Uniformly stable semidiscrete approximation schemes are desirable for constructing approximate solutions of certain optimal control problems for distributed parameter systems. We discuss construction of uniformly stable spline-based approximation schemes for a scalar delay equation. A method is used which employs an equivalent inner product. Convergence is established via a `hybrid' Trotter-Kat...

An optimal control problem for 2d and 3d Stokes equations is investigated with pointwise control constraints. This paper is concerned with the discretization of the control by piecewise constant functions. The state and the adjoint state are discretized by finite element schemes. In the paper a postprocessing strategy is suggested, which allows for significant improvement of the accuracy.

A numerical method is proposed for constructing an approximation of the Pareto front of nonconvex multi-objective optimal control problems. First, a suitable scalarization technique is employed for the multi-objective optimal control problem. Then by using a grid of scalarization parameter values, i.e., a grid of weights, a sequence of single-objective optimal control problems are solved to obt...

In this paper, we investigate the discretization of general convex optimal control problem using the mixed finite element method. The state and co-state are discretized by the lowest order Raviart-Thomas element and the control is approximated by piecewise constant functions. We derive error estimates for both the control and the state approximation. Moreover, we present the superconvergence an...

A primal-dual interior point method for optimal control problems is considered. The algorithm is directly applied to the infinite dimensional problem. Existence and convergence of the central path are analyzed, and linear convergence of a short step pathfollowing method is established.

In this paper design of low pass optimal block digital filter is compared with traditional low pass overlap-save block digital filter. Simulation results show that global error obtained by optimal method is lower than that obtained by traditional overlap-save method. Index Terms Block digital filters, optimum design, overlap-save method, frobenius norm, aliasing, time-varying system.

For a nonlinear optimal control problem with state constraints, we give conditions under which the optimal control depends Lipschitz continuously in the L2 norm on a parameter. These conditions involve smoothness of the problem data, uniform independence of active constraint gradients, and a coercivity condition for the integral functional. Under these same conditions, we obtain a new nonoptima...

This paper proposes a framework for optimal control of mechanical systems possessing conserved quantities such as control moment gyros (CMGs). It will be shown that output regulation theory is appropriate to handle such constraints and that the center-stable manifold method for solving the associated Hamilton-Jacobi equation is effective for computing the optimal feedback control. With this fra...

A priori estimates on the length of the primal-dual path that results from a MoreauYosida approximation of the feasible set for state constrained optimal control problems are derived. These bounds depend on the regularity of the state and the dimension of the problem. Numerical results indicate that the bounds are indeed sharp and are typically attained in cases where the active set consists of...

In this paper we deal with the derivation of state-realizations of linear operators that are solutions to certain operator linear differential equations in one-dimensional bounded domains. We develop two approaches in the framework of diffusive representations: one with complex diffusive symbols; the other with real diffusive symbols. Then, we illustrate the theories and develop numerical metho...