Double Iterative Algorithm for Heterogeneous Constrained Solution of a Discrete Time Algebraic Riccati Matrix Equation
Niu Ting-tin · Gongcheng shuxue xuebao · 2014
An iterative method is studied to compute the heterogeneous constrained solution of the discrete time algebraic Riccati matrix equation(DTARME) in optimal control system.Firstly, the multivariable DTARME is processed by matrix series. Secondly, Newton's method is applied to find the heterogeneous constrained solution of multivariable DTARME and then we find the heterogeneous constrained solution or heterogeneous constrained least-square solution of the linear matrix equation derived from each step of Newton's method by the modified conjugate gradient method. Finally, a double iterative method is established to find the heterogeneous constrained solution of multivariable DTARME. Multivariable DTARME is only required to have heterogeneous constrained solutions by our double iterative algorithm, and the solution may not be unique.Besides, there are not additional limits to the coefficient matrices of multivariable DTARME. Numerical experiments confirm that the double iterative algorithm is effective.