Explicit MPC for LPV Systems: Stability and Optimality

This paper considers high-speed control of constrained linear parameter-varying systems using model predictive control. Existing model predictive control schemes for control of constrained linear parameter-varying systems typically require the solution of a semi-definite program at each sampling ins...

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Bibliographic Details
Published in:IEEE transactions on automatic control 2012-09, Vol.57 (9), p.2322-2332
Main Authors: Besselmann, T., Lofberg, J., Morari, M.
Format: Article
Language:English
Subjects:
Applied sciences
Asymptotic properties
Automatic control
Computation
Computer science
control theory
systems
Constrained control
Constraints
Control systems
Control theory. Systems
Cost function
Dynamic programming
Exact sciences and technology
explicit model predictive control (MPC)
Information technology
Informationsteknik
Linear parameter-varying (LPV) systems
Mathematical models
Modelling and identification
Optimal control
Optimization
Polynomials
Predictive control
Processor scheduling
Reglerteknik
Studies
TECHNOLOGY
TEKNIKVETENSKAP
Terminals
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Summary:This paper considers high-speed control of constrained linear parameter-varying systems using model predictive control. Existing model predictive control schemes for control of constrained linear parameter-varying systems typically require the solution of a semi-definite program at each sampling instance. Recently, variants of explicit model predictive control were proposed for linear parameter-varying systems with polytopic representation, decreasing the online computational effort by orders of magnitude. Depending on the mathematical structure of the underlying system, the constrained finite-time optimal control problem can be solved optimally, or close-to-optimal solutions can be computed. Constraint satisfaction, recursive feasibility and asymptotic stability can be guaranteed a priori by an appropriate selection of the terminal state constraints and terminal cost. The paper at hand gathers previous developments and provides new material such as a proof for the optimality of the solution, or, in the case of close-to-optimal solutions, a procedure to determine a bound on the suboptimality of the solution.
ISSN:0018-9286
1558-2523
1558-2523
DOI:10.1109/TAC.2012.2187400