Mathieu Claeys

Semi-definite relaxations for optimal control problems with oscillation and concentration effects

  • Mathieu Claeys
  • Didier Henrion
  • Martin Kružík
    • Categories Control Applications, Semi-definite Programming

    Converging hierarchies of finite-dimensional semi-definite relaxations have been proposed for state-constrained optimal control problems featuring oscillation phenomena, by relaxing controls as Young measures. These semi-definite relaxations were later on extended to optimal control problems depending linearly on the control input and typically featuring concentration phenomena, interpreting the control as a measure of time with a … Read more

    Modal occupation measures and LMI relaxations for nonlinear switched systems control

  • Mathieu Claeys
  • Didier Henrion
  • Jamal Daafouz
    • Categories Control Applications, Infinite Dimensional Optimization, Linear, Cone and Semidefinite Programming

    This paper presents a linear programming approach for the optimal control of nonlinear switched systems where the control is the switching sequence. This is done by introducing modal occupation measures, which allow to relax the problem as a primal linear programming (LP) problem. Its dual linear program of Hamilton-Jacobi-Bellman inequalities is also characterized. The LPs … Read more

    Efficient upper and lower bounds for global mixed-integer optimal control

  • Mathieu Claeys
  • Sebastian Sager
  • Frédéric Messine
    • Categories (Mixed) Integer Nonlinear Programming, Global Optimization Applications, Optimization of Simulated Systems

    We present a control problem for an electrical vehicle. Its motor can be operated in two discrete modes, leading either to acceleration and energy consumption, or to a recharging of the battery. Mathematically, this leads to a mixed-integer optimal control problem (MIOCP) with a discrete feasible set for the controls taking into account the electrical … Read more