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Piecewise affine model-based H∞ static output feedback control of constrained non-linear processes

Piecewise affine model-based H∞ static output feedback control of constrained non-linear processes

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  • Author(s): J. Qiu 1 ; T. Zhang 2 ; G. Feng 3 ; H. Liu 4
    • View affiliations
    • Affiliations: 1: Space Control and Inertial Technology Research Center, Harbin Institute of Technology, Harbin, People's Republic of China
      2: Center for Automation Technologies and Systems, Rensselaer Polytechnic Institute, Troy, USA
      3: Department of Manufacturing Engineering and Engineering Management, City University of Hong Kong, Kowloon, Hong Kong
      4: Department of Computer Science and Technology, Tsinghua University, Beijing, People's Republic of China
  • Source: Volume 4, Issue 11, November 2010, p. 2315 – 2330
    DOI:  10.1049/iet-cta.2009.0235 , Print ISSN 1751-8644, Online ISSN 1751-8652
© The Institution of Engineering and Technology
Published

This study develops two efficient static output feedback (SOF) control approaches for a class of constrained non-linear processes represented by uncertain piecewise affine models. The parameter uncertainties in the piecewise affine models are assumed to be time varying and norm bounded. With the aid of the congruence transformation, degenerate ellipsoids-based -procedure, and some bounding inequalities, the piecewise SOF controller can be easily obtained by solving a convex semi-definite programming problem subject to some linear matrix inequalities. The resulting closed-loop system stability can be guaranteed as well as the H∞ control performance, and the stabilising design is less conservative owing to the piecewise quadratic Lyapunov functions. The performance of the proposed control approaches are demonstrated by simulation results on a non-linear benchmark plant.

Inspec keywords: convex programming; closed loop systems; stability; linear matrix inequalities; H∞ control; nonlinear control systems; feedback; uncertain systems; Lyapunov methods

Other keywords: ellipsoid-based S-procedure; constrained nonlinear process; piecewise quadratic Lyapunov function; linear matrix inequalities; closed-loop system stability; convex semidefinite programming; SOF control; H∞ static output feedback control; congruence transformation; uncertain piecewise affine model

Subjects: Optimisation techniques; Algebra; Optimal control; Stability in control theory; Nonlinear control systems

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