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Convex inner approximations of nonconvex semialgebraic sets applied to fixed-order controller design

INTERNATIONAL JOURNAL OF CONTROL 2012年第8期85卷 1083-1092页

作者： Henrion, Didier Louembet, Christophe CNRS LAAS F-31077 Toulouse France Univ Toulouse LAAS UPS F-31400 Toulouse France Czech Tech Univ Fac Elect Engn CZ-16626 Prague Czech Republic

We describe an elementary algorithm to build convex inner approximations of nonconvex sets. Both input and output sets are basic semialgebraic sets given as lists of defining multivariate polynomials. Even though no optimality guarantees can be given (e.g. in terms of volume maximisation for bounded sets), the algorithm is designed to preserve convex boundaries as much as possible, while removing regions with concave boundaries. In particular, the algorithm leaves invariant a given convex set. The algorithm is based on Gloptipoly 3, a public-domain Matlab package solving nonconvex polynomial optimisation problems with the help of convex semidefinite programming (optimisation over linear matrix inequalities, or LMIs). We illustrate how the algorithm can be used to design fixed-order controllers for linear systems, following a polynomial approach.

关键词： polynomials nonconvex optimisation LMI fixed-order controller design

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HIFOO - A MATLAB PACKAGE FOR fixed-order controller design AND H ∞ OPTIMIZATION

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IFAC Proceedings Volumes 2006年第9期39卷 339-344页

作者： J.V. Burke D. Henrion A.S. Lewis M.L. Overton Department of Mathematics University of Washington Seattle WA 98195 USA LAAS-CNRS 7 Avenue du Colonel Roche 31077 Toulouse France and Department of Control Engineering Faculty of Electrical Engineering Czech Technical University in Prague Technická 2 16627 Prague Czech Republic School of Operations Research and Industrial Engineering Cornell University Ithaca NY 14853 USA Courant Institute of Mathematical Sciences New York University New York NY 10012 USA

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 COMPl e ib database indicate that HIFOO could be an efficient and reliable computer-aided control system design (CACSD) tool, with a potential for realistic industrial applications.

关键词： fixed-order controller design H ∞ Control Nonconvex Optimization Nonsmooth Optimization Computer-Aided Control System design

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fixed-order Linear Parameter Varying controller design for a 2DOF Gyroscope

Fixed-order Linear Parameter Varying Controller Design for a...

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1st IFAC Workshop on Linear Parameter Varying Systems LPVS 2015

作者： Emedi, Zlatko Karimi, Alireza Ecole Polytech Fed Lausanne Lab Automat CH-1015 Lausanne Switzerland

This paper presents an approach for fixed-order Linear Parameter Varying (LPV) controller design with application to a 2 Degree-of-Freedom (2DOF) gyroscope experimental setup. Inner convex approximation of the non-convex set of all stabilizing fixed-order LPV controllers is characterized through a set of Linear Matrix Inequalities (LMIs). This is achieved through the use of two slack matrices which enable decoupling of the controller and Lyapunov matrix parameters in the derivative of Lyapunov function. The LPV model obtained by the approximation of the nonlinear model of the 2DOF gyroscope is used for the design of a second-order LPV controller. Experimental results show good tracking performance in the presence of scheduling parameter variations. (C) 2015, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

关键词： LPV System Control fixed-order controller design LMIs in Control Parameter Dependent Lyapunov Function 2DOF Gyroscope

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Robust fixed-order Discrete-time LPV controller design

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IFAC Proceedings Volumes 2014年第3期47卷 6914-6919页

作者： Zlatko Emedi Alireza Karimi Laboratoire d'Automatique Ecole Polytechnique Fédérale de Lausanne EPFL-STI-IGM-LA Station 9 CH-1015 Lausanne Switzerland

A new method for the design of fixed-order dynamic output-feedback Linear Parameter Varying (LPV) controllers for discrete-time LPV systems with bounded scheduling parameter variations is presented. Sufficient conditions for stability and induced l 2 -norm performance of an LPV system are given through a set of Linear Matrix Inequalities (LMIs) and exploited for design. controller parameters appear directly as decision variables in the convex optimisation program, which enables preserving a desired controller structure in addition to the low order. Efficiency of the proposed method is illustrated on a simulation example, with an iterative convex optimisation scheme used for the control system performance improvement.

