一类非线性互联大系统的近似最优扰动抑制

Approximate optimal disturbances rejection for a class of nonlinear interconnected large-scale systems

研究一类受外界扰动非线性互联动态大系统的最优扰动抑制问题。根据有限时域二次型性能指标,提出了一种基于逐次逼近思想的大系统近似最优扰动抑制方法。利用该方法将由原系统得到的高阶耦合的非线性两点边值问题简化为一族解耦的线性两点边值问题序列。证明了该序列的解一致收敛于原非线性互联大系统的最优控制。通过截取最优控制序列的有限次逼近值,可以得到非线性互联大系统近似最优扰动抑制控制律。最后通过数值仿真表明了该方法的有效性。

The optimal disturbances rejection problem for nonlinear interconnected large-scale dynamic systems with external disturbances is considered. A successive approximation approach designing optimal controller is proposed with respect to the finite-domain quadratic performance indexes. By using the approach, a high order, coupling, nonlinear two-point boundary value （TPBV） problem is transformed to a linear decoupling TPBV problem sequence. The fact that the TPBV problem sequence uniformly converges to the optimal control for nonlinear interconnected large-scale systems is proved. An approximate optimal disturbances rejection control law is obtained by intercepting a finite iterative result of optimal control law sequence. Finally, simulation examples show the effectiveness of the presented approach.