On the design of model predictive controllers based on turnpike properties

In the last two decades the design of nonlinear model predictive control (NMPC) schemes has received widespread attention by theoreticians and practitioners in the field of systems and control. The main reasons for this interest are (a) that NMPC allows considering input and state constraints in a structured manner, and (b) that NMPC allows handling nonlinear systems with multiple inputs. NMPC is built upon the repeated solution of an optimal control problem and the partial application of optimal input trajectories. Often, stability of NMPC schemes is enforced by means of computationally intensive terminal constraints and end penalties. In this talk, we discuss the design of NMPC schemes based on turnpike properties. We show that these properties enable avoiding terminal constraints. We begin the talk with a formal introduction of turnpike properties of optimal control problems. It is worth to be mentioned that the concept of turnpike properties has received widespread attention in optimal control approaches to economic dynamic systems. However, it is surprising that turnpike properties have received only limited attention in the context of NMPC. In this presentation, we present results attempting to partially bridge this gap. We show that exact turnpikes allow establishing stability of NMPC controlled systems as well as recursive feasibility without any terminal constraints. We draw upon examples from different areas such as process control and biology to illustrate our results.