Research On Adaptive Fuzzy Control Algorithm Of Nonlinear Systems

In many practical cases, it is very difficult that nonlinear systems are described by known functions accurately. Uncertainties are inevitable in dynamical systems such as errors in system modeling, unknown physical phenomena (e.g., frictions in a mechanical system), and affect of working environments etc. Fuzzy systems or neural networks techniques are esPecially efficacious approaches for transacting uncertainty because it has been demonstrated that they can uniformly approximate an arbitrary continuous function to a given accuracy. Although significant progress has been made in adaptive control of nonlinear systems, there are still some problems that need to be solved for practical implementations. Therefore several adaptive control algorithms are proposed in the doctoral dissertation for some problems at present stage. The main research works are stated as follows:An adaptive robust fuzzy control algorithm is presented for uncertain SISO nonlinear systems satisfying matching conditions. The system's state is estimated by designing an observer. Therefore, the assumption that the system's state is full observable is not necessary. In this algorithm the key assumptions are that the norm of the difference (between optimal approximation parameter vector and nominal parameter vector) and the approximation error are bounded by the unknown bounds. The presented algorithm reduces the online computation quantity and improves robustness of the systems by tuning only estimations of the unknown bounds online. It is proved that the proposed adaptive robust fuzzy control algorithm can guarantee uniform boundedness of all the signals in the closed-loop system and the estimation of tracking error is proven to converge to a small neighborhood of the origin. Effectiveness is illustrated by simulation results of applying the proposed algorithm to a dc motor connected to a gearbox. At the same time, a stable adaptive control scheme is also presented for uncertain MIMO systems satisfying matching conditions with the external disturbances. The distinct property of the MIMO systems is that it is not need to assume that the disturbance coefficients are known constants. The presented scheme guarantees that H_∞tracking performance is achieved.Based on Backstepping method, two stable adaptive control approaches are developed for a class of uncertain SISO strict-feedback nonlinear systems. Using the RBF neural network approximator, the main assumption of the first approach is that the minimal approximation errors satisfy certain bounding conditions. By a special design scheme, the controller singularity problem is avoided perfectly. The developed scheme improves the control performance of the closed-loop system and extends the application scope of nonlinear systems. On the basis of the first approach and using the fuzzy approximator, the second approach alleviates the computation burden online by adjusting the estimations of bounds of the norms on the approximation parameter vectors. The two control approaches verify that all the signals of the closed-loop system are uniformly bounded and the tracking error converges to a small neighborhood of zero by suitably choosing the design parameter.It is common knowledge that the pure-feedback systems are much more generalized and complicated compared with strict-feedback systems and systems in match conditions. An adaptive fuzzy control approach is developed to stabilize a class of uncertain MIMO pure-feedback systems using Lyapunov stability analysis method. This approach relaxes restriction condition of the system model in the existing literatures. Based on backstepping method, fuzzy systems are used to approximate unknown functions of each subsystem. Designed robust control terms are utilized to compensate the approximation error vectors in the control input. The developed control approach achieves that all the signals in the closed-loop system are bounded and the norm of the tracking error vector converges to an arbitrarily small neighborhood around zero by suitably choosing the design parameters.Controlling nonaffine nonlinear systems is a challenging problem in control theory community. Two adaptive fuzzy control schemes are developed for two classes of different structure nonlinear nonaffine systems. It is difficult and complicated to control such classes of systems due to the existence of unknown nonaffine functions and the couplings among the subsystems. This difficulty is overcome by constructing some special type Lyapunov functions and taking advantage of the mean-value theorem, the backstepping design method and the approximation property of the fuzzy systems and introducing Nussbaum-type functions. The developed control schemes can guarantee that all the signals in the closed-loop system are bounded. Simulation experiments are utilized to verify the feasibility of the developed approaches.