Pontryagin's Principle For Local Solutions of Control Problems with Mixed Control-State Constraints
Eduardo Casas, J.-P. Raymond, Hasnaa Zidani · SIAM Journal on Control and Optimization · 2000
This paper deals with optimal control problems of semilinear parabolic equations with pointwise state constraints and coupled integral state-control constraints. We obtain necessary optimality conditions in the form of a Pontryagin's minimum principle for local solutions in the sense of $L^p$, $p \leq +\infty$.