We consider a discretization and the corresponding error analysis for a linear quadratic parabolic optimal control problem with box constraints on the timedependent control variable. For such problems one can show that a time-discrete solution with second order convergence can be obtained by a first order discontinuous Galerkin time discretization for the state variable and either the variation...

A neural network based optimal control synthesis approach is presented for systems modeled by partial di!erential equations. The problem is formulated via discrete dynamic programming and the necessary conditions of optimality are derived. For synthesis of the controller, we propose two sets of neural networks: the set of action networks captures the mapping between the state and control, while...

A nonconvex optimal control problem is considered, for systems governed by a parabolic partial differential equation, nonlinear in the state and control variables, with control and state constraints. Since this problem may have no classical solutions, it is reformulated in the relaxed form. The relaxed problem is discretized by using a finite element method in space and an implicit theta-scheme...

A class of parametric optimal control problems for semilinear parabolic equations is considered. Using recent regularity results for solutions of such equations, suucient conditions are derived under which the solutions to optimal control problems are locally Lipschitz continuous functions of the parameter in the L 1-norm. It is shown that these conditions are also necessary, provided that the ...

In this paper we study evolution inclusions generated by time dependent convex subdifferentials, with the orientor field F depending on a parameter. Under reasonable hypotheses on the data, we show that the solution set S(λ) is both Vietoris and Hausdorff metric continuous in λ ∈ Λ. Using these results, we study the variational stability of a class of nonlinear parabolic optimal control problems.

We consider stochastic optimal control problems in Banach spaces, related to nonlinear controlled equations with dissipative non linearity. These problems are treated via the backward stochastic differential equations approach, that allows also to solve in mild sense Hamilton Jacobi Bellman equations in Banach spaces. We apply the results to controlled stochastic heat and wave equations with co...

We study the finite-horizon optimal control problem with quadratic functionals for an established fluid-structure interaction model. The coupled PDE system under investigation comprises a parabolic (the fluid) and a hyperbolic (the solid) dynamics; the coupling occurs at the interface between the regions occupied by the fluid and the solid. We establish several trace regularity results for the ...

In this paper, we consider a stabilization problem for a fluid flow. For a perturbation of the velocity of an incoming flow on a flat plate, the laminar-to-turbulent transition location varies. We want to stabilize it by a suction velocity trough the plate. The linearization of the nonlinear model around a steady state solution leads to a linear degenerate parabolic equation. We look for a suct...

In this article we summarize recent results on a priori error estimates for space-time finite element discretizations of linear-quadratic parabolic optimal control problems. We consider the following three cases: problems without inequality constraints, problems with pointwise control constraints, and problems with state constraints pointwise in time. For all cases, error estimates with respect...

In this paper, we consider the controllability of a strongly degenerate parabolic equation with a degenerate one-order transport term. Despite the strong degeneracy, we prove a result of well-posedness and null controllability with a Dirichlet boundary control that acts on the degenerate part of the boundary. Then, we study the uniform controllability in the vanishing viscosity limit and prove ...