非线性时滞系统基于降阶观测器的反步镇定控制

针对一类状态未知的非线性严格反馈时滞系统, 本文提出了一种基于静态增益函数的输出反馈控制方案. 首先构造了降阶观测器以估计非线性系统的未知状态. 然后在Backstepping设计的每一步定义了具有控制增益函数 的新型Lyapunov-Krasovskii泛函以补偿未知时变时滞, 定义新的选择不唯一的连续控制增益函数以补偿非匹配项 以及Lyapunov-Krasovskii泛函补偿时滞时产生的非负项. 提出了一种无记忆输出反馈控制方案. 理论分析表明: 该 控制方案消除了未知时滞的影响, 保证了闭环系统所有信号的有界性, 并使系统实现渐近稳定. 最后仿真结果验证 了此控制方案的有效性.

Reduced-order observer-based backstepping stabilization control for nonlinear time-delay systems

For a class of nonlinear strict-feedback time-delay systems with unknown system states, this paper proposes an output feedback control scheme based on a novel static gain function. Firstly, a reduced-order observer is constructed to estimate the unmeasured states of the nonlinear time-delay system. Then, a new Lyapunov-Krasovskii functional with an explicit control gain expression is defined in each step of the backstepping design process to compensate for the unknown time-varying delays, novel continuous control gain functions are defined to compensate for unmatched terms and the nonnegative terms that are generated when the Lyapunov-Krasovskii function compensates for time delays. A memoryless output feedback control scheme is proposed. It shows that the control scheme eliminates the influence of unknown time delay, ensures the boundedness of all signals of the closed-loop system, and makes the system asymptotically stable. Finally, simulation results verify the effectiveness of the control scheme.