Direct Design of a Polynomial Model Predictive Controller

摘要

Suboptimal design of a model predictive controller is considered with a piecewise polynomial defined on a given partition of the state space. The motivation is that the optimal controller is piecewise affine and its computation requires computational geometric methods, which are difficult to apply when the plant is of high order and/or when its piecewise structure is nearly degenerate. The proposed approach can avoid geometric computation by using a regular partition and the sum-of-squares method. It is more flexible than the existing suboptimal approach with a regularly partitioned piecewise affine controller. It is also direct in that it does not need the computation of the optimal controller and is carried out with minimization of the distance to optimality. The asymptotic optimality of the proposed approach is discussed together with the stability of the resulting closed-loop system.