Aurelian Cernea

A Connection Between the Maximum Principle and Dynamic Programming for Constrained Control Problems

We consider the Mayer optimal control problem with dynamics given by a nonconvex differential inclusion, whose trajectories are constrained to a closed set and obtain necessary optimality conditions in the form of the maximum principle together with a relation between the costate and the value function. This additional relation is applied in turn to show that the maximum principle is nondegenerate. We also provide a sufficient condition for the normality of the maximum\break principle. To derive these results we use convex linearizations of differential inclusions and convex linearizations of constraints along optimal trajectories. Then duality theory of convex analysis is applied to derive necessary conditions for optimality. In this way we extend the known relations between the maximum principle and dynamic programming from the unconstrained problems to the constrained case.

A note on the existence of solutions for some boundary value problems of fractional differential inclusions

We study the existence of solutions for fractional differential inclusions of order q ∈ (1, 2] with families of mixed and closed boundary conditions. We establish Filippov type existence results in the case of nonconvex setvalued maps.

The connection between the maximum principle and the value function for optimal control problems under state constraints

We consider the Mayer optimal control problem with dynamics given by a non convex differential inclusion, whose trajectories are constrained to a closed set and obtain necessary optimality conditions in the form of the maximum principle together with a relation between the costate and the value function. This additional relation is applied in turn to show that the maximum principle is non degenerate.

On the set of solutions of some nonconvex nonclosed hyperbolic differential inclusions

We consider a class of nonconvex and nonclosed hyperbolic differential inclusions and we prove the arcwise connectedness of the solution set.

Filippov Lemma for a Class of Hadamard-Type Fractional Differential Inclusions

Abstract We study a class of fractional integro-differential inclusions with integral boundary conditions and establish a Filippov type existence result in the case of nonconvex set-valued maps.

A note on the value function for constrained control problems

Abstract We consider the Mayer optimal control problem with dynamics given by a nonconvex differential inclusion, whose trajectories are constrained to a given set and we obtain a relation between the costate function that appears in the maximum principle and the value function. This relation extends the known conditions existing in the literature for unconstrained problems to those for problems under state constraints.

Directionally Continuous Selections and Nonconvex Evolution Inclusions

AbstractIn Bressan and Staicu, Set-Valued Anal.2 (1994), 415–437, qualitative properties for solutions of the evolution inclusion

On a boundary value problem for a Sturm-Liouville type differential inclusion

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