Stochastic receding horizon control with output feedback and bounded controls

• DOI: 10.1016/j.automatica.2011.09.048
• Publication Date: 2011-10-25T05:24:58Z
• Authors: Peter Hokayem; Eugenio Cinquemani; Debasish Chatterjee; Federico Ramponi; John Lygeros
• Keywords: Model-Predictive Control; 0209 industrial biotechnology; Optimality; 330; [INFO.INFO-TS] Computer Science [cs]/Signal and Image Processing; [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS]; [MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS]; Robust Optimization; 02 engineering and technology; 510; [SPI.AUTO]Engineering Sciences [physics]/Automatic; Constrained control; [INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing; 0203 mechanical engineering; Constrained Control; Predictive control; Stochastic Control; Policies; [INFO.INFO-BI] Computer Science [cs]/Bioinformatics [q-bio.QM]; [SPI.SIGNAL] Engineering Sciences [physics]/Signal and Image processing; Systems; [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC]; State Estimation; 004; Output feedback; Predictive Control; [SPI.AUTO] Engineering Sciences [physics]/Automatic; Stochastic control; Constraints; Constrained control, Output feedback, Predictive control, State estimation, Stochastic control; [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]; [INFO.INFO-BI]Computer Science [cs]/Bioinformatics [q-bio.QM]; Stability; [SPI.SIGNAL]Engineering Sciences [physics]/Signal and Image processing; Output Feedback; State; State estimation

We study the problem of receding horizon control for stochastic discrete-time systems with bounded control inputs and incomplete state information. Given a suitable choice of causal control policies, we first present a slight extension of the Kalman filter to estimate the state optimally in mean-square sense. We then show how to augment the underlying optimization problem with a negative drift-like constraint, yielding a second-order cone program to be solved periodically online. We prove that the receding horizon implementation of the resulting control policies renders the state of the overall system mean-square bounded under mild assumptions. We also discuss how some quantities required by the finite-horizon optimization problem can be computed off-line, thus reducing the on-line computation.