Strong bi-metric regularity in affine optimal control problems

Abstract: The paper presents new sufficient conditions for the property of strong bi-metric regularity of the optimality map associated with an optimal control problem which is affine with respect to the control variable ({\em affine problem}). The optimality map represents the system of first order optimality conditions (Pontryagin maximum principle), and its regularity is of key importance for the qualitative and numerical analysis of optimal control problems. The case of affine problems is especially challenging due to the typical discontinuity of the optimal control functions. A remarkable feature of the obtained sufficient conditions is that they do not require convexity of the objective functional. As an application, the result is used for proving uniform convergence of the Euler discretization method for a family of affine optimal control problems.