Survey paper: Set invariance in control

State-dependent Riccati equation (SDRE) techniques are rapidly emerging as general design methods which provide a systematic and effective means of designing nonlinear controllers, observers, and filters. This paper provides an overview of several SDRE design techniques including SDRE nonlinear regulation, SDRE nonlinear H/sub /spl infin//, SDRE nonlinear H/sub 2/, and SDRE nonlinear filtering.

State-dependent Riccati equation techniques: an overview

In this paper we offer a novel approach to control-oriented model validation problems. The problem is to decide whether a postulated nominal model with bounded uncertainty is consistent with measured input-output data. Our approach directly uses time-domain input-output data to validate uncertainty models. The algorithms we develop are computationally tractable and reduce to (generally nondifferentiable) convex feasibility problems or to linear programming problems. In special cases, we give analytical solutions to these problems. >

A time-domain approach to model validation

This note gives a qualitative analysis of the dynamics of a system consisting of several mobile robots coordinating their motion using simple local nearest neighbor rules. We show that under some assumptions the headings of all robots will be eventually constant.

Coordinated collective motion of Groups of autonomous mobile robots: analysis of Vicsek's model

Given an interconnection of a nominal discrete-time plant and a stabilizing controller together with structured, norm-bounded, nonlinear/time-varying perturbations, necessary and sufficient conditions for robust stability and performance of the system are provided. It is shown that performance robustness is equivalent to stability robustness in the sense that both problems can be dealt with in the framework of a general stability robustness problem. The resulting stability robustness problem is shown to be equivalent to a simple algebraic one, the solution of which provides the desired necessary and sufficient conditions for performance/stability robustness. These conditions provide an effective tool for robustness analysis and can be applied to a large class of problems. In particular, it is shown that some known results can be obtained immediately as special cases of these conditions. >

Performance robustness of discrete-time systems with structured uncertainty

The problem considered in this paper is the design of a closed-loop system consisting of a MIMO discrete-time plant and compensator in such a way that the system is internally stable and optimally tracks all persistent bounded inputs. The solution consists of two parts: first the calculation of the minimum value of the performance index (a weighted transfer function), which is done by solving a linear programming problem; and second, construction of the optimal transfer function by solving a set of linear equations. It is shown that, in general, the discrete-time problem will have a rational solution and thus appears to be of considerable practical significance.

M. Dahleh

Papers

l^{1} -optimal feedback controllers for MIMO discrete-time systems