Testing of linear models for optimal control of second-order dynamical system based on model-reality differences

Abstract

In this paper, the testing of linear models with different parameter values is conducted for solving the optimal control problem of a second-order dynamical system. The purpose of this testing is to provide the solution with the same structure but different parameter values in the model used. For doing so, the adjusted parameters are added to each model in order to measure the differences between the model used and the plant dynamics. On this basis, an expanded optimal control problem, which combines system optimization and parameter estimation, is introduced. Then, the Hamiltonian function is defined and a set of the necessary conditions is derived. Consequently, a modified model-based optimal control problem has resulted. Follow from this, an equivalent optimization problem without constraints is formulated. During the calculation procedure, the conjugate gradient algorithm is employed to solve the optimization problem, in turn, to update the adjusted parameters repeatedly for obtaining the optimal solution of the model used. Within a given tolerance, the iterative solution of the model used approximates the correct optimal solution of the original linear optimal control problem despite model-reality differences. The results obtained show the applicability of models with the same structures and different parameter values for solving the original linear optimal control problem. In conclusion, the efficiency of the approach proposed is highly verified.