Sensitivity of the minimum cost function to parameter perturbations, for state constrained optimal control problems (Reference: ESR2) ***this position has been filled***

• Title: Sensitivity of the minimum cost function to parameter perturbations, for state constrained optimal control problems.     
• Location: Imperial College
• Secondment (6 months): University of Porto
• Contact: Richard Vinter
• Reference: ESR2
• Key Words: Sufficient optimality conditions, sensitivity analysis, parameter perturbations, multiple state constraints
• Description of the subject:    Many key issues in optimal control, including the validity of non-degenerate forms of the Pontryagin Maximum Principle (PMP) and the question of whether it is possible to characterize the value function as a solution to the Hamilton-Jacobi equation (see Task 2.1), are linked to the sensitivity properties of the minimum cost to modeling parameters. For unconstrained systems, differentiability of the value function is, in many cases, related to the uniqueness of optimal solutions and is a key requirement for the derivation of sufficient conditions for optimality. At the same time, the differentiability properties of the minimum cost are not adequately understood for state constrained problems; this is an obstacle to the derivation of sufficient optimality conditions and the solution of optimal control problems when state constraints are present. We aim to establish differentiability properties in a number of situations not covered by previous theory, and examine their implications for the derivation of optimality conditions and the feedback synthesis of optimal controls. These include multiple state constraint problems and state constraints associated with obstacle avoidance problems, where the constraint set cannot be described simply in terms of a collection of functional inequality constraints.
• Requirements:  MSc degree in mathematics or a related subject.  Background in optimal control and/or nonsmooth analysis and/or optimisation theory
  

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