Multiple-model based predictive control of nonlinear hybrid systems based on global optimization using the Bernstein polynomial approach

In this paper, we propose a Bernstein polynomial based global optimization algorithm for the optimal feedback control of nonlinear hybrid systems using a multiple-model approach. Specifically, we solve at every sampling instant a polynomial mixed-integer nonlinear programming problem arising in the model predictive control strategy. The proposed algorithm uses the Bernstein polynomial form in a branch-and-bound framework, with new ingredients such as branching for integer decision variables and fathoming for each subproblem in the branch-and-bound tree. The performance of the proposed algorithm is tested and compared with existing algorithms on a benchmark three-spherical tank system. The test results show the superior performance of the proposed algorithm.

► Novel Bernstein global optimization algorithm proposed for multiple-model based predictive control of nonlinear hybrid system.
► The algorithm guarantees global optimum to user specified accuracy ϵ for MPC optimization problems solved unlike existing algorithms.
► The benefits of the algorithm, viz., optimal control solution and faster systems response times compared to the existing algorithms is demonstrated on a benchmark three-spherical tank system.