainly concern maritime ships, submarines, blimps, etc. Another probable reason is historical: aerospace and naval engineering communities involved in the control of these vehicles have not addressed common issues (the design of autopilots, for instance) in a coordinated manner, nor at the same time, nor with the same constraints, nor even with the same tools and techniques of Control Theory. In this talk, I will give some insights to take a good step in this direction by proposing a unified control strategy that considers aerodynamic (resp. hydrodynamic) forces in the control design of a large class of aerial vehicles.

Keywords: Biological and Biomedical Systems, Input-To-State Stability, Lyapunov Methods
Abstract: For mitigation of the spread of human infectious diseases, this paper proposes nonlinear PI control laws of vaccination, isolation, and contact regulation. Using the SIQR model, the control laws are designed to achieve not only internal stability on an arbitrarily large domain in the state space, but also input-to-state stability with respect to inflow perturbations of immigrants and newborns. The control laws get rid of the precise knowledge of the nominal rates required by feedback control. This paper pursues incorporation of integral action in control to render a coarse estimate a real equilibrium. It is demonstrated how to accomplish it in the presence of severe range limitations of control inputs.

Keywords: Stabilization, Adaptive Filters, Robustness
Abstract: n this study, we consider a model free control technique for a class of minimum phase nonlinear systems with unknown dynamics. We propose a timescale transformation approach that can be used to estimate the drift and the high frequency gain of the output dynamics of nonlinear systems with a well defined relative degree. The proposed controller provides an effective output regulation mechanism that avoids the need for direct disturbance model estimation and high gain output feedback controllers. A simulation study is conducted to demonstrate the effectiveness of the proposed approach.

Keywords: Stabilization, Dissipativity, Stability
Abstract: In this paper, we investigate the necessary and sufficient conditions under which a class of nonlinear systems are state feedback equivalent to nonlinear negative imaginary (NI) systems with positive definite storage functions. The nonlinear systems of interest have a normal form of relative degree less than or equal to two. The nonlinearity of the system is restricted with respect to a subset of the state variables, which are the state variables that have external dynamics. Under mild assumptions, such systems are state feedback equivalent to nonlinear NI systems and nonlinear output strictly negative imaginary (OSNI) systems if and only if they are weakly minimum phase. Such a state feedback control approach can also asymptotically stabilize the systems in question against nonlinear OSNI system uncertainties. A numerical example is provided to show the process of the state feedback equivalence control and stabilization of uncertain systems.

Keywords: Input-To-State Stability, Small Gain Theorems, Lyapunov Methods
Abstract: This paper introduces a new class of singularly perturbed systems in which the small, but constant, perturbation coefficient in standard singular perturbation theory is replaced by a state-dependent function. This generalization is aimed at broadening the applicability of singular perturbation theory in practice. For this class of singularly perturbed systems, it is assumed that the boundary-layer subsystem is globally asymptotically stable (GAS) at the origin and the reduced subsystem is input-to-state stable (ISS) with respect to the state of the boundary-layer subsystem. Under a mild monotonicity condition, sufficient conditions on the perturbation functions are given under which the singularly perturbed system is GAS at the origin. ISS and nonlinear small-gain techniques are exploited in the stability analysis. The efficacy of the proposed theoretical result is validated via its applications to tackling integral control and feedback optimization problems.

Keywords: Stability, Input-To-State Stability, Hybrid Nonlinear Control Systems
Abstract: This paper considers the class of control systems containing so-called split-path nonlinear (SPAN) filters, which are designed to overcome some of the well-known fundamental limitations in linear time-invariant (LTI) control. In this work, we are interested in developing tools for the stability analysis of such systems using frequency-domain techniques. Hereto, we explicitly show the equivalence between a set of linear matrix inequalities (LMIs) with S-procedure terms, guaranteeing stability of the closed-loop (SPAN) system, and a frequency- domain condition. We also provide a systematic procedure for verifying the frequency-domain conditions in a graphical manner. The results are illustrated through a nummerical case study.

Keywords: Aerospace, Stability, Dynamical Systems Techniques
Abstract: Liquid propelled rocket engines (LPRE) are highly non-linear systems that require complex stability analysis and regulation. Most often, this is performed by linearizing in the neighborhood of a functioning point which makes it difficult to account for changes of points textit{e.g.} for reusable launchers. In this paper the objective is to propose a non linear control law to regulate the thrust of the engine, which is represented by the reaction chamber pressure, and the mixture ratio between the fuel and oxidizer. This control law must provide stability guarantees for the system for a variety of functioning points. The new design is based on Contraction theory and is shown to address both stability and regulation objectives as illustrated with simulation results.

