Low-complexity control of hybrid systems using approximate multi-parametric MILP. (January 2016) - Habibi, Jalal; Moshiri, Behzad; Khaki Sedigh, Ali; Morari, Manfred
Abstract: Control of hybrid systems faces computational complexity as a main challenging problem. To reduce the computational burden, multi-parametric programming has been proposed to obtain the explicit solution of the optimal control problems for some classes of hybrid systems. This strategy provides the solution as a function of the state variables which can be obtained in an off-line fashion. A shortcoming of this technique is that the complexity of the explicit solution is again prohibitive for large problems. The main contribution of this paper is the introduction of an approximation algorithm for solving a general class of multi-parametric mixed-integer linear programming (mp-MILP) problems. The algorithm selects those binary sequences that make significant improvement in the objective function, if considered. It is shown that significant reduction in computational complexity can be achieved by introducing adjustable level of suboptimality. A family of suboptimal controllers is obtained by the proposed approach for which the level of error and complexity can be adjusted by a tuning parameter. It is shown that no part of the parameter space is disregarded during the approximation. Also it is proved that the error in the achieved approximate solutions is a monotonically increasing function of the tuning parameter. Assuming that the closed-loop stability is ensured by including some constraints in the formulation of hybrid control, it will be preserved by the suboptimal low-complexity controllers. Illustrative examples are presented to demonstrate the achieved complexity reduction.