An alternative formulation of the interpolation based constrained H∞ control of discrete-time LPV systems

The paper presents an alternative formulation of the interpolation based constrained ℋ∞ control presented originally in [16], [12], [17]. The concept itself has not been changed: by interpolating among unconstrained state feedback gains both the ℋ∞ performance and the satisfaction of the hard state, input and output constraints can be guaranteed. The novelty is in the computation of the region of applicability of the controller. It is now based on the d-invariant sets of the individual controllers and not on the high dimensional extended system comprising all of the closed loops generated by the controllers.

[1]  Marko Bacic,et al.  Interpolation based computationally efficient predictive control , 2004 .

[2]  Jozsef Bokor,et al.  Constrained H∞ control for discrete-time LPV systems using interpolation , 2008, 2008 47th IEEE Conference on Decision and Control.

[3]  J. Bokor,et al.  Constraint H[infinity] control for discrete-time LPV systems by inerpolating among linear feedback gains , 2008 .

[4]  D. Mayne,et al.  Characterization of the solution to a constrained H ∞ optimal control problem , 2005 .

[5]  Francesco Borrelli,et al.  Constrained Optimal Control of Linear and Hybrid Systems , 2003, IEEE Transactions on Automatic Control.

[6]  Jozsef Bokor,et al.  Induced L2 Norm Improvement by Interpolating Controllers for Discrete-time LPV Systems , 2009, Eur. J. Control.

[7]  Isaac Kaminer,et al.  Mixed H2/H∞ control for discrete-time systems via convex optimization , 1992, American Control Conference.

[8]  E..  Receding horizon H , control for nonlinear discrete-time systems , 2004 .

[9]  Hong Chen,et al.  Moving horizon I control with performance adaptation for constrained linear systems , 2006, Autom..

[10]  P.J. Goulart,et al.  A convex formulation for receding horizon control of constrained discrete-time systems with guaranteed l2 gain , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[11]  B. De Moor,et al.  Interpolation based MPC for LPV systems using polyhedral invariant sets , 2005, Proceedings of the 2005, American Control Conference, 2005..

[12]  E. Gilbert,et al.  Theory and computation of disturbance invariant sets for discrete-time linear systems , 1998 .

[13]  David Q. Mayne,et al.  Invariant approximations of the minimal robust positively Invariant set , 2005, IEEE Transactions on Automatic Control.

[14]  J. Suykens,et al.  The efficient computation of polyhedral invariant sets for linear systems with polytopic uncertainty , 2005, Proceedings of the 2005, American Control Conference, 2005..

[15]  Johan A. K. Suykens,et al.  A SIMPLE ALGORITHM FOR ROBUST MPC , 2005 .

[16]  Eduardo F. Camacho,et al.  Explicit solution of min-max MPC with additive uncertainties and quadratic criterion , 2006, Syst. Control. Lett..

[17]  Éva Gyurkovics,et al.  Quadratic stabilisation with H∞-norm bound of non-linear discrete-time uncertain systems with bounded control , 2003, Syst. Control. Lett..

[18]  C. Scherer,et al.  Linear Matrix Inequalities in Control , 2011 .

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

[20]  Lawton H. Lee,et al.  Control of linear parameter-varying systems using dynamic parameter measurement , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

[21]  C. Scherer,et al.  A game theoretic approach to nonlinear robust receding horizon control of constrained systems , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).