In this work linear-quadratic optimal control problems for parabolic equations with control and state constraints are considered. Utilizing a Lavrentiev regularization we obtain a linear-quadratic optimal control problem with mixed controlstate constraints. For the numerical solution a Galerkin discretization is applied utilizing proper orthogonal decomposition (POD). Based on a perturbation me...

We study a class of time–domain decomposition based methods for the solution of distributed linear quadratic optimal control problems. Our methods are based on a multiple shooting reformulation of the distributed linear quadratic optimal control problem as a discrete–time optimal control (DTOC) problem in Hilbert space. The optimality conditions for this DTOC problem lead to a linear system wit...

In this paper we study the solution to optimal control problems for constrained discrete-time linear hybrid systems based on quadratic or linear performance criteria. The aim of the paper it twofold. First we give basic theoretical results on the structure of the optimal state feedback solution and of the value function. Second we describe how the state feedback optimal control law can be effic...

The numerical treatment of the linear-quadratic optimal control problem requires the solution of Riccati equations. In particular, the differential Riccati equations (DRE) is a key operation for the computation of the optimal control in the finite-time horizon case. In this work, we focus on large-scale problems governed by partial differential equations (PDEs) where, in order to apply a feedba...

In this paper the quasilinearization technique along with the Chebyshev polynomials of the first type are used to solve the nonlinear-quadratic optimal control problem with terminal state constraints. The quasilinearization is used to convert the nonlinear quadratic optimal control problem into sequence of linear quadratic optimal control problems. Then by approximating the state and control va...

The use of piecewise quadratic cost functions is extended from stability analysis of piecewise linear systems to performance analysis and optimal control. Lower bounds on the optimal control cost are obtained by semi-definite programming based on the Bellman inequality. This also gives an approximation to the optimal control law. An upper bound to the optimal cost is obtained by another convex ...

The state space approach to the synthesis of a class of discrete linear control systems is given. Both time-optimal and quadratic-cost problems are considered and a comparison to classical methods is made via the technique of pole assignment.