Keywords: Mechatronic Systems, Automotive Systems Marine Systems, Lyapunov Methods
Abstract: In recent years, the rapid aging of farmers and the decrease in their numbers have become a major concern. The automation of agriculture, via the implementation of autonomous driving technology in agricultural vehicles, has drawn considerable attention as a potential tool to address this issue. However, the existing techniques for the linear tracking control of on–off driven crawler vehicles, which are often used as agricultural vehicles, are time-consuming and expensive.

This study designs a two-degree-of-freedom control system with feedforward for a discrete-value-driven crawler to improve the tracking performance. The proposed method was characterized by a quadratic formal evaluation function, which enables control with both feedforward and feedback inputs.

The feedforward input was applied to obtain the effect of a two-degree-of-freedom control system, and the feedback input was superimposed according to the value of the evaluation function to prevent the system from becoming unstable. In addition, the controller containing an integrator can be cut off by the value of the evaluation function to avoid chattering problems in discrete-valued input systems.

Keywords: Mechatronic Systems, Lyapunov Methods, Performance Issues
Abstract: This manuscript introduces a passivity-based control methodology for fully-actuated mechanical systems with symmetric or asymmetric dead-zones. To this end, we find a smooth approximation of the inverse of the function that describes such a nonlinearity. Then, we propose an energy and damping injection approach---based on the PI-PBC technique---that compensates for the dead-zone. Moreover, we provide an analysis of the performance of the proposed controller near the equilibrium. We conclude this paper by experimentally validating the results on a two degrees-of-freedom planar manipulator.

Keywords: Robotics, Mechatronic Systems, Dynamical Systems Techniques
Abstract: In recent years, control barrier functions have attracted much attention for ensuring safety in collision avoidance and human assist control. However, control laws cannot guarantee the solution of differential equations without properly considering the shape of the target system. In this study, we designed a control law that considers the shape of the control target and designs a control barrier function for non-convex safe sets. Based on this, we proposed an integral control barrier function and confirmed its effectiveness by testing it for the collision avoidance between a two-links robot arm and an obstacle through simulations.

Keywords: Transportation Systems, Lyapunov Methods, Dynamical Systems Techniques
Abstract: To avoid collisions, human assist control based on a control barrier function (CBF) attracts attentions in recent years. A lot of human assist control method have been proposed, particularly using a relaxed CBF and a strict zeroing CBF (SZCBF). However, to design CBFs is still a difficult task. Hence in this study, we propose a method to design a SZCBF via transformation of a control Lyapunov function (CLF) derived by the backstepping. The effectiveness of the human assist control using the SZCBF is confirmed by computer simulation and actual experiments using an electric wheelchair.

Keywords: Filter Design, Observer and Filter Design By Observer Error Linearization, State Estimation and Applications
Abstract: Observers for systems with Lie group symmetries are an active area of research that is seeing significant impact in a number of practical domains, including aerospace, robotics, and mechatronics. This paper builds on the theory of the recently proposed Equivariant Filter (EqF), which is a general observer design for systems on homogeneous spaces that takes advantage of symmetries to yield significant performance advantages. It is shown that the EqF error dynamics are invariant to transformation of the input signal and equivariant as a parametrised vector field. The main theorem shows that two EqF's with different choices of local coordinates and origins and with equivalent noise modelling yield identical performance. In other words, the EqF is intrinsic to the system equations and symmetry. This is verified in a simulation of a 2D robot localisation problem, which also shows how the ability to choose an origin for the EqF can yield practical performance advantages by mitigating floating point precision errors.

Keywords: Observability and Observer Design, State Estimation and Applications, Applications of Observer Design
Abstract: The paper addresses the problem of attitude estimation for rigid bodies using (possibly time-varying) vector measurements, for which we provide a necessary and sufficient condition of distinguishability. Such a condition is shown to be strictly weaker than those previously used for attitude observer design. Thereafter, we show that even for the single vector case the resulting condition is sufficient to design almost globally convergent attitude observers, and an explicit design is obtained. To overcome the weak excitation issue, the design employs to make full use of historical information. Simulation results illustrate the accurate estimation despite noisy measurements.

Keywords: State Estimation and Applications, Applications of Observer Design, Observability and Observer Design
Abstract: Inertial Velocity-Aided Attitude (VAA), the estimation of the velocity and attitude of a vehicle using gyroscope, accelerometer, and inertial-frame velocity (e.g. GPS velocity) measurements, is an important problem in the control of Remotely Piloted Aerial Systems (RPAS). Existing solutions provide limited stability guarantees, relying on local linearisation, high gain design, or assuming specific trajectories such as constant acceleration of the vehicle. This paper proposes a novel non-linear observer for inertial VAA with almost globally asymptotically and locally exponentially stable error dynamics. The approach exploits Lie group symmetries of the system dynamics to construct a globally valid correction term. To the authors' knowledge, this construction is the first observer to provide almost global convergence for the inertial VAA problem. The observer performance is verified in simulation, where it is shown that the estimation error converges to zero even with an extremely poor initial condition.

