MIMO仿射型极值搜索系统的输出反馈滑模控制

Output-feedback sliding mode control for MIMO affine extremum seeking systems

针对一类多输入多输出(MIMO)仿射型非线性极值搜索系统的控制问题,提出了一种输出反馈滑模控制方法。将原系统分解为若干个单输入单输出(SISO)极值搜索子系统,并针对每个极值搜索子系统,考虑到系统状态量不可测的特点,以斜坡函数作为新系统输出量的参考跟踪信号,采用输出跟踪误差以及该误差符号函数的积分值建立切换函数,设计得到基于输出反馈的滑模极值搜索控制律。稳定性分析证明:在任意初始条件下,本文方法可使系统的输出量全局收敛至期望极值的任意小邻域内,并且所有状态量均一致范数有界。仿真结果验证了本文方法的有效性。

An output-feedback sliding mode control method is proposed for a class of multi-input multioutput（ MIMO） affine nonlinear extremum seeking systems. Firstly,the original MIMO affine nonlinear extremum seeking system is decomposed into several single-input single-output（ SISO） extremum seeking subsystems. Considering the subsystem＇s states are unmeasurable,the control method uses a simple ramp time function as the reference signal of the subsystem ＇s output,constructs the sliding mode manifold by the output tracking error and the integral of the sign function of the tracking error,and designs the output-feedback extremum seeking control law with sliding mode. The stability analysis shows that the MIMO nonlinear seeking extremum system with the proposed control method is possible to achieve an arbitrarily small neighborhood of the desired optimal point under all initial conditions,and all the states in the closed-loop system remain uniformly bounded. Simulation results are presented to illustrate the effectiveness of the control method.