Homotopic approach for turnpike and singularly perturbed optimal control problems

an optimal control approach for arbitrary order singularly perturbed boundary value problems

the aim of this paper is to introduce a new approach for obtaining the numerical solution of singulary perturbed boundary value problems based on an optimal control technique. in the proposed method, first the mentioned equations are converted to an optimal control problem. then, control and state variables are approximated by chebychev series. therefore, the optimal control problem is reduced ...

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

Abstract – In this paper we present a unified approach for optimal control and filtering of linear continuous-time singularly perturbed linear systems that facilitates complete and exact decomposition of optimal control and filtering tasks into pure-slow and pure-fast time scales. The presented methodology eliminates numerical ill-conditioning of the original singularly perturbed problems, intr...

Fem for Singularly Perturbed Problems

We consider the numerical approximation of singularly perturbed elliptic boundary value problems over non-smooth domains. We use a decomposition of the solution that contains a smooth part, a corner layer part and a boundary layer part. Explicit guidelines for choosing mesh-degree combinations are given that yield nite element spaces with robust approximation properties. In particular, we const...

Error Bounds for Control Constrained Singularly Perturbed Linear-quadratic Optimal Control Problems∗

We present a methodology for bounding the error term of an asymptotic solution to a singularly perturbed optimal control (SPOC) problem whose exact solution is known to be computationally intractable. In previous works, reduced or computationally tractable problems that are no longer dependent on the singular perturbation parameter , where represents a small, nonnegative number, have provided a...

High Accuracy Techniques for Singularly Perturbed Optimal Control and Filtering Problems