On Stabilizing Receding Horizon Controls for Linear Systems

Ki Baek Kim, Computer Sci. & Electrical Eng., California Institute of Technology

Abstract: Receding horizon control (RHC) uses the current control law obtained by solving the optimization problem every sampling instant. It is also called generalized predictive control (GPC) or model predictive control (MPC). Since RHC can consider a finite horizon cost function, it can easily handle time-varying tracking commands, time-varying systems, input/state constraints, uncertainty, disturbances, etc. For this reason, it has been widely investigated in academia and industry.

Stability has been a main issue in control theory. The stability of the RHC for linear systems are very important since they can be extended to various problems including guidance laws, delayed control, adaptive control, output feedback control, tracking control, or nonlinear control. Therefore, any slight extension to existing results will be very significant.

This talk will give a brief overview of stabilizing RHC and introduce speaker's recent results on stabilizing RHCs for linear systems. First, we introduce general terminal inequality conditions and state/control weighting matrices, which guarantee the closed-loop stability for linear continuous and discrete time-varying systems. Second, we introduce how to implement stabilizing RHCs for input/state constrained time-varying systems in terms of feasibility and computational burden. Third, we introduce how to implement receding horizon tracking controls for unconstrained/constrained time-varying systems in terms of feasibility and computational burden. Fourth, we extend the above whole results to H-infinity problem. Fifth, we talk about intervalwise RHC briefly. Finally, we discuss future works about stabilizing RHCs. Related papers are available from http://cisl.snu.ac.kr/~kkb.