A dimension reduction analysis is undertaken using ?-convergence techniques within a relaxation theory for 3D nonlinear elastic thin domains of the form where ! is a bounded domain of R 2 and f" is an "-dependent proole. An abstract representation of the eeective 2D energy is obtained, and speciic characterizations are found for nonhomogeneous plate models, periodic pro-les, and within the cont...

Discretizations of optimal control problems for elliptic equations by finite element methods are considered. The problems are subject to constraints on the control and may also contain pointwise state constraints. Some techniques are surveyed to estimate the distance between the exact optimal control and the associated optimal control of the discretized problem. As a particular example, an erro...

We present new theorems characterizing robust Lyapunov functions and infinite horizon value functions in optimal control as unique viscosity solutions of partial differential equations. We use these results to further extend Zubov’s method for representing domains of attraction in terms of partial differential equation solutions.

In this paper, we consider the error estimates of the numerical solutions of a class of fourth order linear-quadratic elliptic optimal control problems by using mixed finite element methods. The state and co-state are approximated by the order k Raviart-Thomas mixed finite element spaces and the control variable is approximated by piecewise polynomials of order k (k ≥ 1). L and L-error estimate...

Time optimal control problems for a class of linear multi-input systems are considered. The problems are regularized and the asymptotic and monotone behavior of the regularisation procedure is investigated. For the regularised problems the applicability of semi-smooth Newton methods is verified. First numerical tests are presented which show that the proposed approach, differently from other me...

The paper deals with connections between optimality and passivity-like properties in discrete time. The problem is set in the framework of differential/difference representations of discrete-time dynamics. The Hamilton–Jacobi–Bellman equality associated with a given cost and the corresponding optimal control solution are characterized. On these bases the connection with u-average passivity is c...

Abstract: We consider three closely related problems in optimal control: (1) minimizing the probability of lifetime ruin when the rate of consumption is stochastic and when the individual can invest in a Black-Scholes financial market; (2) minimizing the probability of lifetime ruin when the rate of consumption is constant but the individual can invest in two risky correlated assets; and (3) a ...

In this talk we consider the following optimal control problem (P)  minJ(u) = ∫ Ω L(x, yu(x)) dx+ N 2 ∫ Γ u(x) dσ(x) subject to (yu, u) ∈ (L∞(Ω) ∩H(Ω))× L(Γ), α ≤ u(x) ≤ β for a.e. x ∈ Γ, where Γ is a smooth manifold, yu is the state associated to the control u, given by a solution of the Dirichlet problem { −∆y + a(x, y) = 0 in Ω, y = u on Γ. (1) To solve the problem (P) numerically, it...

O ptimal control problems governed by partial differential equations with state constraints are considered. The state constraints are treated by two types of regularization techniques, namely the Lavrentiev type and the Moreau-Yosida type regularization. For the realization of the numerical solution, a multigrid method is applied to the regularized problems. The main purpose of this research is...

We consider the discretized optimality system of a special class of elliptic optimal control problems and propose an all-at-once multigrid method for solving this discretized system. Under standard assumptions the convergence of the multigrid method and the robustness of the convergence rates with respect to the involved parameter are shown. Numerical experiments are presented for illustrating ...