Probabilistic tubes in linear stochastic model predictive control

This paper considers constrained control of linear systems with additive and multiplicative stochastic uncertainty and linear input/state constraints. Both hard and soft constraints are considered, and bounds are imposed on the probability of soft constraint violation. Assuming the plant parameters to be finitely supported, a method of constraint handling is proposed in which a sequence of tubes, corresponding to a sequence of confidence levels on the predicted future plant state, is constructed online around nominal state trajectories. A set of linear constraints is derived by imposing bounds on the probability of constraint violation at each point on an infinite prediction horizon through constraints on one-step-ahead predictions. A guarantee of the recursive feasibility of the online optimization ensures that the closed loop system trajectories satisfy both the hard and probabilistic soft constraints. The approach is illustrated by a numerical example.

[1]  Jun Yan,et al.  Incorporating state estimation into model predictive control and its application to network traffic control , 2005, Autom..

[2]  B. Kouvaritakis,et al.  Successive linearization NMPC for a class of stochastic nonlinear systems , 2009 .

[3]  Basil Kouvaritakis,et al.  Constrained receding horizon predictive control for nonlinear systems , 2002, Autom..

[4]  Basil Kouvaritakis,et al.  Who needs QP for linear MPC anyway? , 2002, Autom..

[5]  Mark Rice,et al.  A numerically robust state-space approach to stable-predictive control strategies , 1998, Autom..

[6]  David Q. Mayne,et al.  Robust model predictive control using tubes , 2004, Autom..

[7]  David Q. Mayne,et al.  Robust model predictive control of constrained linear systems with bounded disturbances , 2005, Autom..

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

[9]  Basil Kouvaritakis,et al.  Model predictive control for systems with stochastic multiplicative uncertainty and probabilistic constraints , 2009, Autom..

[10]  Basil Kouvaritakis,et al.  Efficient robust predictive control , 2000, IEEE Trans. Autom. Control..

[11]  Basil Kouvaritakis,et al.  Probabilistic Constrained MPC for Multiplicative and Additive Stochastic Uncertainty , 2009, IEEE Transactions on Automatic Control.

[12]  Basil Kouvaritakis,et al.  Robust receding horizon predictive control for systems with uncertain dynamics and input saturation , 2000, Autom..

[13]  P. Couchman,et al.  MPC on state space models with stochastic input map , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[14]  S. Weiland,et al.  Optimal control of linear, stochastic systems with state and input constraints , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[15]  Pu Li,et al.  A probabilistically constrained model predictive controller , 2002, Autom..

[16]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[17]  J. Rossiter,et al.  Robust predictive control using tight sets of predicted states , 2000 .

[18]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .