Occupational Measures Approach to Long Run Average and Singularly Perturbed Optimal Control Problems
(V Gaitsgory, S Rossomakhine, N Thatcher with V Borkar, L Finlay and I Lebedev)
We propose to develop a new approach to long run average optimal control problems based on the fact that these problems are “asymptotically equivalent” to certain infinite dimensional linear programming problems. The latter can be approximated by readily solvable linear programs of finite dimensions, the solutions of which can be used for a numerical construction of the optimal controls. We also propose to show that this approach is applicable to finding numerical solutions of singularly perturbed optimal control problems. The significance of the proposed research stems from the fact that problems of both types arise in many applications and finding their solutions in a general nonlinear case is a challenge.
Collaborators: Prof V. Borkar, Tata Inst. Of Fundamental research, Mumbai, India Dr Luke Finlay, DSTO (Former PhD student) Dr Ivan Lebedev, WorkCover Corporation of South Australia Mr. S. Rossomakhine, Research Associate and PhD student Mr N. Thatcher, PhD student
Funding
ARC- Discovery Project, “Occupational Measures Approach to Long Run Average and Singularly Perturbed Optimal Control Problems” (2006-2008), Sole CI: Vladimir Gaitsgory
Publications
V. Borkar and V. Gaitsgory, “On Existence of Limit Occupational Measures Ser of a Controlled Stochastic Differential Equation”, SIAM J on Control and Optimization, 44:4 (2005/2006), pp. 1436-1473.
V. Gaitsgory and S. Rossomakhine, “Linear Programming Approach to Deterministic Long Run Average Problems of Optimal Control”, SIAM J. on Control and Optimization, 44:6 (2005/2006), pp. 2006-2037.
V. Gaitsgory, “Averaging and Near Viability of Singularly Perturbed Control Systems”, Journal of Convex Analysis, 13:2(2006), pp. 329-352
L. Finlay, V. Gaitsgory, and I. Lebedev, “Linear Programming Solutions of Periodic Optimization Problems: Approximation of the Optimal Control”, Journal of Industrial and Management Optimization, 3:2(2007), pp. 399 – 413.
V. Borkar and V. Gaitsgory, Singular Perturbations in Ergodic Control of Diffusions“”, SIAM J on Control and Optimization, 46:5 (2007), pp. 1562-1577 6.
V. Borkar and V. Gaitsgory, “Averaging of Singularly Perturbed Controlled Stochastic Differential Equations”, Applied Mathematics and Optimization, 56(2007), pp 169-209. 7.
L. Finlay, V. Gaitsgory, and I. Lebedev, “Duality in Linear programming Problems Related to deterministic Long Run Average Problems of Optimal Control”, SIAM J on Control and Optimization, 47:4 (2008), pp. 1667-1700