Parametric approximation of maximal output admissible sets and its application to multi-mode switching control under unknown constant Reference

This paper shows a procedure for approximately parameterizing maximal output admissible sets by ellipsoids, and then, theoretically proves that an union of the ellipsoids, which is no longer invariant, is continuously parametrized in terms of a reference. The parameterized set allows online judgment of whether the constraints are fulfilled when considering a tracking control of a constrained system under an unknown constant reference, which requires realtime computation of the output admissible sets. Therefore, the resulting consequence is so useful as to broaden a treatable control problem with conventional constrained control techniques, one of which is multi-mode switching control. Finally, a practical example presents its effectiveness and applicability.

[1]  S. Oh-Hara,et al.  Experimental evaluation of on-line reference governors for constrained systems , 2003, SICE 2003 Annual Conference (IEEE Cat. No.03TH8734).

[2]  Ilya V. Kolmanovsky,et al.  Nonlinear tracking control in the presence of state and control constraints: a generalized reference governor , 2002, Autom..

[3]  D. Mayne,et al.  Computation of invariant sets for piecewise affine discrete time systems subject to bounded disturbances , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[4]  K. T. Tan,et al.  Linear systems with state and control constraints: the theory and application of maximal output admissible sets , 1991 .

[5]  Takeshi Hatanaka,et al.  Probabilistic output admissible set for systems with time-varying uncertainties , 2008, Syst. Control. Lett..

[6]  David P. Dobkin,et al.  The quickhull algorithm for convex hulls , 1996, TOMS.

[7]  J. Lofberg,et al.  YALMIP : a toolbox for modeling and optimization in MATLAB , 2004, 2004 IEEE International Conference on Robotics and Automation (IEEE Cat. No.04CH37508).

[8]  Ilya V. Kolmanovsky,et al.  Parameter governors for discrete-time nonlinear systems with pointwise-in-time state and control constraints , 2006, Proceedings of the 2004 American Control Conference.

[9]  Edoardo Mosca,et al.  An ellipsoidal off-line MPC scheme for uncertain polytopic discrete-time systems , 2008, Autom..

[10]  Masayuki Fujita,et al.  Multimode switching state feedback control of constrained linear discrete-time systems , 1998, Proceedings of the 1998 IEEE International Conference on Control Applications (Cat. No.98CH36104).

[11]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[12]  Kenji Hirata,et al.  Exact Determinations of the Maximal Output Admissible Set for a Class of Nonlinear Systems , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

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

[14]  E. Mosca,et al.  Nonlinear control of constrained linear systems via predictive reference management , 1997, IEEE Trans. Autom. Control..

[15]  Alberto Bemporad,et al.  Reference governor for constrained nonlinear systems , 1998, IEEE Trans. Autom. Control..

[16]  K. T. Tan,et al.  Discrete‐time reference governors and the nonlinear control of systems with state and control constraints , 1995 .