Iterative Solutions Of Riccati Equation In It? Markovian Jump System

The It? differential equation is widely used to describe actual systems with structural mutations and random disturbances.Such systems are called It?-type Markovian Jump systems.Because these systems above can describe the structural mutations and external disturbances in the actual systems,they are of great significance in theory and engineering.When studying the linear quadratic optimal control of the It?-type Markovian jump systems,the coupled Riccati matrix equation plays an important role.Because of the structural nonlinearity of coupled Riccati matrix equations,the solution of this kind of equations is a hot issue.Based on the above research background,this thesis uses iterative techniques to study the solution of a class of coupled Riccati equations related to the It?-type Markovian jump systems.The details are as follows:In order to improve the convergence precision of the iterative algorithm further,the improved Riccati iterative algorithms and the improved Lyapunov iterative algorithms are proposed respectively.Using the latest estimation information and weighting factors,the Riccati iterative algorithm and the Lyapunov iterative algorithm are improved respectively,and the new algorithms are proposed to solve the coupled Riccati matrix equation.Then,under certain initial conditions,the correlation between mathematical inductive method and Riccati and Lyapunov equations is compared.The theorem proves that the matrix sequence generated by the proposed algorithm has monotonicity and boundedness,which is convergence and converges to the unique positive definite solution of the Riccati matrix equation.Finally,numerical simulation is used to find the weighting factor that making the proposed algorithms have the fastest convergence.Compared with the existing algorithms and the proposed two improved algorithms,it is found that the improved algorithms proposed in this thesis converges faster.The application of It?-type Markov jump system model reference tracking control in spacecraft orbit control is studied.The dynamic model of spacecraft relative orbit motion is established.The proposed improved algorithms are used to solve the corresponding Riccati equations.The feedback controller is designed for the spacecraft space hovering task to make the output of the Markov jump system track the given reference model output.The MATLAB simulation experiment proves the effectiveness of the research further in practical application.