Optimal inputs design for a class of parametric linearizable system identification

YANG Ya-jun; ZHENG Yu-xin; LIAO Ying

doi:10.7641/CTA.2016.50506

Abstract：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.