Periodic receding horizon LQ regulators for discrete-time systems

A derived optimal control law based on optimizing a finite horizon (N) linear quadratic (LQ) criterion at time k for a discrete-time system only yield N time varying feedback gains independent of time k and thus is of an open-loop nature. Applying such a control law at each time iN, i=0, 1, . . ., naturally leads to an N-periodic closed-loop controller called the periodic receding horizon controller. Its closed-loop asymptotic stability and performance properties are studied. Several sufficient conditions for closed-loop asymptotic stability are obtained, one of which, in particular, is weaker than that the solution of the associated Riccati difference equation (RDE) is monotonically nonincreasing and can be rendered satisfied by suitable choice of the initial condition of the RDE. The evaluated infinite time performance of both the periodic receding horizon controller and the receding horizon controller is proved to converge to the optimal one related to the infinite time regulator problem as the horizon N tends to infinity.<>