Stability of Receding Horizon Control with Smooth Value Functions

• Published in: Proceedings of the IEEE Conference on Decision & Control pp. 4295 - 4300
• Main Authors: Layeghi, Hamed, Caines, Peter E.
• Format: Conference Proceeding
• Language: English
• Published: IEEE 01.12.2018
• Subjects: Asymptotic stability; Common Information Model (computing); Continuous time systems; Nonlinear systems; Optimal control; Stability analysis
• DOI: 10.1109/CDC.2018.8619656

Receding Horizon Control (RHC) is a very effective control methodology which has been employed in an extensive range of industrial applications. However, most of the stability results involve terminal costs or constraints which are sometimes not computationally desirable. In this work, it is shown that the smoothness of the value function is sufficient to ensure stability for control affine systems under RHC laws with no terminal cost or constraint. In order to find the infimum for all stabilizing horizons, an ODE problem based on the linearized system is developed that provides the set of stabilizing and destabilizing horizons. It is shown that the infimum of stabilizing horizons can be estimated without the need to solve the nonlinear optimal control problem, and that subject to certain conditions the exact infimum can be obtained. Simulations are provided to illustrate the application of these methods to some nonlinear systems.