Partial differential inclusions governing feedback controls.
A Second-Order Maximum Principle in Optimal Control Under State Constraints
A second-order variational inclusion for control systems under state constraints is derived and applied to investigate necessary optimality conditions for the Mayer optimal control problem. A new pointwise condition verified by the adjoint state of the maximum principle is obtained as well as a second-order necessary optimality condition in the integral form. Finally, a new sufficient condition for normality of the maximum principle is proposed. Some extensions to the Mayer optimization problem...
Normality of the maximum principle for absolutely continuous solutions to Bolza problems under state constraints
Some inverse mapping theorems
Interior sphere property of attainable sets and time optimal control problems
This paper studies the attainable set at time for the control system showing that, under suitable assumptions on , such a set satisfies a uniform interior sphere condition. The interior sphere property is then applied to recover a semiconcavity result for the value function of time optimal control problems with a general target, and to deduce C-regularity for boundaries of attainable sets.
Value functions for Bolza problems with discontinuous lagrangians and Hamilton-Jacobi inequalities
Hyperbolic systems of partial differential inclusions
Value functions for Bolza problems with discontinuous Lagrangians and Hamilton-Jacobi inequalities
We investigate the value function of the Bolza problem of the Calculus of Variations with a lower semicontinuous Lagrangian and a final cost , and show that it is locally Lipschitz for whenever is locally bounded. It also satisfies Hamilton-Jacobi inequalities in a generalized sense. When the Lagrangian is continuous, then the value function is the unique lower semicontinuous solution to the corresponding Hamilton-Jacobi equation, while for discontinuous Lagrangian we characterize the value...
Poincaré's recurrence theorem for set-valued dynamical systems
Abstract. The existence theorem of an invariant measure and Poincare's Recurrence Theorem are extended to set-valued dynamical systems with closed graph on a compact metric space.
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