Model Reference Tracking Control For Markov Jump Systems And Its Application In Spacecraft Orbit Control

Model reference tracking control is an important research topic in control field, while it has extensive applications in many practical engineering problems. Spacecraft orbital control of the many practical problems can be attributed to model reference output tracking problem for Markov jump systems. In this paper, the traditional model reference tracking control of linear time-invariant systems is extended to jump systems, and a complete parametric algorithm is proposed to solve this kind of problem, then its applications in several typical spacecraft orbital control are provided. The proposed approach brings some new ideas for solving spacecraft orbital control problem. The main results are as follows:A parametric approach is established to solve the model reference tracking problem for Markov jump systems. Firstly, the general form of the model reference output tracking controller is given, as well as the existence condition and its proof. Then, two approaches are established to design the feedback stabilizing controller: one is a Linear Matrix Inequation approach with maximum input constraint, the other is an iterative algorithm for optimal feedback controller with minimum energy consumption indicator.Finally, the problem of solving the model reference tracking controller is transformed into the problem of solving the inhomogeneous generalized Sylvester equations. Referring to a complete parametric solution of the generalized Sylvester equations, a general complete parametric expression for the controller is presented. The proposed parametric expression is succinct, and the approach is very convenient for programming. The free parameter matrices contained in the complete parametric solution brings extra degree of freedom for controller design, which can be used to cope with some additional performance optimization.A general approach to solve the spacecraft orbital control problem with stochastic thruster fault is established. Clohessy–Wiltshire equations with Markov jump parameters are given as a mathematical description of the orbital maneuvering problem, and the maneuvering problem is boiled down to a model reference output tracking control problem for Markov jump systems. For two orbital maneuvering tasks, hovering and flying around, with stochastic actuator faults, design the appropriate reference models respectively. Then the proposed parametric approach is used for obtaining the controller, and a numerical simulation by Matlab is given. The simulation results show that: Under the condition of stochastic thruster fault, the controlled system can also track the reference signal rapidly and smoothly, and satisfy the performance requirement of maximum thrust constraints and other indicators.Model reference output tracking approach for Markov jump systems is given in the application of the spacecraft anti-interception orbital maneuvering control. Considering that spacecraft along its fixed trajectory will easily be tracked and intercepted, a general approach based on jump control input is proposed for the spacecraft anti-interception model-reference tracking control problem. The problem is formulated as a model reference output tracking control problem for Markov jump systems, and the mathematical description of the spacecraft tracking problem with random switching control is put forward. The existence condition of the controller is given, and then a general complete parametric approach for the controller is established. Finally, a numerical simulation is presented to illustrate the e?ectiveness of the proposed approach.