关键词： Linear Parameter-Varying fixed-order controller design Parameter Dependent Lyapunov Function Induced l 2 -Norm Performance

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TDS-CONTROL: a MATLAB package for the analysis and controller-design of time-delay systems 18

TDS-CONTROL: a MATLAB package for the analysis and controlle...

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18th IFAC Workshop on Control Applications of Optimization (CAO)

作者： Appeltans, Pieter Silm, Haik Michiels, Wim Katholieke Univ Leuven Dept Comp Sci NUMA Celestijnenlaan 200A B-3001 Leuven Belgium

This paper presents TDS-CONTROL, a MATLAB package for the analysis and design of controllers for linear time-invariant systems with discrete delays. The code is based on a state-space representation of such systems in terms of delay-differential algebraic equations with input, output, and state delays. As such, a broad class of (interconnected) systems can be considered, including neutral systems. The controller design algorithms are based on optimizing a certain objective function, such as the spectral abscissa, the H-infinity norm, or the pseudo-spectral abscissa, with respect to the controller parameters. For example, to design a stabilizing controller the spectral abscissa, i.e., the real part of the right-most characteristic root, is minimized. As a strictly negative spectral abscissa is a necessary and sufficient condition for stability, the presented design method is not conservative and a stabilizing controller can be computed whenever it exits. This comes however at the cost of having to solve a non-smooth, non-convex optimization problem. The class of considered controllers consists of static and dynamic output-feedback controllers. By allowing to fix certain entries in the controller matrices, it is also possible to design structured controllers such as decentralized, overlapping and PID controllers. Finally, as a wide-range of delay systems can be considered, the software package takes the sensitivity of certain quantities, such as the spectral abscissa and the H-infinity norm, with respect to infinitesimal delay perturbations explicitly into account. Copyright (C) 2022 The Authors.

关键词： Systems with time-delays stability of delay systems optimization based controller design fixed-order controller design

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TDS-CONTROL: a MATLAB package for the analysis and controller-design of time-delay systems*

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IFAC-PapersOnLine 2022年第16期55卷 272-277页

作者： Pieter Appeltans Haik Silm Wim Michiels

关键词： Systems with time-delays stability of delay systems optimization based controller design fixed-order controller design

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Stabilization via nonsmooth, nonconvex optimization

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2006年第11期51卷 1760-1769页

作者： Burke, James V. Henrion, Didier Lewis, Adrian S. Overton, Michael L. Univ Washington Dept Math Seattle WA 98195 USA CNRS LAAS F-31077 Toulouse France Czech Tech Univ Dept Control Engn Prague 16627 Czech Republic Cornell Univ Sch Operat Res & Ind Engn Ithaca NY 14853 USA NYU Courant Inst Math Sci New York NY 10012 USA

Nonsmooth variational analysis and related computational methods are powerful tools that can be effectively applied to identify local minimizers of nonconvex optimization problems arising in fixed-order controller design. We support this claim by applying nonsmooth analysis and methods to a challenging "Belgian chocolate" stabilization problem posed in 1994: find a stable, minimum phase, rational controller that stabilizes a specified second-order plant. Although easily stated, this particular problem remained unsolved until 2002, when a solution was found using an eleventh-order controller. Our computational methods find a stabilizing third-order controller without difficulty, suggesting explicit formulas for the controller and for the closed loop system, which has only one pole with multiplicity 5. Furthermore, our analytical techniques prove that this controller is locally optimal in the sense that there is no nearby controller with the same order for which the closed loop system has all its poles further left in the complex plane. Although the focus of the paper is stabilization, once a stabilizing controller is obtained, the same computational techniques can be used to optimize various measures of the closed loop system, including its complex stability radius or H-infinity performance.

