Polyhedral functions and multiparametric linear programming
Journal of Optimization Theory and Applications
Introduction to Linear Optimization
Introduction to Linear Optimization
Automatica (Journal of IFAC)
The explicit linear quadratic regulator for constrained systems
Automatica (Journal of IFAC)
Brief An algorithm for multi-parametric quadratic programming and explicit MPC solutions
Automatica (Journal of IFAC)
Computation of the constrained infinite time linear quadratic regulator
Automatica (Journal of IFAC)
Actuator Fault Tolerance in Control Systems with Predictive Constrained Set-Point Optimizers
International Journal of Applied Mathematics and Computer Science - Issues in Fault Diagnosis and Fault Tolerant Control
Automatica (Journal of IFAC)
A distributed simplex algorithm for degenerate linear programs and multi-agent assignments
Automatica (Journal of IFAC)
Hi-index | 22.15 |
Optimal control problems for constrained linear systems with a linear cost can be posed as multiparametric linear programs (mpLPs) 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 mpLP 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 method for computing the optimal solution in an adjacent region, which is very efficient in all cases and reduces to a single simplex pivot for non-degenerate regions. The proposed algorithm is particularly suited for the calculation of the explicit solution to a class of constrained optimal control problems, since it ensures that the control input is everywhere continuous and unique, thereby removing the danger of chattering in problems with linear costs. The algorithm is compared through example to existing proposals and a significant complexity improvement is demonstrated.