Adaptive Tracking Control For Several Classes Of Nonlinear Uncertain Systems

Dynamical systems are one of the important tools for the human to understand the development and evolution laws of various phenomena in nature.It is usually difficult to model real phenomena by using dynamical systems,especially when the evolution laws of real phenomena or processes are not well understood.Therefore,the proposed model cannot fully characterize the phenomenon itself and its environment,which is usually manifested as uncertainty in the form of parameters or functions and external disturbances in the systems,and thus it brings great difficulties to the control of systems.Fortunately,adaptive control technology can estimate and suppress the influence of system uncertainty on the premise of ensuring control performance,so the adaptive control problem of nonlinear uncertain systems has gradually become a research hotspot.In addition,because the fractional-order derivative is very suitable for describing the heredity and memory of many processes and materials,a large number of natural phenomena or artificial systems have been modeled by fractional-order differential equations in recent years.To make the dynamic behavior of the system meet the actual needs,the control problem of fractional-order systems has also become a central issue concerned by researchers.Based on the above discussions,this thesis first studies the adaptive neural networks control of integer-order nonlinear uncertain systems with state constraints and input delays,and then considers the adaptive control problem of Markovian jump nonlinear systems.Furthermore,the processing method for integer-order unmodeled dynamics is extended to the fractional-order case,and the adaptive control problem of fractionalorder nonlinear systems with unmodeled dynamical disturbances is studied.Finally,by considering more general incommensurate fractional-order nonlinear systems,the eventtriggered and practical finite-time adaptive control problems are studied,respectively.The specific research contents and main contributions of this thesis are summarized as follows:(1)The problem of adaptive neural networks control for nonlinear uncertain systems with asymmetric time-varying state constraints and time-varying input delay is studied.The unknown state-dependent external disturbance is considered in the system,and its upper bound is assumed to be a function of the state variable rather than a constant.Besides,the radial basis function neural networks are used to approximate the unknown functions,in which only the norms of the neural networks weight vector are estimated,and thus the online computational burden is significantly reduced.When dealing with time-varying input delays,an auxiliary function is introduced to weaken the conditions of time-varying delay.Then,by constructing asymmetric barrier Lyapunov function,adaptive neural networks controllers are designed,which not only makes the system output have good tracking performance,but also ensures that the state variables will not violate the asymmetric time-varying state constraints.Finally,numerical examples are given to verify the effectiveness of the designed controllers.(2)The adaptive neural networks control problem for Markovian jump nonlinear systems with partial mode information and input saturation is studied.The existing adaptive controllers for Markovian jump systems are only applicable to the case where the mode information of system is completely known,but in practice,the mode information of system is usually not completely known.For this reason,the concept of partial mode information of Markovian chain is embedded into the framework of adaptive backstepping control method,so that a mode detector can correctly detect the system mode with probability.Thus,state observer and adaptive controllers that only rely on the detected mode are designed,which provides an avenue to the control problem of Markovian jump systems with incomplete mode information.In addition,an auxiliary signal is introduced into the Markovian jump systems to compensate for the effect of input saturation,which makes the form of proposed controllers more concise than that in existing literature.Finally,some numerical examples are given to verify the effectiveness of the proposed controllers.(3)The issue of event-triggered adaptive neural networks control is studied for fractional-order nonlinear systems with unmodeled dynamics and input saturation.Firstly,to avoid the state variables of unmodeled dynamics directly appearing in the controllers,the concept of exponential input-to-state practical stability for integer-order unmodeled dynamics and related properties are extended to the fractional-order case.Then,based on the traditional event-triggered mechanism,an adaptive event-triggered mechanism is proposed,in which the threshold parameter can be dynamically adjusted with the tracking performance,and the triggered times are further reduced.In addition,different from the previous works where the derivative of hyperbolic tangent function tanh(·)needs to have a positive lower bound,in this thesis,a new type of auxiliary signal generated by fractional-order filtering is proposed to handle the impact of input saturation.Based on these,event-triggered adaptive neural networks controllers are designed.Finally,the proposed controllers are verified by numerical simulations and compared with the results in related literature.(4)The event-triggered and practical finite-time adaptive control problems of incommensurate fractional-order nonlinear systems are studied.For the event-triggered adaptive control problem of incommensurate fractional-order systems,the continuity of fractional-order derivative with respect to the order is applied to avoid the frequency distribution model and the assumption of the disturbance-like function used in the literature.To further reduce the communication burden,the exponential convergence term is introduced into the traditional dynamic event-triggered mechanism.On this foundation,by utilizing the backstepping control method,an event-triggered adaptive controller is designed to ensure the tracking performance of the system output,in which the derivative order of the parameter adaptive laws does not depend on the derivative order of the system and thus can be flexibly selected.For the practical finite-time adaptive control problem of incommensurate fractional-order systems,the practical finite-time stability criterion for fractional-order systems is established by using the one for integer-order systems,which provides a way to deal with the problem of practical finite-time adaptive control for incommensurate fractional-order systems.Based on the established criterion and the properties of fractional-order calculus,a practical finite-time adaptive controller is designed.Different from the results in the literature,the control signal here is generated by some fractional-order filters,which can relatively reduce the fluctuation range of control input(especially near the initial time).In addition,a compensation signal is introduced in the processes of controller design,which can not only compensate for the deviation caused by the filters of the control input but also simplify the processes of controller design and stability analysis of the controlled system.Finally,some numerical examples are given to verify the effectiveness of the proposed controllers.