Accelerated Iterative Algorithms For Solving RICCATI Equations In Linear Stochastic Systems

To achieve an industrial system with high performance, a control system which complies with the design goal and has strong anti-interference ability, and good stability should be established. So the design of the controller is the main task of a control system. Since the design of linear quadratic optimal state feedback controller (linear quadratic regulator, LQR) based on the robust control is related to the only stabilizing positive definite solution of Riccati equation, the iterative algorithm for solving the Riccati equation has become a research hotspot of scholars at home and abroad. Based on this research background, we propose different types of iterative algorithms for solving Riccati equation. The specific research contents are as follows:In this dissertation, a sufficient condition is given for the convergence of the algorithm based on accelerated Lyapunov iteration, and the convergence is proved when the initial condition is satisfied. By utilizing the mathematical induction method, the solution sequence is monotonic bounded and approaching to the unique positive-definite stabilizing solution when the convergence factor is in a certain range of values. Meanwhile, we analyze the influence of the convergence factor on the convergence of the accelerated iterative algorithm.For the accelerated Riccati iterative algorithm, the convergence of this algorithm is demonstrated under the zero initial condition. Through employing the comparison principle, a conclusion can be drawn that when the convergence factor is in a certain range, the solution sequence of this algorithm is monotone and bounded, approximating to a unique positive-definite stabilizing solution. Then the effect of the convergent factor is analyzed on the convergence of the accelerated iterative algorithm.With the initialization process, we can obtain the initial conditions of accelerated Lyapunov iterative algorithm and the improved accelerated Lyapunov iterative algorithm. And the initial conditions need to satisfy the iterative precision. In the numerical experiments, the traversal search method is utilized to find out the optimal convergence factors, and further illustrate the relationship between the convergence of algorithms and the values of convergent factors.