María M. Seron

Fundamental Limitations in Filtering and Control

The issue of fundamental limitations in filtering and control lies at the very heart of any feedback system design, since it reveals what is and is not achievable on the basis of that systems structural and dynamic characteristics. Alongside new succinct treatments of Bodes original results from the 1940s, this book presents a comprehensive analysis of modern results, featuring contemporary developments in multivariable systems, sampled-data, periodic and nonlinear problems. The text gives particular prominence to sensitivity functions which measure the fundamental qualities of the system, including performance and robustness. With extensive appendices covering the necessary background on complex variable theory, this book is an ideal self-contained resource for researchers and practitioners in this field.

A systematic method to obtain ultimate bounds for perturbed systems

In this paper, we develop a systematic method to obtain ultimate bounds for both continuous- and discrete-time perturbed systems. The method is based on a componentwise analysis of the system in modal coordinates and thus exploits the system geometry as well as the perturbation structure without requiring calculation of a Lyapunov function for the system. The method is introduced for linear systems having constant componentwise perturbation bounds and is then extended to the case of state-dependent perturbation bounds. This extension enables the method to be applied to non-linear systems by treating the perturbed non-linear system as a linear system with a perturbation bounded by a non-linear function of the state. Examples are provided where the proposed systematic method yields bounds that are tighter or at least not worse than those obtained via standard Lyapunov analysis. We also show how our method can be combined with Lyapunov analysis to improve on the bounds provided by either approach.

Positive invariant sets for fault tolerant multisensor control schemes

This article deals with fault tolerant multisensor control schemes for systems with linear dynamics. Positive invariance is a common analysis and control design tool for systems affected by bounded constraints and disturbances. This article revisits the construction of ε-approximations of minimal robust positive invariant sets for linear systems upon contractive set-iterations. The cases of switching between different sets of disturbances and the inclusion of a predefined region of the state space are treated in detail. All these results are used in multisensor control schemes which have to deal with specific problems originated by the switching between different estimators and by the presence of faults in some of the sensors. The construction of positive invariant sets for different operating regimes provides, in this context, effective fault detection information. Within the same framework, global stability of the switching strategies can be assured if the invariant sets topology allows the exclusive selection of estimates obtained from healthy sensors.

Global analytical model predictive control with input constraints

We derive a closed-form global analytical solution for model predictive control (MPC) of linear, discrete-time systems, subject to a quadratic performance index and hard magnitude constraints at the system input. The solution is shown to be a partition of the state space in regions for which an analytic expression is given for the corresponding control law. Both the regions and the control law are characterised in terms of the parameters of the open-loop optimal control problem that underlies MPC. The result exploits the geometric properties of quadratic programming.

Multisensor switching control strategy with fault tolerance guarantees

In this paper we propose a novel fault tolerant multisensor switching strategy for feedback control. Each sensor of the proposed multisensor scheme has an associated state estimator which, together with a state feedback gain, is able to individually stabilise the closed-loop system. At each instant of time, the switching strategy selects the sensor-estimator pair that provides the best closed-loop performance, as measured by a control-performance criterion. We establish closed-loop stability of the resulting switching scheme under normal (fault-free) operating conditions. More importantly, we show that closed-loop stability is preserved in the presence of faulty sensors if a set of conditions on the system parameters (such as bounds on the sensor noises, maximum and minimum values of the reference signal, etc.) is satisfied. This result enhances and broadens the applicability of the proposed multisensor scheme since it provides guaranteed properties such as fault tolerance and robust closed-loop stability under sensor fault. The results are applied to the problem of automotive longitudinal control.

Nonlinear adaptive control of feedback passive systems

An adaptive controller that solves the problem of rendering a system passive is presented for a special class of systems with parametric uncertainty. The proposed control uses techniques of speed-gradient methodology from the Russian literature. Stability results can be given that do not require commonly used assumptions such as linearity in the parameters. Algorithms that render the system strictly passive clarify some already known in the control of mechanical systems.

Enlarged terminal sets guaranteeing stability of receding horizon control

Abstract The purpose of this paper is to relax the terminal conditions typically used to ensure stability in model predictive control, thereby enlarging the domain of attraction for a given prediction horizon. Using some recent results, we present novel conditions that employ, as the terminal cost, the finite-horizon cost resulting from a nonlinear controller u =−sat( Kx ) and, as the terminal constraint set, the set in which this controller is optimal for the finite-horizon constrained optimal control problem. It is shown that this solution provides a considerably larger terminal constraint set than is usually employed in stability proofs for model predictive control.

Anti-windup and model predictive control: Reflections and connections.

Anti-windup strategies for dealing with input constraints date from the earliest stages of automatic control. They are ad-hoc procedures which achieve input saturation in an instantaneous fashion. Not surprisingly, anti-windup methods have a strong appeal to practitioners because of their simplicity. On the other hand, model predictive control (MPC) is a well established strategy for dealing with input constraint problems. The essential feature of the method is a receding horizon optimal quadratic control problem which is solved subject to input constraints. Both methods are known to perform well in practice and each has its strong advocates. In this paper, we explore connections between the methods for constrained single-input linear systems. In particular, we show that there are cases in which anti-windup schemes are identical to MPC schemes. In other cases, we show that anti-windup has performance which is close to that of MPC strategies. These comparisons are facilitated by formulating a general class of anti-windup algorithms in a form which highlights the connection with the state space formulations which are traditionally used in the MPC area.

Feedback limitations in nonlinear systems: from Bode integrals to cheap control

This paper links the Bode integral characterization of performance limitations in linear control systems with the limiting cost of a particular linear cheap control. This link allows us to establish analogous feedback limitations in nonlinear systems. We show how unstable zero dynamics impose unavoidable obstructions to the closed-loop performance.

Brief paper: Componentwise ultimate bound and invariant set computation for switched linear systems

We present a novel ultimate bound and invariant set computation method for continuous-time switched linear systems with disturbances and arbitrary switching. The proposed method relies on the existence of a transformation that takes all matrices of the switched linear system into a convenient form satisfying certain properties. The method provides ultimate bounds and invariant sets in the form of polyhedral and/or mixed ellipsoidal/polyhedral sets, is completely systematic once the aforementioned transformation is obtained, and provides a new sufficient condition for practical stability. We show that the transformation required by our method can easily be found in the well-known case where the subsystem matrices generate a solvable Lie algebra, and we provide an algorithm to seek such transformation in the general case. An example comparing the bounds obtained by the proposed method with those obtained from a common quadratic Lyapunov function computed via linear matrix inequalities shows a clear advantage of the proposed method in some cases.