一类MIMO非线性系统的L_2增益干扰抑制方法

L_2 gain disturbance attenuation for a class of MIMO nonlinear systems

针对一类带有干扰的多输入多输出(MIMO)非线性系统的鲁棒非线性控制问题,提出一种以增益为指标的干扰抑制协调控制方法.将原MIMO非线性系统分为两个多维子系统,首先构造第一个子系统的严格耗散不等式,然后递推得到全系统的严格耗散不等式,在递推过程中,同时构造了实现干扰抑制和镇定控制的协调控制律,可以抑制干扰对系统稳定性的影响.所用的递推方法避免了求解HJI不等式.最后利用一个简单的MIMO非线性系统为例,验证该方法的有效性.

To overcome the robust nonlinear control problem for a class of multi-input multi-output (MIMO) nonlinear systems with disturbances, a disturbance attenuation method in the sense of L2 gain was presented. After dividing the plant system into two multi-dimension sub-systems, the strictly dissipative inequality for the first sub-system was constructed, then the strictly dissipative inequality for the whole system was deduced through recursive method. In the recursive process, the coordinated control laws, which can realize disturbance attenuation with stabilization were derived. The recursive method avoids solving Hamilton-Jacobi-Isaacs (HJI) inequality. Lastly, a simple MIMO nonlinear system with disturbances is used to assess the effectiveness of the proposed method.