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Trelat, E. (2000) Some Properties of the Value Function and Its Level Sets for Affine Control Systems with Quadratic Cost. Journal of Dynamical and Control Systems, 61, 511-541.

has been cited by the following article:

• TITLE: On Global Minimization for the Value Function in Affine Optimal Control Problems

  AUTHORS: Jinghao Zhu

  KEYWORDS: Global Minimization, Value Function, Affine Optimal Control, Regularity, Extremal Flow, Riccati Differential Equation

  JOURNAL NAME: Open Access Library Journal, Vol.10 No.7, July 19, 2023

  ABSTRACT: In this paper we provide a computational approach to a minimization problem for the value function associated with an affine optimal control problem subject to terminal-constraint with quadratic cost plus a potential, for a fixed final time and initial point. We study the global minimization problem of the value function over the attainable set and the regularity properties of the value function at a global minimizer point. On the other hand, in the global minimization of the value function, by an example in this computational approach, we also focus on a numerical method by Riccati matrix differential equations.