Keywords: State Estimation and Applications, Dynamical Systems Techniques
Abstract: Estimating and detecting random processes on a circle has been studied for many decades. The Neyman-Pearson detector, which evaluates the likelihood ratio, requires first the conditional mean estimate of the circle-valued signal given noisy measurements, which is then correlated with the measurements for detection. This is the estimator-correlator detector. However, generating the conditional mean estimate of the signal is very rarely solvable. In this paper, we propose an approximate estimator-correlator detector by estimating the truncated moments of the signal, with estimated signal substituted into the likelihood ratio. Instead of estimating the random phase, we estimate the complex circle-valued signal directly. The effectiveness of the proposed method in terms of estimation and detection is shown through numerical experiments, where the tracking accuracy and receiver operating curves, compared with the extended Kalman filter are shown under various process/measurement noise.

Keywords: Performance Issues, Optimal Control, Bilinear Systems
Abstract: The classical notion of controllability provides us with a boolean variable --- whether a given system is controllable or not. However, often as engineers we seek a notion of how `controllable' a given system is, so as to classify systems that are `emph{easier to control}' from those which are `emph{difficult to control}'. In this article, we derive a quantitative measure of controllability for bilinear systems defined on the Lie group of rotations mathsf{SO}(3). Our controllability measure is based on the emph{worst case cost} of transferring the system from a given initial condition to a given final condition arbitrarily chosen over a set of interest. Here we consider a few frequently encountered cost functions such as control energy optimization and time-optimal control, and obtain a relation between the worst-case cost and the system parameters.

Keywords: Hybrid Nonlinear Systems, Parameter Estimation

Keywords: Observability and Observer Design, Hybrid Nonlinear Control Systems, Passivity
Abstract: In this note, we extend a recent hybrid passive momentum observer for mechanical systems to nonholonomic systems. The momentum observer assumes that configuration measurements of the underlying system are available, but measurements of the momentum or velocity are not available. Utilising a hybrid observer definition, the resulting observer converges at an exponential rate and has a lower dimension when compared to similar results. The observer additionally has a passive input-output pair which is used to interconnect with a control-by-interconnection (CbI) scheme, guaranteeing stability of the joint observer and controller system.

Keywords: Quantized Feedback and Feedback with Communication Constraints, Control of Sampled Data Systems, Hybrid Nonlinear Control Systems
Abstract: When designing networked control systems (NCS), stability guarantees are typically derived based on the maximum possible time between successive transmissions. A bound on this time is called the maximum allowable transmission interval (MATI). In order to minimize network usage, one is often interested in the maximum value of the MATI for which stability can still be guaranteed for the NCS. However, in many practical scenarios, the worst case transmission behavior occurs only seldom, rendering an analysis based solely on the MATI unnecessarily conservative. It was recently shown in the literature that considering information about the average allowable transmission interval in the form of a reverse average dwell time (RADT) can be used to increase the maximum value of the MATI for which stability can be guaranteed. Using the same assumptions, we show that stability guarantees can even be obtained for any arbitrary given value of the MATI as long as the RADT is small enough.

Keywords: Control of Sampled Data Systems, Stability, Stabilization
Abstract: Homogeneity, as a generalization of linearity to nonlinear systems, has proven to be a very powerful in systems and control. Nevertheless, only recently a notion of homogeneity was proposed for discrete-time control systems. However, this so-called D-Homogeneity directly couples the stability behaviour with the degree of homogeneity---in contrast to the continuous-time case. As an alternative, we propose the notion of S-Homogeneity, which avoids this coupling. S-Homogeneity uses a state-dependent time step that is compatible with sampling and discretization in time. We show that this concept preserves a contraction property and null-controllabilty for state-dependent sampling. For fixed sampling time, it yields (practical/semi-global) null controllability for sufficiently fast sampling, depending on the degree of homogeneity.

Keywords: Marine Systems
Abstract: In this talk, I will show how nonlinear control theory has made it possible to analyse and understand, and thus to design and control, efficient robots for autonomous operations. I will present the motivation and foundations of our research on snake robots, as well as our most recent results on snake robot control, and how this has led to a new class of marine robots in the subsea industry. Snake robots are motivated by the long, slender and flexible body of biological snakes, which allows them to move in virtually any environment on land and in water. Since the snake robot is essentially a manipulator arm that can move by itself, it has a number of interesting applications including firefighting applications and search and rescue operations. In water, the robot is a highly flexible and dexterous manipulator arm that can swim by itself like a sea snake. This highly flexible snake-like mechanism has excellent accessibility properties; it can for instance access virtually any location on subsea energy installations, move into the confined areas of shipwrecks, inside ice caves, or be used for observation of biological systems. Furthermore, not only can the swimming manipulator access narrow openings and confined areas, but it can also carry out highly complex manipulation tasks at this location since manipulation is an inherent capability of the system.