控制增益未知的多变量极值搜索系统神经网络自适应协同控制

针对一类控制增益未知的多变量极值搜索系统,提出了一种神经网络自适应协同控制方法.该方法利用协同控制实现状态变量之间的协同收敛,并确保对系统内部参数扰动和外界干扰具有不变性；以极值搜索控制方法得到的搜寻变量作为输入量,设计多层神经网络逼近状态变量的极值变化率和未知的变量与函数；采用Nussbaum函数解决系统控制增益未知的问题；同时运用自适应参数抵消神经网络逼近误差的影响.稳定性分析证明了系统的状态跟踪误差、输出量与其极值之间的误差、极值搜索变量的跟踪误差以及神经网络各参数的估计误差均指数收敛至原点的一个有界邻域.理论分析与仿真结果验证了该方法的有效性.

Neural network adaptive synergetic control for multivariable extremum seeking system with unknown control gain

In the proposed synergetic control, the synergetic convergence of states can be realized, and the invariance against the system parameter variation and external perturbation can also be achieved. By using the search variables from the extremum-seeking control as the inputs, multilayer neural networks (MNN) are applied to approximate the differential of the state extrema as well as unknown parameters and functions. The problem of the unknown control gain is well solved by using Nussbaum gain function. At the same time, an adaptive parameter is adopted to compensate for the influence of MNN approximation errors. The stability analysis shows that tracking errors of states, errors between the output and its extrema, tracking errors of search variables, and estimation errors of MNN parameters, all converge exponentially to a small neighborhood of the origin by appropriately choosing design parameters. Theoretical analysis and simulation results show the effectiveness of the proposed control method.