非仿射纯反馈不确定系统预设性能鲁棒自适应控制

摘要

针对一类结构和参数及控制方向均未知的非仿射纯反馈非线性不确定系统,提出了一种保预设性能鲁棒自适应控制方案.首先引入性能函数和误差转换函数,通过误差转换将原始的输出误差存在性能约束的受限系统转换为等价的非受限系统;其次,基于中值定理将非仿射型系统转化为具有线性结构形式的时变系统,并同时利用自适应投影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技术项进行补偿;随后综合运用反演技术和Nussbaum函数设计控制器并进行稳定性分析.所设计的控制器不仅能够保证闭环系统所有信号有界且输出误差满足预设的瞬态及稳态性能要求;最后,仿真结果验证了所设计控制方案的可行性与有效性.%A prescribed performance adaptive robust control law is proposed for a class of uncertain non-affine nonlinear system with unknown structures,parameters and control directions.Firstly,performance function and an output error transformation function are introduced to transform the original "constrained" system into an equivalent "unconstrained" one.Subsequently,the non-affine system was transformed into a time-varying system with a linear structure by using the mean value theorem.At the same time,the bounded time varying parameters are estimated by adaptive algorithms with projection,and the estimation error and external disturbance were compensated by employing nonlinear damping technique.Then,Nussbaum function and backstepping technique were combined to design the controller and the system stability was analyzed.The controller guarantees that all closed-loop signals are bounded and the prescribed transient and steady-state performance are satisfied.Finally,the simulation results demonstrate the feasibility and validity of the proposed control schemes.