Data-Driven Weighted H∞ Control of Persistent Dwell Time Switched Systems With Optimal Disturbance Attenuation Guaranteed

摘要

Persistent dwell-time switched systems (PDTSSs) are being increasingly employed for modeling the dynamics of systems with non-uniform time-dependent switching rules. The existing attempts to design control methods for PDTSSs necessitate a prior knowledge of system dynamics. In this article, we propose a data-driven reinforcement learning (RL) method to solve the weighted <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\mathcal {H}}_{\infty }$ </tex-math></inline-formula> control problem for PDTSSs with completely unknown system dynamics. The proposed method aims to calculate the weighted <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\mathcal {H}}_{\infty }$ </tex-math></inline-formula> control gain for PDTSSs with optimal disturbance attenuation guaranteed by solving a set of linear matrix inequalities related to system data, as opposed to solving it with the exact model information. To ensure the stability of the overall switched system, we establish the criterion for exponential mean-square stability of the closed-loop PDTSSs, as well as analyze the convergence of the proposed data-driven RL algorithm. Finally, the efficacy of the designed algorithms is illustrated via an electric circuit model. Note to Practitioners—First, at a practical level, we consider a more general PDT switching rule that can effectively model the phenomenon of simultaneous fast and slow switching in real systems, which finds wide application in various engineering domains, including capacitor monolithic filters, robot manipulators, and power grids. Then, we aim to address the challenges associated with acquiring accurate system model information and ensuring stable operation with optimal disturbance attenuation performance. On the one hand, the existing <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$ {\mathcal {H}}_{\infty }$ </tex-math></inline-formula> control methods of PDTSSs only guarantee system stability with a prescribed level of disturbance attenuation, and achieving mean-square stability while maintaining an optimal level of disturbance attenuation remains a challenge. On the other hand, existing <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {H} _{\infty }$ </tex-math></inline-formula> control methods incorporate precise system dynamics that are difficult or costly to acquire in practical systems. To tackle the aforementioned challenges, we propose a data-driven weighted <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {H} _{\infty }$ </tex-math></inline-formula> control approach for PDTSSs with unknown system dynamics. This method ensures that the closed-loop PDTSSs exhibit exponential mean-square stability while achieving an optimal disturbance attenuation level. Furthermore, by leveraging RL algorithms, our controller design process only relies on system data rather than precise system dynamics.