Hamiltonian Approach to Linear Continuous-Time Singularly Perturbed Optimal Control and Filtering Problems

Exact slow± fast decomposition of a class of non-linear singularly perturbed optimal control problems via invariant manifolds

We study a Hamilton± Jacobi partial di€ erential equation, arising in an optimal control problem for an a ne non-linear singularly perturbed system. This equation is solvable i€ there exists a special invariant manifold of the corresponding Hamiltonian system. We obtain exact slow± fast decomposition of the Hamiltonian system and of the special invariant manifold into slow and fast components....

High Accuracy Techniques for Singularly Perturbed Optimal Control and Filtering Problems

A hybrid method for singularly perturbed delay boundary value problems exhibiting a right boundary layer

The aim of this paper is to present a numerical method for singularly perturbed convection-diffusion problems with a delay. The method is a combination of the asymptotic expansion technique and the reproducing kernel method (RKM). First an asymptotic expansion for the solution of the given singularly perturbed delayed boundary value problem is constructed. Then the reduced regular delayed diffe...

The asymptotic expansion for a class of non-linear singularly perturbed problems with optimal control

In this article, we discuss a class of three-dimensional non-linear singularly perturbed systems with optimal control. Firstly, we confirm the existence of heteroclinic orbits connecting two equilibrium points about their associated systems by necessary conditions of optimal control and functional theory. Secondly, we study the asymptotic solutions of the singularly perturbed optimal control pr...

Control of Singularly Perturbed Markov Chains: a Numerical Study

This work is devoted to numerical studies of nearly optimal controls of systems driven by singularly perturbed Markov chains. Our approach is based on the ideas of hierarchical controls applicable to many large-scale systems. A discrete-time linear quadratic control problem is examined. Its corresponding limit system is derived. The associated asymptotic properties and near optimality are demon...