Output-feedback controlled-invariant polyhedra for constrained linear systems

A design method is proposed for output-feedback control of linear systems subject to state and control constraints, additive disturbances and measurement noise. First, necessary and sufficient conditions for a polyhedral set to be controlled-invariant under output-feedback are presented, which can be checked by the solution of a set of Linear Programming problems. Then, a dynamic output-feedback compensator structure is proposed to guarantee constraint satisfaction, through the construction of an output-feedback controlled-invariant set, from a pair composed by a conditioned-invariant and a controlled-invariant polyhedron. Based on the available measurements and on the state of the compensator, a suitable control sequence can be computed to enforce the state constraints. Differently from other approaches, the proposed method does not rely on pre-computed linear controllers or observers. Therefore, it is likely to provide a solution for larger amplitudes of disturbances and noise, and larger uncertainties on the initial state, as illustrated by numerical examples.

[1]  Elmer G. Gilbert,et al.  The minimal disturbance invariant set: Outer approximations via its partial sums , 2006, Autom..

[2]  Franco Blanchini,et al.  Stabilization of LPV systems: state feedback, state estimation and duality , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[3]  Franco Blanchini,et al.  Set-theoretic methods in control , 2007 .

[4]  David Q. Mayne,et al.  Optimized robust control invariance for linear discrete-time systems: Theoretical foundations , 2007, Autom..

[5]  C.E.T. Dorea.  Set-Invariant Estimators for Multiple-Output Discrete-Time Systems , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[6]  Franco Blanchini,et al.  Set invariance in control , 1999, Autom..

[7]  G. Basile,et al.  Controlled and conditioned invariants in linear system theory , 1992 .

[8]  Eric C. Kerrigan,et al.  Output feedback receding horizon control of constrained systems , 2007, Int. J. Control.

[9]  J. Schumacher.  Compensator synthesis using (C,A,B)-pairs , 1980 .

[10]  Graham C. Goodwin,et al.  Robust output-feedback model predictive control for systems with unstructured uncertainty , 2008, Autom..

[11]  C. Dórea,et al.  Design of Set-Invariant Estimators for Linear Discrete-Time Systems , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[12]  B. Kouvaritakis,et al.  Receding horizon output feedback control for linear systems with input saturation , 2001 .

[13]  David Q. Mayne,et al.  Robust output feedback model predictive control of constrained linear systems , 2006, Autom..

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

[15]  B. Kouvaritakis,et al.  Receding horizon output feedback control for linear systems with input saturation , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[16]  Franco Blanchini,et al.  Ultimate boundedness control for uncertain discrete-time systems via set-induced Lyapunov functions , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

[17]  David K. Smith.  Theory of Linear and Integer Programming , 1987 .

[18]  Yasushi Hada,et al.  Constrained Model Predictive Control , 2006 .

[19]  Eduardo F. Camacho,et al.  Output feedback Robust tube based MPC for tracking of piece-wise constant references , 2007, 2007 46th IEEE Conference on Decision and Control.

[20]  J. Hennet,et al.  (A, B)-Invariant Polyhedral Sets of Linear Discrete-Time Systems , 1999 .