A receding horizon state dependent Riccati equation approach to suboptimal regulation of nonlinear systems

The problem of rendering the origin an asymptotically stable equilibrium point of a nonlinear system while, at the same time, optimising 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_∞, ℋ₂ and L¹) 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. We propose a suboptimal regulator for nonlinear affine systems based upon the combination of receding horizon and state dependent Riccati equation techniques. The main result of the paper shows that this controller is nearly optimal provided that a certain finite horizon problem can be solved online. Additional results include sufficient conditions guaranteeing closed loop stability even in cases where there is not enough computational power available to solve this optimization online, and an analysis of the suboptimality level of the proposed method