未知初始跟踪条件的非线性系统预设性能有限时间有界$H_infty$控制

研究一类具有外部扰动的非线性系统在初始跟踪条件未知情况下的预设性能有限时间有界$H_\infty$控制问题.针对预设性能控制设计,提出一个新的误差转换思想,并据此设计新的预设性能函数,解决预设性能控制依赖于系统被约束量初始条件的问题.基于所提出预设性能函数、有限时间控制理论以及有界$H_\infty$的设计方法,获得系统无需初始跟踪条件的预设性能有限时间有界$H_\infty$控制器,同时解决非线性系统在有界稳定情况下难以设计$H_\infty$控制器的问题,保证跟踪误差以预先设定的动态性能在有限时间内收敛至平衡点附近的小邻域内,并对外部干扰有较强的鲁棒性能.

Finite-time bounded-$H_infty$ control with prescribed performance for nonlinear systems with unknown initial tracking conditions

The problem of prescribed performance finite-time bounded-$H_\infty$ tracking control is investigated for a class of nonlinear systems with unknown initial tracking conditions and external disturbances. A new error transformation idea is proposed aiming at the design of prescribed performance control. On this basis, the new prescribed performance functions are designed to solve the problem that the prescribed performance control depends on the initial condition of the constrained variable. By means of the prescribed performance functions, finite-time control theory and bounded-$H_\infty$ design method, a prescribed performance finite-time bounded-$H_\infty$ tracking controller is obtained, which is independent of the initial tracking condition. Meanwhile, the problem that it is difficult to design the $H_\infty$ controller for a nonlinear system with bounded stability is solved. The designed controller ensures that the tracking error converges to a small neighbourhood near the equilibrium point with prespecified dynamic performance within a finite time, and has stronger robustness to external disturbances.