Optimality conditions of the type of the maximum principle in Goursat-Darboux systems

Optimal control of Goursat–Darboux systems with discontinuous co-state

“…The variation δJ, under a variation δu of the control, can analogously computed as Maximum principles of Pontryagin's type have been proved in [BDMO,E1,E2,E3,PS,S,VST] for controlled Goursat-Darboux systems over rectangular domains. A maximum principle for an optimal control problem has two main components: the Hamiltonian part, i.e.…”

“…There are also more general existence and uniqueness results, but those are not relevant to the optimal control issues that we study in the present paper. An optimal control problem for the system {(1.1), (1.2)} concerns the minimization of a functional J given by Necessary conditions for optimality, in a form analogous to Pontryagin's maximum principle, have be obtained for the problem {(1.1), (1.2), (1.3)} in [BDMO,E1,E2,E3,PS,S,VST]; related work, from the point of view of dynamic programming with twodimensional "time" variable, has been done in [B1, B2, B3]. so that, in reality, v becomes the control function; this approach has been introduced in [B1].…”

On the numerical scheme of a 2D optimal control problem with the hyperbolic system via Bernstein polynomial basis

“…The important role of the Goursat–Darboux problem is in the optimization theory of distributed systems (Vasil’ev, 2002; Vasil’ev et al, 1990). The authors of Egorov (1965), Egorov (1966), Kazemi–Dehkordi (1986), Plotnikov and Sumin (1972a), Plotnikov and Sumin (1972b), Srochko (1984), Suryanarayana (1972) and Suryanarayana (1973) have studied the continuous Goursat–Darboux optimal control problem from the point of view of Pontryagin’s maximum principle. Though in Belbass (1990), the author has utilized the dynamic programming approach to optimal control problem for the continuous Goursat–Darboux systems with distributed controls.…”