关键词： fixed-order controller design nonconvex optimization nonsmooth optimization polynomials stability

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Polynomial LPV synthesis applied to turbofan engines

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CONTROL ENGINEERING PRACTICE 2010年第9期18卷 1077-1083页

作者： Gilbert, Wilfried Henrion, Didier Bemussou, Jacques Boyer, David Univ Toulouse CNRS LAAS F-31077 Toulouse France Czech Tech Univ FEL Prague Czech Republic Snecma Villaroche France

Results on polynomial fixed-order controller design are extended to SISO gain-scheduling with guaranteed stability and H.. performance over the whole scheduling parameter range. Salient features of the approach are: (a) the use of polynomials as modeling objects: (b) the use of flexible linear matrix inequalities (LMI) conditions allowing polynomial dependence of the open-loop system and controller transfer functions in the scheduling parameters: and (c) the decoupling in the LMI conditions between the Lyapunov variables and the controller variables, allowing both parameter-dependent Lyapunov functions and fixed-order controller design. The synthesis procedure is integrated into the ATOL framework developed by the manufacturer of aircraft and space engines Snecma to systematically design reduced complexity gain-scheduled control laws for aircraft turbofan engines. (C) 2008 Elsevier Ltd. All rights reserved.

关键词： Turbofan engine control Linear parameter varying (LPV) systems fixed-order controller design Linear matrix inequalities (LMI) Polynomials

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Optimizing simultaneously over the numerator and denominator polynomials in the Youla-Kucera parametrization

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2005年第9期50卷 1369-1374页

作者： Henrion, D Kucera, V Molina-Cristóbal, A CNRS LAAS F-31077 Toulouse France Czech Tech Univ Fac Elect Engn Dept Control Engn CR-16627 Prague Czech Republic Univ Sheffield Dept Automat Control & Syst Engn Sheffield S1 3JD S Yorkshire England

Traditionally, when approaching controller design with the Youla-Kucera parametrization of all stabilizing controllers, the denominator of the rational parameter is fixed to a given stable polynomial, and optimization is carried out over the numerator polynomial. In this note, we revisit this design technique, allowing to optimize simultaneously over the numerator and denominator polynomials. Stability of the denominator polynomial, as well as fixed-order controller design with H-infinity performance are ensured via the notion of a central polynomial and linear matrix inequality (LMI) conditions for polynomial positivity.

关键词： fixed-order controller design linear matrix inequality (LMI) parameterization of stabilizing controllers polynomials

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fixed-order H_∞ controller Based on HIFOO for a Doubly-Fed Induction Generator Wind Turbine

Fixed-order H<sub>∞</sub> Controller Based on HIFOO for a D...

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4th International Renewable and Sustainable Energy Conference (IRSEC)

作者： Bouiadjra, Rochdi Bachir Sedraoui, Moussa Univ Mustapha Stambouli Comp Sci Dept Mascara Algeria 8 Mai 1945 Univ Telecommun Lab Guelma Algeria

ISBN: (纸本)9781509057139

The paper reports on the application of full-order H-infinity controller and H-infinity fixed-order Optimisation (HIFOO) controller to a Doubly-Fed Induction Generator wind turbine (DFIG). These controllers use the H-infinity mixed sensitivity problem to achieve an enhancement in both, Nominal Performance (NP) and Robust Stability (RS) margins for the uncertain DFIG plant while respecting constraints, such as dynamic tracking of the set-point references, load disturbances rejection and measurement noises attenuation. The simulation results show that with order reduction by half, the HIFOO controller presents effectiveness and efficiency with respect to the classical full-order H-infinity controller.

关键词： fixed-order controller design H-infinity Control Robust Control Nominal Performance Robust Stability Doubly Fed Induction Generator

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