Antonie Arij Stoorvogel

Semi-global stabilization of linear discrete-time systems subject to input saturation via linear feedback-an ARE-based approach

We revisit the problem of semiglobal stabilization of linear discrete-time systems subject to input saturation and give an algebraic Riccati equation (ARE)-based approach to the proof of a fact established earlier (Lin and Saberi, 1995), i.e. a linear discrete-time system subject to input saturation is semiglobally stabilizable via linear feedback as long as the linear system in the absence of the saturation is stabilizable and detectable and all its open-loop poles are located inside or on the unit circle. Moreover, we drastically relax the requirements on the characteristic of the saturation elements as imposed in the earlier work.

Stochastic disturbance rejection in model predictive control by randomized algorithms

In this paper we consider model predictive control with stochastic disturbances and input constraints. We present an algorithm which can solve this problem approximately but with arbitrary high accuracy. The optimization at each time step is a closed loop optimization and therefore takes into account the effect of disturbances over, the horizon in the optimization. Via an example it is shown that this gives a clear improvement of performance although at the expense of a large computational effort.

The Design of Multi-Lead-Compensators for Stabilization and Pole Placement in Double-Integrator Networks

We study decentralized controller design for stabilization and pole-placement, in a network of autonomous agents with double-integrator internal dynamics and arbitrary observation topology. We show that a simple multi-lead-compensator architecture, in particular one in which each agent uses a derivative-approximation compensator with three memory elements, can achieve both stabilization and effective pole placement. Through a scaling argument, we also demonstrate that the multi-lead-compensator can stabilize the double-integrator network under actuator saturation constraints. The multi-lead-compensator design is practical for modern dynamical network applications, in that it subdivides actuation effort and complexity among the agents and in many cases is robust to agent failure.

Generalized output regulation for linear systems

One of the most important problems in linear multivariable control theory is that of controlling a given plant in order to have its output track (or reject) a reference (or disturbance) signal produced by some external generator, called the exosystem. The disturbance or reference contains only the frequency components of the exosystem. This is called the output regulation problem. We generalize the problem framework in several directions. One is to model disturbances and references by an exosystem that is not, unlike the traditional approach, autonomous but is driven. Another direction is to incorporate the derivative information in the problem formulation. Consequently, we formulate two classes of generalized exact and almost output regulation problems. We provide solvability conditions and the solutions to these problems. Finally, and most importantly, we show that if solvability conditions for regulation are not satisfied, one can design a regulator to achieve best tracking (or rejection) of reference (or disturbance) signal is any desired induced norm sense.

Consensus for multi-agent systems — Synchronization and regulation for complex networks

In this paper, we consider three problems, namely, the consensus (synchronization) problem, the model-reference consensus problem, and the regulation of consensus problem, for a network of identical linear time-invariant (LTI) multi input and multi-output (MIMO) agents. For each problem, we propose a distributed LTI protocol to solve such a problem for a broad class of time-invariant network topologies including not only Laplacian topologies, but a wide family of asymmetric topologies.

Stabilization of linear system with input saturation and unknown constant delays

In this paper, we study the stabilization of linear critically unstable systems subject to input saturation and multiple unknown input delays. We find tight upper bounds for delays which are inversely proportional to the maximal magnitude of open-loop eigenvalues on the imaginary axis. For delays satisfying these upper bounds, linear low-gain state and finite dimensional dynamic measurement feedbacks are constructed to solve the semi-global stabilization problem. The effectiveness of the proposed design is illustrated by an example.

Simultaneous global external and internal stabilization of linear time-invariant discrete-time systems subject to actuator saturation

Simultaneous external and internal stabilization in global framework of linear time-invariant discrete-time systems subject to actuator saturation is considered. Internal stabilization is in the sense of Lyapunov while external stabilization is in the sense of ℓp stability with different variations, e.g. with or without finite gain, with fixed or arbitrary initial conditions, with or without bias. Several simultaneous external and internal stabilization problems all in global framework are studied in depth, and appropriate adaptive low-and-high gain feedback controllers that achieve the intended simultaneous external and internal stabilization are constructed whenever such problems are solvable.

A multiple-derivative and multiple-delay paradigm for decentralized controller design: Introduction using the canonical double-integrator network

We are engaged in a major effort to design decentralized controllers for modern networks, that is fundamentally based on 1) applying feedback of multiple derivatives of local observations and 2) implementing these derivative feedbacks using multiple-delay controllers. Here, we fully motivate and introduce the design paradigm in the context of a canonical sensing-network model, namely a network of saturating double integrators with general sensing topology that is subject to measurement delays. In this context, we illustrate that our design paradigm yields practical high-performance (in particular, group pole-placement) decentralized controllers that exploit the network topology while distributing the complexity and actuation requirements among the agents.

Synchronization for a network of identical discrete-time agents with unknown, nonuniform constant input delay

This paper studies the synchronization problem for a network of identical discrete-time agents with unknown, nonuniform constant input delays. The agents are at most critically stable and non-introspective (i.e. the agents have no access to their own states or outputs). There exists full state coupling among the agents. An upper bound for the delay tolerance is obtained which explicitly depends on agent dynamics. For any unknown delay satisfying this upper bound, a controller design methodology is proposed without relying on exact knowledge of the network topology so that synchronization in a set of unknown networks can be achieved.

Stabilization of Discrete-Time Linear Systems Subject to Input Saturation and Multiple Unknown Constant Delays

In this technical note, we study the semi-global stabilization of general linear discrete-time critically unstable systems subject to input saturation and multiple unknown input delays. Based on a simple frequency-domain stability criterion, we find upper bounds for delays that are inversely proportional to the argument of open-loop eigenvalues on the unit circle. For delays satisfying these upper bounds, linear low-gain state and finite dimensional dynamic measurement feedbacks are constructed to solve the semi-global stabilization problems.