On the convergence of stochastic MPC to terminal modes of operation

Conference item

The stability of stochastic Model Predictive Control (MPC) subject to additive disturbances is often demonstrated in the literature by constructing Lyapunov-like inequalities that guarantee closed-loop performance bounds and boundedness of the state, but convergence to a terminal control law is typically not shown. In this work we use results on general state space Markov chains to find conditions that guarantee convergence of disturbed nonlinear systems to terminal modes of operation, so that they converge in probability to a priori known terminal linear feedback laws and achieve time-average performance equal to that of the terminal control law. We discuss implications for the convergence of control laws in stochastic MPC formulations, in particular we prove convergence for two formulations of stochastic MPC.

Authors: Munoz-Carpintero, D; Cannon, M

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Institute of Electrical and Electronics Engineers
• Host title: 2019 18th European Control Conference (ECC)
• Journal: 2019 18th European Control Conference (ECC)
• Pages: 1356-1361
• Publication date: 2019-08-15
• Acceptance date: 2019-02-20
• DOI: 10.23919/ECC.2019.8795946
• Keywords: Markov processes; predictive control for linear systems; stochastic control