Time-Driven Adaptive Control of Switched Systems With Application to Electro-Hydraulic Unit

Abstract

This article focuses on the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> adaptive tracking problem of uncertain switched systems. A key point of the study is to set up a multiple piecewise Lyapunov function framework which provides an effective tool for designing an adaptive switching controller consisting of a state-feedback and time-driven switching signal and a time-driven adaptive law. The proposed switching signal guarantees the solvability of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> adaptive tracking problem for uncertain switched systems. Significantly, it provides plenty of adjusting time for the adaptive tracking control strategy to damp the transient caused by switching and avoids frequent switching. A novel time-driven adaptive switching controller is established such that the tracking error asymptotically converges to zero and all the signals in the error dynamic system are bounded under an achieved disturbance attenuation level. The solvability criterion ensuring an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> adaptive tracking performance is established for the uncertain switched systems, where the solvability of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> adaptive tracking problem for individual subsystems is not required. Finally, the proposed method is applied to the electro-hydraulic unit.

Topics & Concepts