Lexicographic perturbation for multiparametric linear programming with applications to control

Optimal control problems for constrained linear systems with a linear cost can be posed as multiparametric linear programs with a parameter in the cost, or equivalently the right-hand side of the constraints, and solved explicitly offline. Degeneracy occurs when the control input, or optimiser, is non-unique, which can cause chattering of the control input and overlap of the polyhedral regions of the explicit solution. This paper introduces a new and efficient approach to the computation of the solution to a degenerate multiparametric linear program with the parameter in the cost. Rather than solve the degenerate problem directly, we solve a lexicographically (symbolically) perturbed version of it that is guaranteed to be non-degenerate. We show that every optimal solution of the perturbed problem is an optimal solution to the original and that the perturbed solution is continuous, unique and defined over a set of non-overlapping polyhedral regions. Furthermore, we introduce a new me...

• Type: Journal
• Year: 2007
• Where: AUTOMATICA
• Authors: Colin Neil Jones, Eric C. Kerrigan, Jan M. Maciejowski
• Keywords: AUTOMATICA 2007, Multiparametric Linear Program, Optimal Control Problems, Solution