An Improved Method in Receding Horizon Control with Updating of Terminal Cost Function
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In this chapter, we propose a modified receding horizon control (RHC) scheme for discrete linear time-invariant systems, called updated terminal cost RHC (UTC-RHC). The standard receding horizon control, also known as model predictive control (MPC) or moving horizon control (MHC), is a suboptimal control scheme that solves a finite horizon open-loop optimal control problem in an infinite horizon context and yields a state feedback control law. The ability to deal with constraints on controls and states makes RHC popular in industry, especially in the process control industry. A lot of successful applications have been reported in the past three decades. The stability issue has been an important topic in the literature and a lot of approaches have been proposed. Most of these approaches impose constraints on either the terminal state, or the terminal cost, or the horizon size, or their different combinations.
Unlike the standard RHC, UTC-RHC algorithm updates the terminal cost function of the corresponding finite horizon optimal control problem at every stage. It ensures the closed-loop system to be uniformly exponentially stable without imposing any constraint on the terminal state, the horizon size, or the terminal cost, thus makes the design of a stabilizing controller more flexible. Moreover, the control law generated by UTC-RHC algorithm converges to the optimal control law of the infinite horizon optimal control problem.
KeywordsOptimal Control Problem Model Predictive Control Linear Quadratic Regulator Approximate Dynamic Programming Recede Horizon Control
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