Monitoring Function Based Adaptive Control For Nonlinear Systems With Unknown Control Direction

With the rapid development of adaptive control technology for nonlinear systems,many fruitful results have been presented in recent years.However,most of the existing results are for the case where the control direction is known.It is sometimes difficult to determine the control direction in practical applications.Therefore,a significant research subject in the field of adaptive control for a long time is how to achieve the control design of nonlinear systems with unknown control direction.As the control direction unknown,there are many methods proposed here,such as Nussbaum function technique,logic switching technology,nonlinear PI control and so on.As one of the methods to deal with the problem of unknown control direction,the monitoring function method has its own advantages(robustness,response speed,overshoot and control design complexity).Herein above mention,the application of monitoring function in solving the problem of unknown control direction is deeply studied in this paper to extend the method to strict feedback nonlinear systems and pure feedback nonlinear systems.The specific contents are shown below:(1)This paper considers the problem of adaptive tracking control for a class of strict-feedback nonlinear systems with unknown control direction.As the control gain is unknown,an adaptive tracking control strategy is proposed by employing the monitoring function to handle the problem of unknown control direction,and combining the backstepping technology and adaptive control technique to solve the trouble of unknown nonlinearities for system.The remarkable characteristic of the presented controller is that no a prior knowledge of system control gain is required,and it assures that all the closedloop signals are uniformly bounded.(2)An adaptive dynamic surface tracking control algorithm is proposed in this paper for a class of strict feedback nonlinear systems with unknown control direction.By referring to the design process of switching mechanism for logic switch technology,the proposed control algorithm simplifies the design steps of monitoring function.Meanwhile,the "complexity expansion" problem caused by the use of backstepping is overcome with the dynamic surface control technology.The designed controller can not only make the tracking error converge to a small neighborhood,but also ensure that all closed-loop signals are uniformly bounded.(3)The adaptive asymptotic tracking control is discussed in this paper for the system with serious uncertainties.Without a prior knowledge of system functions,an adaptive asymptotic tracking control strategy is presented by combining monitoring function and the concept of barrier Lyapunov function.The proposed control strategy further simplifies the process of obtaining the monitoring function,and employs the characteristics of barrier Lyapunov function to make the severe uncertainty of system be a bounded “disturbance-like” term,so as to compensate it adaptively at each step.It can be known that the presented controller not only achieves the tracking error converge to zero asymptotically,but also assures the uniform boundedness of all the closed-loop signals.(4)A new adaptive asymptotic tracking control strategy is presented in this paper for a type of unknown pure-feedback systems.It first employs the median theorem to transform the structure of system,and then designs a monitoring function to deal with the problem of unknown control direction,and uses the characteristics of barrier Lyapunov function to make the other unknown nonlinearities of system be a bounded “disturbancelike” term,finally compensated by the adaptive law at each step.The designed controller realizes the asymptotic tracking control of system on the basis of assuring the boundedness of the closed-loop signals.