Towards a less conservative model predictive control based on mixed ℋ2/ℋ ∞ control approach

A novel approach to the design of a less conservative model predictive control is proposed, using mixed ℋ2/ℋ∞ design method for time-invariant discrete-time linear systems. The controller has the form of a state-feedback, satisfies input and state constraints and is constructed from the solution of a set of feasibility linear matrix inequalities. The control law takes into account the disturbances naturally and the input constraint is less conservative in the sense that the full control is used. Numerical examples comparing the proposed algorithm with some existing techniques are provided to demonstrate the applicability and the advantage of the proposed algorithm.

[1]  Chi-Kwong Li,et al.  Extremal Characterizations of the Schur Complement and Resulting Inequalities , 2000, SIAM Rev..

[2]  M. Morari,et al.  Stability of model predictive control with mixed constraints , 1995, IEEE Trans. Autom. Control..

[3]  R. E. Kalman,et al.  Contributions to the Theory of Optimal Control , 1960 .

[4]  David Q. Mayne,et al.  Constrained model predictive control: Stability and optimality , 2000, Autom..

[5]  Brian D. O. Anderson,et al.  Network Analysis and Synthesis: A Modern Systems Theory Approach , 2006 .

[6]  J. Richalet,et al.  Model predictive heuristic control: Applications to industrial processes , 1978, Autom..

[7]  Andrew Packard,et al.  Robust H2 and H∞ filters for uncertain LFT systems , 2005, IEEE Trans. Autom. Control..

[8]  Xiang Chen,et al.  Multiobjective \boldmathHt/Hf Control Design , 2001, SIAM J. Control. Optim..

[9]  G. D. Halikias,et al.  Hierarchical optimisation in ℋ/sub ∞/ , 1995 .

[10]  K.V. Ling,et al.  A FPGA implementation of model predictive control , 2006, 2006 American Control Conference.

[11]  Manfred Morari,et al.  Robust constrained model predictive control using linear matrix inequalities , 1994, Proceedings of 1994 American Control Conference - ACC '94.

[12]  J. Rawlings,et al.  The stability of constrained receding horizon control , 1993, IEEE Trans. Autom. Control..

[13]  Imad M. Jaimoukha,et al.  A numerical solution to the matrix ℋ2/ℋ∞ optimal control problem , 1997 .

[14]  U. Shaked,et al.  Minimum H/sub infinity /-norm regulation of linear discrete-time systems and its relation to linear quadratic discrete games , 1990 .

[15]  I.M. Jaimoukha,et al.  Model Predictive Control based on Mixed H2/H Control Approach , 2007, 2007 American Control Conference.

[16]  Imad M. Jaimoukha,et al.  Robust model predictive control based on mixed ℋ2/ℋ∞ control approach , 2009, 2009 European Control Conference (ECC).

[17]  Roger M. Goodall,et al.  Model predictive control based on mixed ℋ2/ℋ∞ control approach for active vibration control of railway vehicles , 2008 .

[18]  Bogdan Dumitrescu,et al.  Bounded real lemma for FIR MIMO systems , 2005, IEEE Signal Processing Letters.