Research On Adaptive Output Tracking Control For Markovian Jump Nonlinear Systems

Markovian jump systems are a special class of stochastic hybrid systems. These systems have broad applications in various engineering fields, such as chemical process, prower systems, aerocraft systems and marine navigation systems. The control problem of Markovian junp nonlinear systems has been a hot and difficult topic in the present control theory investigation. The jump behavior renders dynamic properties of the systems so complex that the control problem becomes more complex and difficult. For the Markovian jump nonlinear systems with various characters, such as partly unknown transition probabilities, unmodeled dynamics, time-varying delays and input saturation, the output tracking control problem will be focused on in this dissertation. The main contents are as follows:Firstly, the fuzzy dynamic output-feedback control problem for a class of Markovian jump nonlinear systems is investigated. Based on the T-S fuzzy bilinear jump system, a dynamic output-feedback controller is designed. By using Lyapunov stability theory and linear matrix inequalities(LMI) technique, the sufficient conditions on the mean square stability of the close-loop system with partly unknown transition probabilities are presented and proved. In the meantime, the controller gain matrices are given by solving LMIs. A simulation example is given and the results show the effectiveness of the proposed control design method.Secondly, for a class of strick-feedback Markovian jump nonlinear systems with unmodeled dynamics, the adaptive tracking control problem is studied. Based on backstepping design method, utilizing RBF neural networks to approximate the unknown nonlinear functions, and using adaptive method to estimate unknown synthetic parameter, a neural network adaptive tracking controller is designed. Only one parameter is required to be estimated online and computational burden is reduced greatly. It is strictly proved that the resulting closed-loop system is uniformly ultimately bounded in probability. Finally, a simulation example is given to show the effectiveness of the proposed scheme.Thirdly, the prescribed performance adaptive tracking control problem for a class of strick-feedback Markovian jump nonlinear systmes with time-varying delay is studied. By defining a novel state transformation, the prescribed performance control problem is transformed to stabilization problem. Then, utilizing RBF neural networks to approximate the composite unknown nonlinear function, and using adaptive method to estimate unknown synthetic parameters, the corresponding tracking controller is designed with the idea of the backstepping method. An appropriate Lyapunov function is constructed to offset uncertain nonlinear delays, such that the designed controller is independented on state dalays. Based on Lyapunov stability theory, the designed controller is proved to guarantee the boundeness of the closed-loop system with the prescribed performance.Finally, a decentralized anti-windup adaptive tracking control problem with prescribed performance is investigated for Markovian jump uncertain nonlinear interconnected systems. The considered system contains unknown interconnected nonlinear functions, unknown control gains, actuator saturation and Markovian jump signals, and the subsystems are in the form of triangular structure. First, by defining a novel state transformation with the performance function, the prescribed performance control problem is transformed to stabilization problem. Then, introducing an intermediate control signal into the control design, employing neural network to approximate the unknown composite nonlinear function, and based on the framework of the backstepping control design and adaptive control method, a corresponding decentralized anti-windup adaptive tracking controller is designed. It is proved that all the signals in the closed-loop system are uniformly ultimately bounded in probability and both transient and steady-state performance of the tracking errors are preserved. A numerical example is provided to illustrate the effectiveness of the proposed control strategy.