Sufficiency conditions for weak local minima in multidimensional optimal control problems with mixed control-state restrictions (Q686823)

The author investigates optimal control problems with mixed control and state constraints where the ``time'' variable belongs to \(\mathbb{R}^ m\), \(m>1\). This paper follows on from previous work where sufficient conditions were given for strong local optimality. In this paper sufficient conditions for weak local optimality are presented. The sufficient conditions are derived using the Hamilton-Jacobi inequality and a dual problem based on solutions to this inequality. By using a linear solution function with concavity assumptions on the original problem, first order sufficiency conditions are obtained. By using a quadratic function, the concavity assumptions can be dropped, and second order sufficiency conditions are derived.