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H ∞ model predictive control for constrained discrete‐time piecewise affine systems
Author(s) -
Sindareh Esfahani Peyman,
Pieper Jeffery Kurt
Publication year - 2017
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.3995
Subject(s) - control theory (sociology) , model predictive control , mathematics , mathematical optimization , lyapunov function , piecewise , norm (philosophy) , discrete time and continuous time , minification , quadratic equation , infimum and supremum , controller (irrigation) , linear matrix inequality , stability theory , computer science , nonlinear system , control (management) , mathematical analysis , agronomy , statistics , physics , geometry , quantum mechanics , artificial intelligence , political science , law , biology
Summary This paper investigates H ∞ stability analysis for piecewise affine (PWA) systems and specifically contributes a new H ∞ robust model predictive control strategy for PWA systems in the presence of constraints on the states and inputs and with l 2 or norm‐bounded disturbances. The proposed controller is based on piecewise quadratic Lyapunov functions. The problem of minimization of the cost function for model predictive control design is changed to minimization of the worst case of the cost function. Then, this objective is reduced to minimization of a supremum of the cost function subject to a terminal inequality by considering the induced l 2 ‐norm. Finally, the predictive controller design problem is turned into a linear matrix inequality feasibility exercise with constraints on the input signal and state variables. It is shown that the closed‐loop system is asymptotically stable with guaranteed robust H ∞ performance. The validity of the proposed method is verified through 3 well‐known examples of PWA systems. Simulation results are provided to show good convergence properties along with capability of the proposed controller to reject disturbances.