Duality, singular perturbations and numerical analysis in infinite dimensional linear programming problems related to problems of control of nonlinear dynamical systems
(V Gaitsgory, S Rossomakhine, N Thatcher with V. Borkar and M. Quincampoix)
We propose to develop duality and perturbations theories for infinite dimensional linear programming (IDLP) problems that arise in dealing with nonlinear deterministic and stochastic problems of optimal control. We plan to approximate IDLP problems and their duals by finite dimensional LP problems and their respective duals and use the solutions of the latter for numerical analysis and construction of near optimal feedback controls. The outcomes of the project will be both theoretical results and readily applicable (linear programming based) algorithms for numerical solution of nonlinear control problems that appear in many applications and may present a significant challenge.
Collaborators: Prof V. Borkar, Tata Inst. Of Fundamental research, Mumbai, India, Prof M. Quincampoix (OI), Universite de Bretagne Occidentale, France Mr S. Rossomakhine, Research Associate and PhD student Mr N. Thatcher, PhD student
Funding
ARC- Discovery Project, “Duality, singular perturbations and numerical analysis in infinite dimensional linear programming problems related to problems of control of nonlinear dynamical systems” (2009-2011), Role - Sole CI.