Fuzzy Adaptive Control For Nonlinear Systems Based On Finite Fuzzy Rules

In1965, cybernetics expert L. A. Zadeh proposed the concept of fuzzy sets, subsequently proposed the concepts of groundbreaking fuzzy algorithms, fuzzy systems, linguistic variables, etc. These concepts have created a theoretical foundation for the development of fuzzy control. Fuzzy logic system is a nonlinear function, after universal approximation been proven, fuzzy control based on the experience gradually developed into fuzzy adaptive control based on experience and data, and the fuzzy logic system can be optimally corrected by the construction of adaptive law, which make the control performance of the system more stable.However, in the process of adaptive fuzzy control design, the control system often has limited experience and knowledge given by experts. This means that the fuzzy rules are limited, while the rules may summarize rough or imperfect, so how to use the limited fuzzy rules to achieve the control objective, how to fix and improve these limited fuzzy rule, that become especially important. This article systematically introduces the basics of fuzzy theory (such as:fuzzy sets, fuzzy relations, membership function, fuzzy logic systems and their universal approximation, etc.) and the conventional method of adaptive fuzzy control, which have laid a solid foundation to complete the latter design for a class of nonlinear systems fuzzy adaptive control.Stabilization and tracking control system is one of the most widely used of linear and nonlinear control theory, the former is to make the states of the control system reach the origin, or within a limited area contains the origin; Latter contains the states tracking and tracing output, that is, making the states of the system achieve the desired states and the system output track the reference output. The research on stabilization and tracking control of linear control systems are already quite mature. However, in a nonlinear system, the nonlinear systems with uncertainty and instability, to achieve stabilization and tracking control objectives, the controller design is a complex problem, the theory is still in the development stage. Indeed, despite the controller design in improve performance, interference immunity, robustness, local or global stability and tracking, have achieved some achievements. But due to the complexity of the bottom of nonlinear systems, many problems still exist so far.In this paper, starting from the practical engineering problems, for a class of second-order nonlinear uncertain systems, first introduced Mamdani fuzzy logic system with Gaussian membership function, through the introduction of the Gaussian membership function of time-varying parameter, forming a new fuzzy logic system with time-varying parameter. Then use Lyapunov method, fuzzy adaptive stabilizing controller can be designed, and can guarantee states of the system uniformly ultimately bounded. Finally, the inverted pendulum simulation results show the effectiveness of this method.In addition, in this paper for the chaotic system with unknown nonlinearities, the improved fuzzy logic system with time-varying parameter is used to approach the unknown nonlinearities in the system, and system output tracking controller can be design and analysis combined Lyapunov stability theory, on this foundation, the simulation example of Duffing forced vibration system demonstrate the feasibility and effectiveness of this method.