一类非仿射非线性不确定系统自适应鲁棒控制

Adaptive robust control for a class of uncertain non-affine nonlinear system

中文关键词  非仿射非线性系统  动态面控制  Nussbaum函数  自适应控制

英文关键词  non-affine nonlinear system  dynamic surface control (DSC)  Nussbaum function  adaptive control

中文摘要

      针对一类结构和参数均未知且控制方向未知的不确定非仿射非线性系统, 提出了一种鲁棒自适应控制算 法. 基于中值定理将非仿射系统转化为具有线性结构的时变系统, 在此基础上, 利用参数投影估计算法对有界时变 参数进行辨识, 参数辨识误差和外界干扰采用非线性阻尼项进行补偿. 同时将动态面控制(DSC)和反推法相结合, 消除了反推法的计算膨胀问题, 并采用Nussbaum型函数处理系统中方向未知的不确定控制增益函数, 避免了可能 存在的控制器奇异值问题. 最后, 采用解耦反推, 基于李雅普诺夫稳定性定理证明了闭环系统的半全局一致最终有 界. 仿真结果验证了所设计控制方案的可行性与有效性.

英文摘要

      An adaptive robust control law is proposed for a class of uncertain non-affine nonlinear system with unknown structure, parameters and control direction. The non-affine system is first transformed into a time-varying system with a linear structure by using the mean value theory; and then, the bounded time-varying parameters are estimated by adaptive algorithms with projection. The estimation error and external disturbance are compensated by employing nonlinear damping terms. By combining dynamic surface control (DSC) with backstepping technique, and employing Nussbaum gain approach, the designed algorithm eliminates not only the ”complexity explosion” problem inherent to the backstepping method, but also the possible ”controller singularity” problem causing by unknown control direction. Finally, based on Lyapunov stability theorem and decoupled backstepping method, the semi-global stability of the close-loop system is proved. The simulation results demonstrate the feasibility and validity of the proposed control schemes.