Data-Driven Switched Model Predictive Control Without Terminal Ingredients

Abstract

In this paper, we propose a switched model predictive control scheme based on the data-driven method without any terminal ingredients. Compared with conventional model-based model predictive control schemes, we utilize a series of input-output data to describe the system dynamics according to the behavioral systems theory. In order to improve system performance, multiple cost functions regulated by a suitable switching strategy are considered. For the nominal case with noise-free data, we prove that the proposed data-driven switched MPC schemes can ensure the exponential stability of the system provided that the switching signal satisfies the average dwell-time condition. Moreover, the robust stability is also analysed mathematically for the robust case considering bounded measurement noise. The effectiveness of the control algorithm is verified by the speed control of a commercial high bypass turbofan engine on a hardware-in-loop platform. The results of the experiment show the advantages of the proposed switched model predictive control scheme over conventional non-switched model predictive control schemes. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —In this paper, we consider the problem of designing a control law to improve the performance of the system with multiple requirements that need a tradeoff. Since the performance criteria can easily be formulated in the cost function in model predictive control algorithm, it is a natural thought to design multiple cost functions which can be switched according to different performance requirements. However, the modelling process of the system is usually complicated and time-consuming for conventional model predictive control. In this paper, the data-driven method replaces the counterpart of the model in conventional model predictive control. The input-output measurements of the system can be directly used to forecast the dynamics of the system. The feasibility and stability of the control scheme are analyzed mathematically. We show that the proposed control law can ensure the above closed-loop performance of the controlled system, provided that the parameters of the controller are suitable and the switch of the cost function is sufficiently slow. The effectiveness of the proposed control scheme is demonstrated by the application of a high bypass ratio turbofan engine on a hardware-in-loop experiment platform. The results show that the turbofan engine can achieve a relatively rapid response with smaller overshoot.