Cyclomonotonicity, riccati equations and periodic receding horizon control

Abstract

In this paper, periodic receding-horizon control of periodic and time-invariant systems is considered. This type of receding-horizon control is based on the periodic extension of the control law that solves a finite-horizon optimal control problem. It is shown that cyclomonotonicity of the solution of the differential Riccati equation entails stability of the closed-loop system. Stability analysis hinges on the so-called ‘fake two-point boundary’ Riccati equation, a differential Riccati equation whose solution is constrained to satisfy a two-point boundary condition. In the case of time-invariant systems, cyclomonotonicity is always achievable by a proper scaling of the terminal condition of the Riccati equation. It is also proven that cyclomonotonic solutions of the Riccati equation not only yield stabilizing controllers, but also constant and stabilizing control laws.