Robust And Optimal Control Design For Spacecraft Orbital Rendezvous

Spacecraft orbit rendezvous has been well recognized as an important issue in aerospaceengineering. Successful rendezvous is the precondition for many astronautic missions,such as intercepting, repair, rescue, docking, large-scale structure assembling and forma-tion flight. However, the spacecraft orbit rendezvous under the controller obtained byusing the current control system theory often tends not to perform satisfactorily. In fact,sometimes even stability may not be guaranteed. Possible reasons include: Diferencebetween the behavior of the mathematical model being constructed and that of the actualphysical system; and detection errors of the system parameters. Therefore, uncertaintiesare being introduced in the control system. Another important reason is that the detectionerrors on the physical actuator are not fully taken into consideration during the controllerdesign. Consequently, the real plant under the theoretical control signal computed usingcontrol theory can often fail to perform accurately or has poor robustness property. Forthese reasons, diferent control design methods are used in this dissertation to solve somepractical problems to be addressed during spacecraft orbit rendezvous, such as uncertain-ties in the system and the controller, external disturbances to the system, limitations onthe control input, collision avoidance constraint, and optimizing fuel consumption. Themain topics covered in this dissertation are detailed as follows:In Chapter1, a brief introduction to the research background, which includes currentdevelopment and important existing results on spacecraft orbit rendezvous, is provided.On this basis, the main contents and the structure organization of the dissertation aregiven.In Chapter2, robust no-fragile guaranteed cost control problem is proposed, whereuncertainty in the C-W equation and disturbance to the controller are taken into accoun-t. Lyapunov stability theory followed by linear matrix inequality (LMI) method is usedto derive a sufcient condition for the construction of a guaranteed cost control of thespacecraft orbit rendezvous. The sufcient condition is given in terms of LMIs. Theupper bound of the control constraint is considered as an optimization index, resultingin a convex optimization problem with LMI constraints. Thus, a robust and optimal no-fragile guaranteed cost controller can be obtained via solving this constrained convexoptimization problem. With this controller, the spacecraft rendezvous mission can be ac-complished successfully under a small thrust. Numerical examples are given to illustrate the efectiveness of the control design method proposed.Within the framework of the C-W equation, we consider the robust no-fragile H∞control design for a spacecraft orbit rendezvous multi-objective optimization control prob-lem, subject to uncertainty within the system, disturbance to the controller, external dis-turbance and control constraint. Lyapunov stability theory and LMI method are utilizedin Chapter3to derive a sufcient condition, expressed in terms of LMIs, for the existenceof robust no-fragile H∞control for the spacecraft orbit rendezvous. The H∞performanceindex is considered as an optimization index, resulting in a convex optimization problemwith LMI constraints. Thus, the robust and optimal no-fragile H∞controller can be ob-tained via solving this constrained convex optimization problem. With this controller, thespacecraft rendezvous mission can be accomplished successfully in the presence of exter-nal disturbances. Numerical examples are solve, showing the efectiveness of the controldesign method proposed.Based on the results obtained in Chapter2and Chapter3, the robust no-fragile H∞guaranteed cost control problem is further considered in Chapter4for spacecraft orbit ren-dezvous. By using Lyapunov stability theory and LMI method, a sufcient condition isderived for the construction of H∞guaranteed cost control of spacecraft orbit rendezvous,which is in the form of LMIs. The upper bound of the control constraint and H∞perfor-mance index are both taken into consideration, giving rise to a new mixed performanceindex. Thus, a convex optimization problem with LMI constraints is obtained. The robustoptimal no-fragile H∞guaranteed cost controller can be given via solving this constrainedconvex optimization problem. With this optimal controller, the spacecraft rendezvousmission can be accomplished successfully in the presence of external disturbances. Nu-merical examples are given to demonstrate the efectiveness of the control design methodproposed.Chapter5considers a constrained fuel optimal control problem arising from space-craft rendezvous, where a new spacecraft rendezvous model is used, and collision avoid-ance constraint and control constraint are being incorporated. By using the control param-eterization method and a time scaling transformation technique, the constrained optimalcontrol problem is approximated by a sequence of constrained optimal parameter selec-tion problems. Each of these constrained optimal parameter selection problems can beregarded as a constrained optimization problem. Then, an exact penalty function methodis used to transform these constrained optimization problems into a sequence of uncon-strained optimization problems. Furthermore, it is shown that, for a sufciently large penalty parameter value, the local optimal solutions of these approximate unconstrainedoptimization problems converge to the locally optimal solution of the original problem.Finally, the efectiveness of the proposed approach is demonstrated through numericalsimulations.Based on the T-H equation, Chapter6considers a robust H∞control problem arisingfrom spacecraft rendezvous on elliptical orbit. By using periodic Riccati-like paramet-ric method, a sufcient condition for the existence of the robust H∞controller is givenin terms of the periodic Riccati-like diferential equation. A fast multi-shot numericalalgorithm is applied to obtain the solution of a periodic Riccati diferential equation. Itis regarded as the initial value, with which the periodic Riccati-like diferential equationis further solved to design an approximate H∞controller. Under the obtained controller,the spacecraft rendezvous mission can be accomplished successfully in the presence ofexternal disturbances. An illustrative example is provided to show the efectiveness of thecontrol design method proposed.Based on the results obtained in Chapters5and6, the robust optimal control prob-lem arising from spacecraft rendezvous on elliptic orbit is further considered in Chapter7.By using the control parameterization method, the constrained min-max optimal controlproblem is approximated by a sequence of constrained finite dimensional optimal parame-ter selection problems. Furthermore, these constrained finite dimensional optimal param-eter selection problems are transformed into optimization problems with LMI constraints.A numerical example is solved, showing the efectiveness of the method developed.