The primary disadvantage of current design techniques for model predictive control (MPC) is their inability to deal explicitly with plant model uncertainty. In this paper, we present a new approach for robust MPC synthesis which allows explicit incorporation of the description of plant uncertainty in the problem formulation. The uncertainty is expressed both in the time domain and the frequency domain. The goal is to design, at each time step, a statefeedback control law which minimizes a "worst-case" infinite horizon objective function, subject to constraints on the control input and plant output. Using standard techniques, the problem of minimizing an upper bound on the "worst-case" objective function, subject to input and output constraints, is reduced to a convex optimization involving linear matrix inequalities (LMIs). It is shown that the feasible receding horizon state-feedback control design robustly stabilizes the set of uncertain plants under consideration. Several extensions...

Abstract: H ∞ controller design for linear systems is a difficult, nonconvex and typically nonsmooth (nondifferentiable) optimization problem when the order of the controller is fixed to be less than that of the open-loop plant, a typical requirement in e.g. embedded aerospace control systems. In this paper we describe a new matlab package called hifoo, aimed at solving fixed-order stabilization and local optimization problems. It depends on a new hybrid algorithm for nonsmooth, nonconvex optimization based on several techniques, namely quasi-Newton updating, bundling and gradient sampling. The user may request hifoo to optimize one of several objectives, including H ∞ norm, which requires either the Control System Toolbox for matlab or, for much better performance, the linorm function in the slicot package. No other external package is required, but the quadratic programming code quadprog from either mosek or the Optimization Toolbox for matlab is recommended. Numerical experiments on benchmark problem instances from the COMPleib database indicate that hifoo could be an efficient and reliable computer-aided control system design (CACSD) tool, with a potential for realistic industrial applications.

We consider a multiobjective robust controller synthesis problem for an LTI system subject to unstructured perturbations. Our design specifications include robust stability, robust performance (H 2 -norm) bounds and time-domain bounds (output and command input peak). We derive sufficient conditions, based on a single quadratic Lyapunov function, for the existence of an LTI controller such that the closed-loop system satisfies all specifications simultaneously. These conditions can be numerically checked using finite-dimensional, convex optimization over LMIs, associated with a two-dimensional search. When considering only a subset of the specifications, we recover previous results from the literature, such as those obtained in mixed H 2 /H1 control. Keywords: Multiobjective robust control, mixed H 2 /H1 , time-domain specification, unstructured perturbation, quadratic Lyapunov function, linear matrix inequality. 1 Introduction In a multiobjective robust control problem, one seeks a co...

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We consider the following problem: find a fixed-order linear controller that maximizes the closed-loop asymptotic decay rate for the classical two-mass-spring system. This can be formulated as the problem of minimizing the abscissa (maximum of the real parts of the roots) of a polynomial whose coefficients depend linearly on the controller parameters. We show that the only order for which there is a non-trivial solution is 2. In this case, we derive a controller that we prove locally maximizes the asymptotic decay rate, using recently developed techniques from nonsmooth analysis. 1 Problem Statement We consider the system shown in Figure 1 consisting of two masses interconnected by a spring, a typical control benchmark problem which is a generic model of a system with a rigid body mode and one vibration mode [10]. If the first mass is pulled sufficiently far apart from the second mass and suddenly dropped, then the two masses will oscillate until they reach their equilibrium position. The control problem we study in this note consists of appropriately moving the second mass so that the first mass settles down to its final position as fast as possible; more 1

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A method is presented for synthesis of fixed order controllers with robustness to mixed real and complex uncertainties. The capabilities of the method are demonstrated on a two-mass/spring benchmark problem and on a flexible satellite example. Several fixed order mixed controllers are designed. A comparison with both full order and reduced order controllers indicates that the method is capable of synthesizing low order controllers achieving robust performance levels similar to full order designs, and superior to reduced order controllers. 1. Introduction Over the past decade modern robust control theory has revolutionized multivariable controller design. H1 and ¯-synthesis techniques consider multiple uncertainty sources at different locations in the plant, external disturbances, as well as performance specifications when designing for robust performance [1] - [3]. While these techniques greatly simplify multivariable controller synthesis, they are accompanied by the inherent disadv...

The purpose of this thesis is to develop an efficient scheme for the design of controllers that guarantee H 2 performance in view of linear or nonlinear real parametric uncertainties. To begin, dissipation techniques are used to design parameter-dependent Lyapunov functions that impose constraints on the magnitude and the time-variation of the uncertainties. This approach reduces the conservatism of the robustness criteria. The robust stability problem is formulated in terms of a linear matrix inequality problem that constitutes a convex constraint and can be solved in polynomial time. The robust performance problem is obtained by the introduction of a performance metric that bounds the H 2 cost of the closed-loop system and is shown to be equivalent to the robust performance problem obtained by the \Omega\Gammah ound framework and the use of Popov multipliers. Although the resulting robust performance criteria are in matrix inequality form, they are not linear in the scaling matrices ...

. We consider a multiobjective robust controller synthesis problem for an LTI system subject to structured perturbations. Our design specifications include robust stability, robust performance (H 2 -norm) bounds and time-domain bounds (output and command input peak). We derive sufficient conditions, based on a single quadratic Lyapunov function, for the existence of an LTI controller such that the closed-loop system satisfies all specifications simultaneously. These nonconvex conditions can be numerically checked with an efficient LMI-based heuristic. We illustrate our results on a three-parameter mass/spring system. Keywords. Multiobjective robust control, mixed H 2 /H1 , time-domain specification, structured perturbation, quadratic Lyapunov function, linear matrix inequality. 1. INTRODUCTION In a multiobjective robust control problem, one seeks a control law such that the closed-loop system satisfies a number of objectives (specifications) despite unkwnonbut -bounded perturbations. I...