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Improved optimisation approach to the robust H2/H∞ control problem for linear systems

Improved optimisation approach to the robust H2/H∞ control problem for linear systems

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  • Author(s): E.N. Gonçalves 1 ; R.M. Palhares 2 ; R.H.C. Takahashi 3
    • View affiliations
    • Affiliations: 1: Department of Electrical Engineering, Federal Center of Technological Education of Minas Gerais, Belo Horizonte, Brazil
      2: Department of Electronics Engineering, Federal University of Minas Gerais, Belo Horizonte, Brazil
      3: Department of Mathematics, Federal University of Minas Gerais, Belo Horizonte, Brazil
  • Source: Volume 152, Issue 2, March 2005, p. 171 – 176
    DOI:  10.1049/ip-cta:20045041 , Print ISSN 1350-2379, Online ISSN 1359-7035
IEE
Published

A strategy for robust H2/H∞ state-feedback control synthesis, with regional pole placement, applied to continuous- or discrete-time linear time-invariant uncertain systems is presented. It is based on a multiobjective optimisation over the space of the controller parameters. In the case of systems with polytope-bounded uncertainty, the H2 and H∞ norms, calculated in all polytope vertices and in possible ‘worst case’ interior points are taken as the optimisation objectives. An a posteriori exact cost norm computation based on a branch-and-bound algorithm is applied for closed-loop performance assessment. The proposed strategy is applied to continuous- and discrete-time examples, including the design of a decentralised controller, and the results are compared with LMI-based formulations.

Inspec keywords: optimisation; robust control; continuous time systems; linear systems; closed loop systems; discrete time systems; H∞ control; control system synthesis

Other keywords: time-invariant uncertain systems; continuous-time systems; H∞ norms; H2 norms; polytope-bounded uncertainty; branch-and-bound algorithm; multiobjective optimisation; decentralised controller; discrete-time systems; linear systems; optimisation approach; robust H2/H∞ control problem; regional pole placement; closed-loop performance assessment; state-feedback control synthesis

Subjects: Stability in control theory; Control system analysis and synthesis methods; Optimisation techniques; Discrete control systems; Optimal control

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