Carsten W. Scherer

Multiobjective output-feedback control via LMI optimization

This paper presents an overview of a linear matrix inequality (LMI) approach to the multiobjective synthesis of linear output-feedback controllers. The design objectives can be a mix of H/sub /spl infin// performance, H/sub 2/ performance, passivity, asymptotic disturbance rejection, time-domain constraints, and constraints on the closed-loop pole location. In addition, these objectives can be specified on different channels of the closed-loop system. When all objectives are formulated in terms of a common Lyapunov function, controller design amounts to solving a system of linear matrix inequalities. The validity of this approach is illustrated by a realistic design example.

LPV control and full block multipliers

A novel construction of linear parameter-varying controllers is presented. For arbitrarily fast parameter variations it is shown how full block multipliers allow to considerably reduce conservatism. Various auxiliary results of independent interest are included.

LMI Relaxations in Robust Control

The purpose of this tutorial paper is to discuss the important role of robust linear matrix inequalities with rational dependence on uncertainties in robust control. We review how various classical relaxations based on the S-procedure can be subsumed to a unified framework. Based on Lagrange duality for semi-definite programs, we put particular emphasis on a clear understanding under which conditions such relaxations can be verified to be exact. We finally address the systematic construction of families of relaxations which can be shown to be asymptotically exact, based on recent results on the sum-of-squares representation of polynomial matrices.

Matrix Sum-of-Squares Relaxations for Robust Semi-Definite Programs

We consider robust semi-definite programs which depend polynomially or rationally on some uncertain parameter that is only known to be contained in a set with a polynomial matrix inequality description. On the basis of matrix sum-of-squares decompositions, we suggest a systematic procedure to construct a family of linear matrix inequality relaxations for computing upper bounds on the optimal value of the corresponding robust counterpart. With a novel matrix-version of Putinars sum-of-squares representation for positive polynomials on compact semi-algebraic sets, we prove asymptotic exactness of the relaxation family under a suitable constraint qualification. If the uncertainty region is a compact polytope, we provide a new duality proof for the validity of Putinars constraint qualification with an a priori degree bound on the polynomial certificates. Finally, we point out the consequences of our results for constructing relaxations based on the so-called full-block S-procedure, which allows to apply recently developed tests in order to computationally verify the exactness of possibly small-sized relaxations.

Relaxations for Robust Linear Matrix Inequality Problems with Verifications for Exactness

Robust semidefinite programming problems with rational dependence on uncertainties are known to have a wide range of applications, in particular in robust control. It is well established how to systematically construct relaxations on the basis of the full block S-procedure. In general, such relaxations are expected to be conservative, but for concrete problem instances they are often observed to be tight. The main purpose of this paper is to suggest novel computationally verifiable conditions for when general classes of linear matrix inequality relaxations do not involve any conservatism. If the convex set of uncertainties is finitely generated, we suggest a novel sequence of relaxations which can be proved to be asymptotically exact. Finally, our results are applied to the particularly relevant robustness analysis problem for linear time-invariant dynamical systems affected by uncertainties that are full ellipsoidal or repeated and contained in intersections of disks or circles. This leads to extensions of known results on relaxation exactness for small block structures, including an elementary proof for tightness of standard structured singular value computations for three full complex uncertainty blocks.

Control of linear parameter varying systems with applications

Part I: Introduction to Modeling and Control of LPV Systems.- An Overview of LPV Systems.- Prediction Error Identification of LPV Systems: Present and Beyond.- Part II: Theoretical Advancements on LPV Control and Estimation.- Parametric Gain-scheduling Control via LPV-stable Realization.- Explicit Controller Parameterizations for Linear Parameter Varying Affine Systems using Linear Matrix Inequalities.- A Parameter-dependent Lyapunov Approach for the Control of Nonstationary LPV Systems.- Generalized Asymptotic Regulation for LPV Systems with Additional Performance Objectives.- Robust Stabilization and Disturbance Attenuation of Switched Linear Parameter Varying Systems in Discrete Time.- Gain-scheduled Output Feedback Controllers with Good Implementability and Robustness.- Decentralized Model Predictive Control of Time-varying Splitting Parallel Systems.- Robust Estimation with Partial Gain-scheduling through Convex Optimization.- Delay-dependent Output Feedback Control of Time-delay LPV Systems.- Part III: Recent Applications of LPV Methods in Control of Complex Systems.- Structured Linear Parameter Varying Control of Wind Turbines.- Attitude Regulation for Spacecraft with Magnetic Actuators: an LPV Approach.- Modeling and Control of LPV Systems: A Vibroacoustic Application.- LPV Modeling and Control of Semi-active Dampers in Automotive Systems.- LPV H[yen] Control for Flexible Hypersonic Vehicles.- Identification of Low-complexity LPV Input-output Models for Control of a Turbocharged Combustion Engines.- Constrained Freeway Traffic Control via Linear Parameter Varying Paradigms.- Linear Parameter Varying Control for the X-53 Active Aeroelastic Wing.- Design of Integrated Vehicle Chassis Control Based on LPV Methods.

Robust output-feedback controller design via local BMI optimization

The problem of designing a globally optimal full-order output-feedback controller for polytopic uncertain systems is known to be a non-convex NP-hard optimization problem, that can be represented as a bilinear matrix inequality optimization problem for most design objectives. In this paper a new approach is proposed to the design of locally optimal controllers. It is iterative by nature, and starting from any initial feasible controller it performs local optimization over a suitably defined non-convex function at each iteration. The approach features the properties of computational efficiency, guaranteed convergence to a local optimum, and applicability to a very wide range of problems. Furthermore, a fast (but conservative) LMI-based procedure for computing an initially feasible controller is also presented. The complete approach is demonstrated on a model of one joint of a real-life space robotic manipulator.

A game theoretic approach to nonlinear robust receding horizon control of constrained systems

In this paper, we present an approach to synthesize a nonlinear model predictive controller with guaranteed robust stability, where uncertainty and input constraints are explicitly included in the formulation of the optimization problem. Conceptually, this approach can be viewed as a suitable combination of nonlinear MPC and H/sub /spl infin// control.

H∞ -optimization without assumptions on finite or infinite zeros

Explicit algebraic conditions are presented for the suboptimality of some parameter in the

Mixed H 2 / H ∞ Control

H_\infty