A Time-Delay Modeling Approach for Data-Driven Predictive Control of Continuous-Time Systems

Abstract

This paper aims to predict future optimal control inputs for unknown continuous-time linear systems. In contrast to most existing approaches that generate control input without observation loss, the proposed control scheme analyzes causality between observation and sequence feedback from the time-delay series model, allowing for the existence of observation loss. These time-delay series can be viewed as multiplayer games over a temporal scale, then a temporal game-theoretic approach ensures system stability and performance. By integrating the Bellman principle, a data-driven adaptive dynamic programming algorithm is proposed to avoid system knowledge. Furthermore, the designed parallel data-driven predictive algorithm reduces the computational complexity. Finally, the applicability and effectiveness of the methodology are demonstrated through numerical simulations and practical experiments. Note to Practitioners—This paper mainly concerns the predictive control of unknown continuous systems, which suffer from unknown dynamics and state observation loss. The proposed methods are suitable for weak information feedback and dynamically changing scenarios, such as autonomous driving in low visibility scenarios and endoscopic surgical robots. Most of the current processing methods are model-driven, which makes them unsuitable for unknown system dynamics changes. To address this issue, we propose a time-delay switched strategy for control prediction with stability and optimality guarantees. The practical application can be divided into three parts: i) Data collection: Collect historical multi-intervals accumulated inputs and outputs data, the amount of data should reach the requirement of the full rank of the data matrix; ii) Iterative learning: the optimal control strategy is learned from the historical data through an adaptive dynamic programming method; iii) Deployment: Control intervals are extended through temporal time-delay feedback on historical state trajectory, and length trigger conditions will switch these feedbacks logically for actuators. Finally, the Quanser QBot 2e robot is used as a demonstration example.