Prescribed-Time Tracking With Guaranteed Performance for a Class of Self-Switching Systems Under Unknown Control Directions
研究了一类自切换系统在未知控制方向和非消失不确定性下的预设时间跟踪控制问题，通过时变反馈增益和约束函数确保跟踪误差在规定时间内收敛到零。
This article investigates the problem of prescribed-time tracking control for a class of self-switching systems subject to nonvanishing/nonparametric uncertainties and unknown control directions. Due to the existence of the unknown inherent nonlinear dynamics and the undetectable actuation faults, the resultant control gain of the system becomes unknown and time varying, making the control impact on the system uncertain and the prescribed-time control synthesis nontrivial. The underlying problem becomes further complex as the switching is arbitrary and unknown. To circumvent the aforementioned difficulties, the following major steps are employed. First, by integrating a novel time-varying feedback gain and performance function into the control synthesis, the nonvanishing uncertainties are completely rejected and the transient performance is guaranteed. Second, to facilitate the stability analysis under arbitrarily switching, the concept of the constraining function is introduced and incorporated into a skillfully chosen common Lyapunov function. Third, to deal with the uncertain control gain, a new Nussbaum-related lemma is derived. The proposed control is shown to be capable of ensuring that the tracking error not only evolves within the prescribed bound during all the operation time but also converges to zero at the rate of convergence that can be preassigned as fast as desired, in the presence of self-switching dynamics and unknown control directions. Both theoretical analysis and numerical simulation confirm the effectiveness of the proposed method.