Quasi-Min-Max MPC algorithms for LPV systems

A scheduling model predictive controller is presented for polytopic linear parameter varying systems with input and output constraints. It is shown that the receding horizon implementation of the feasible solutions guarantees closed-loop stability. In this paper a new model predictive controller (MP...

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Bibliographic Details
Published in:	Automatica (Oxford) Vol. 36; no. 4; pp. 527 - 540
Main Authors:	Lu, Yaohui, Arkun, Yaman
Format:	Journal Article
Language:	English
Published:	Elsevier Ltd 01.04.2000
Subjects:	Closed-loop stability Linear matrix inequality Linear parameter varying systems Model predictive control Scheduling Linear matrix inequality Model predictive control Scheduling Closed-loop stability Linear parameter varying systems
ISSN:	0005-1098, 1873-2836
Online Access:	Get full text
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Summary:	A scheduling model predictive controller is presented for polytopic linear parameter varying systems with input and output constraints. It is shown that the receding horizon implementation of the feasible solutions guarantees closed-loop stability. In this paper a new model predictive controller (MPC) is developed for polytopic linear parameter varying (LPV) systems. We adopt the paradigm used in gain scheduling and assume that the time-varying parameters are measured on-line, but their future behavior is uncertain and contained in a given polytope. At each sampling time optimal control action is computed by minimizing the upper bound on the “quasi-worst-case” value of an infinite horizon quadratic objective function subject to constraints on inputs and outputs. The MPC algorithm is called “quasi” because the first stage cost can be computed without any uncertainty. This allows the inclusion of the first move u( k\| k) separately from the rest of the control moves governed by a feedback law and is shown to reduce conservatism and improve feasibility characteristics with respect to input and output constraints. Proposed optimization problems are solved by semi-definite programming involving linear matrix inequalities. It is shown that closed-loop stability is guaranteed by the feasibility of the linear matrix inequalities. A numerical example demonstrates the unique features of the MPC design.
ISSN:	0005-1098 1873-2836
DOI:	10.1016/S0005-1098(99)00176-4