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Constrained linear MPC with time-varying terminal cost using convex combinations. (English) Zbl 1093.93012

Summary: Recent papers [M. Bacic et al., IEEE Trans. Autom. Control 48, No. 6, 1092–1096 (2003), H. H. J. Bloemen et al., Automatica 38, No. 6, 1061–1068 (2002; Zbl 1010.93041), Z. Wan et al. Syst. Control Lett. 48, 375–383 (2003)] have introduced dual-mode MPC algorithms using a time-varying terminal cost and/or constraint. The advantage of these methods is the enlargement of the admissible set of initial states without sacrificing local optimality of the controller, but this comes at the cost of a higher computational complexity. This paper delivers two main contributions in this area. First, a new MPC algorithm with a time-varying terminal cost and constraint is introduced. The algorithm uses convex combinations of off-line computed ellipsoidal terminal constraint sets and uses the associated cost as a terminal cost. In this way, a significant on-line computational advantage is obtained. The second main contribution is the introduction of a general stability theorem, proving stability of both the new MPC algorithm and several existing MPC schemes. This allows a theoretical comparison to be made between the different algorithms. The new algorithm using convex combinations is illustrated and compared with other methods on the example of an inverted pendulum.

MSC:

93B40 Computational methods in systems theory (MSC2010)
93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
49M30 Other numerical methods in calculus of variations (MSC2010)

Citations:

Zbl 1010.93041

Software:

SeDuMi; Mosek
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Full Text: DOI

References:

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[10] Pluymers, B., Roobrouck, L., Buijs, J., Suykens, J. A. K., & De Moor, B. (2004a). Model-predictive control with time-varying terminal cost using convex combinations. Internal Report 04-028, ESAT-SISTA, K. U. Leuven (Leuven, Belgium), http://www.esat.kuleuven.ac.be/sista/; Pluymers, B., Roobrouck, L., Buijs, J., Suykens, J. A. K., & De Moor, B. (2004a). Model-predictive control with time-varying terminal cost using convex combinations. Internal Report 04-028, ESAT-SISTA, K. U. Leuven (Leuven, Belgium), http://www.esat.kuleuven.ac.be/sista/ · Zbl 1093.93012
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