Predictive Control for Unknown Dynamics With Observation Loss: A Temporal Game-Theoretic Approach

This article is concerned with a model-free predictive control problem on systems with unknown dynamics. Different from existing predictive control, the predictive feedback strategy is designed to take control inputs to cover the infinite horizon when the system exists the observation loss. To predict future control inputs, a temporal game-theoretic approach is presented to model such a predictive control issue as an optimization problem and ensure the optimality of the system performance. Moreover, a predictive algebraic Riccati equation (PARE) is constructed to solve such an optimization problem. By leveraging offline datasets and the real-time data of state and input, a data-driven parallel computational framework is developed to iteratively solve the PARE. In this way, the prior knowledge of the systems is avoided and the computational complexity of the proposed algorithm is reduced. Finally, numerical and practical examples are presented to show the applicability of the proposed results.

I. Introduction

The objective of predictive control is to predict the future output of a process based on the current control inputs of the system and historical information. Early studies on predictive control can be dated back to Taken's theorem proposed in 1980 [1], which reconstructed the phase space by integrating the state sequence and generating the data from the delayed sliding time window. The proposed Taken's theorem can predict the next state sequence of an autonomous system and improve the prediction robustness of dynamics. After that, the phase space reconstruction method has been widely applied [2], [3]. At the same time, one natural trend is using the predictive control algorithm to solve optimization problems. Many feasible control approaches have been developed to solve such a problem, the two main types of approaches are model predictive control (MPC) [4] and data-driven predictive control (DPC) [5].