一类非线性系统的广义预测控制研究

针对一类难以线性化的单输入单输出非线性离散系统，就其实际输出信号跟踪参考输出信号的控制问题，研究了它的广义预测控制律设计方法。在系统数学模型非线性项的系数多项式满足一定条件的情况下，通过适当的数学处理，使问题的本质归结为求解线性差分系统的一组Diophantine方程，从而解出了非线性系统广义预测控制律表达式中的各个系数多项式，并给出了广义预测控制律的具体解析形式。通过仿真实例验证了所提出设计方法的正确性和有效性。

Research on Generalized Predictive Control for a Class of Nonlinear Systems

Generalized predictive control is discussed for a class of single input single output nonlinear discrete systems which are difficult to linearize. The aim of the control is to make the real output signal of the system track the referenced one. The problem is transformed into solving a set of Diophantine equations via appropriate mathematical treatment, when the coefficient polynomials of the nonlinear terms satisfy certain conditions. Thus, all the coefficient polynomials of the generalized predictive control law are solved. The analytic expression of the generalized predictive control law is deduced. A simulation example demonstrates the correctness and the effectiveness of the design method presented above.