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AUTOMATICA
2007

Lexicographic perturbation for multiparametric linear programming with applications to control

13 years 3 months ago
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...
Colin Neil Jones, Eric C. Kerrigan, Jan M. Maciejo
Added 08 Dec 2010
Updated 08 Dec 2010
Type Journal
Year 2007
Where AUTOMATICA
Authors Colin Neil Jones, Eric C. Kerrigan, Jan M. Maciejowski
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