Exact turnpike properties and economic NMPC

Abstract

We discuss the design of sampled-data receding-horizon control schemes for continuous-time systems based on exact turnpike properties. We present sufficient convergence conditions that do not require any kind of terminal constraints or terminal penalties. We prove that, in the presence of state constraints, the existence of an exact turnpike implies recursive feasibility of the optimization. Furthermore, we show that turnpike exactness implies that the performance realized by the receding-horizon controller is equivalent to the infinite-horizon performance. We also state sufficient conditions for the exactness of turnpikes. Finally, we draw upon examples to illustrate our findings.