一类离散非线性系统反步递推黄金分割自适应控制

针对一类含参数不确定的离散时间严反馈非线性系统，提出了反步递推（Backstepping）算法与黄金分割原理相结合的新型控制策略。采用反步递推控制方法处理前n-2阶子系统，利用其结果重构余下的二阶非线性子过程，再通过黄金分割自适应算法对二阶子过程进行控制。该策略一方面解决了单纯反步递推算法在过渡阶段参数失配时，控制量剧烈波动的问题；另一方面减少了反步递推算法的计算量。给出了闭环系统有界稳定性的证明，并通过仿真实例验证了该反步递推黄金分割自适应控制方法的有效性和优越性。

Backstepping Golden-section Adaptive Control Design for a Class of Discrete-time Uncertain Nonlinear Systems

For a class of strict-feedback discrete-time nonlinear systems with uncertain parameters, a novel control approach combined backstepping algorithm and golden-section adaptive control law is presented. It consists of n-2 steps of recursive backstepping procedure to compute all the quantities needed to build a second order auxiliary nonlinear subsystem, which is controlled via golden-section adaptive approach. Its motivation relies on the intent of avoiding the large control-input fluctuate caused by mismatch parameters at initial stage, as well as reducing the computational load of the n-step backstepping design. The bounded stability of closed-loop system is proved. Finally, a typical simulation example is given to demonstrate the efficiency and advantages of the backstepping golden-section adaptive control method.