Model Predictive Control of Nonlinear Parameter Varying Systems via Receding Horizon Control Lyapunov Functions.

摘要

The problem of rendering the origin an asymptotically stable equilibrium point of a nonlinear system while, at the same time, optimizing some measure of performance has been the object of much attention in the past few years. in contrast to the case of linear systems where several optimal synthesis techniques such as H infinity, H2 and l(exp 1) are well established, their nonlinear counterparts are just starting to emerge. Moreover, in most cases these tools lead to partial differential equations that are difficult to solve. In this chapter we propose a suboptimal regulator for nonlinear parameter varying, control affine systems based upon the combination of model predictive and control Lyapunov function techniques. The main result of the chapter shows that this controller is nearly optimal provided that a certain finite horizon problem can be solved on-line. Additional results include: (a) sufficient conditions guaranteeing closed loop stability even in cases where there is not enough computational power available to solve this optimization on-line; and (b) an analysis of the suboptimality level of the proposed method.