On September 28, 2018, Dr. Timm Faulwasser from KIT Karlsruhe, Germany, delivered a scientific talk on "Economic NMPC: Turnpike Properties and the Role of Adjoints".
Speaker: Dr. Timm Faulwasser, KIT Karlsruhe, Germany
Title: Economic NMPC: Turnpike Properties and the Role of Adjoints
Date, time, place: September 28, 2018, 10:00, room no. 641 (6th floor, B block)
In recent years, Economic MPC (EMPC) has gained popularity due to the promise of increasing performance by directly optimizing the performance index rather than tracking a given steady state. Moreover, EMPC formulations without terminal cost nor constraints are appealing for the simplicity of implementation. However, the stability and convergence analysis for such formulations is rather involved and so far only practical stability (in discrete time), respectively, practical convergence (in sampled-data continuous time) has been proven; i.e., convergence to a horizon-dependent neighborhood of the optimal steady state.
In this talk, we investigate this problem. We begin by recalling the notion of turnpike properties of optimal control problems. Here, we show that, whenever the cost has a non-zero gradient at the optimal steady-state and the MPC formulation satisfies a regularity assumption, nominal stability to the economic optimum cannot be achieved. We propose to solve this problem by introducing a linear terminal penalty correcting the gradient at steady state. We prove that this simple correction enforces uniform exponential stability of the economically optimal steady state. We illustrate our findings in simulations using several examples.