The quadratic optimal control problem for linear time-delay singularly perturbed systems is investigated via successive approximation approach (SAA) in this paper. Based on singular perturbation theory, the system is decomposed into two subsystems of a slow-time scale and a fast-time scale. The slow-time scale time-delay optimal control problem is transformed first into a sequence of nonhomogen...

The optimal control problem for linear discrete-time, time-varying systems with state dependent noise and quadratic control is considered. The asymptotic behavior of the solution of the related discrete-time Riccati equation is investigated. The existence of an optimal control, under stabilizability and uniform observability (respectively detectability) conditions, for the given quadratic cost ...

We propose a novel Galerkin discretization scheme for stochastic optimal control problems on an indefinite time horizon. The control problems are linear-quadratic in the controls, but possibly nonlinear in the state variables, and the discretization is based on the fact that problems of this kind admit a dual formulation in terms of linear boundary value problems. We show that the discretized l...

In this paper, optimal control problems with pointwise state constraints for linear and semilinear elliptic partial differential equations are studied. The problems are subject to perturbations in the problem data. Lipschitz stability with respect to perturbations of the optimal control and the state and adjoint variables is established initially for linear–quadratic problems. Both the distribu...

A linear-like discrete-time fuzzy controller was designed to control and stabilize a single-pool irrigation canal. Saint Venant equations for open-channel flow were linearized using the Taylor series and a finite-difference approximation of the original nonlinear partial differential equations. Using the linear optimal control theory, a traditional linear quadratic regulator (LQR) was first dev...

Analysis and synthesis for linear systems with parameters that vary according to a set-valued map are investigated. It is shown that the optimal controllers are continuous and homogeneous, but not additive. A computational method based on approximating the nonquadratic cost by a piece-wise quadratic function is developed. Such an approximation determines stability nonconservatively and preserve...