Feedback controls and optimal trajectories (ESR 14) **** this position has been filled ****

• Title: Feedback controls and optimal trajectories
• Location: INRIA (Paris)
• Secondment: University of Padova
• Contact: Hasnaa Zidani
• Funding: 36 months

Description: For optimal control problems with no state, control or endpoint constraints, the Hamilton-Jacobi approach permits us to obtain approximations of optimal strategies in feedback form and guarantees that the corresponding trajectories are close to being global minimizers. When constraints are present however, several issues need to be investigated, such as the development of appropriate discretization schemes for control systems that fail to be controllable, the convergence of discrete control strategies to the correct continuous strategy and accelerated procedures for solving the discretized optimal control problems. It is now known that for certain broad classes of nonlinear control systems the only stabilizing feedback control strategies are discontinuous, giving rise to a closed loop state equation which is discontinuous with respect to the state variable. It is of interest then to develop a well-posedness theory of discontinuous ordinary differential equations arising in this way. For this purpose, a particular class of discontinuous piecewise smooth vector fields (patchy vector fields) was introduced by Ancona and Bressan; it was shown that, by patching together open loop controls of an asymptotically controllable system, one can always construct a stabilizing feedback that generates a discontinuous vector field belonging to this class: a patchy feedback. It is intended to investigate the robustness properties of patchy feedback strategies and to develop patchy feedback strategies for optimal control problems with state constraints.
 

• Requirements: Msc degree in mathematics. Background in optimal control and/or optimisation theory, scientific computing.
  

Applications including a full curriculum vitae, and the names and addresses of at least two referees should be sent to Contacts.