一类参数线性系统辨识的最优输入设计

Optimal inputs design for a class of parametric linearizable system identification

对未知参数进行估计时,得到的结果与激励系统所选用的输入信号有较大的关系.针对一类参数可线性化系统,本文提出了一种利用多维同步正交信号和直接配点法设计最优输入信号的方法.首先根据最小二乘原理,利用法矩阵构造Mayer型性能指标函数.然后利用不同频率的正弦基函数构造相互正交的多维输入,通过添加幅值与相位的等式约束,使得输入信号在初/末时刻取值均为零.之后采用直接配点法离散状态变量,将动态的最优输入问题转化为静态的非线性规划问题.最后采用从可行解到优化解的串行优化策略进行求解,不仅提高了寻优效率,还确保了优化结果为原问题的可行解.仿真结果表明,与工程上常用的输入信号相比,本文方法获取的最优输入信号可以提高参数估计精度并加快收敛速率.

The selection of input signals for system excitation plays an important role to the result when one estimates the unknown parameters. Motivated by the direct collocation method, a general optimal input design approach based on the multiple simultaneous orthogonal inputs is proposed for parametric linearizable systems in this paper. First, according to the least square principle, the cost function is constructed as so-called Mayer form by using the normal matrix. Then, to design multiple simultaneous orthogonal inputs, each input is assigned based on the sum of sinusoid with a unique frequency, an equality constraint condition between amplitudes and phases are presented to make the input signals are zeros at initial and terminal time. Third, the system states are parameterized based on direct collocation method, therefore the original dynamic inputs optimization problem is converted into a static nonlinear programming problem. Finally, the optimization problem is solved by using the sequential minimal optimization strategy; it can be ensure that the solution is feasible for the original problem and convergence rate in optimal-searching is improved greatly. Simulation result show that, by comparing with 3211 and doublet inputs, the optimal inputs which is synthesized by proposed approach can improve the convergence rate and estimation accuracy of system identification.