Event-triggered Control And Learning For Strict-feedback Nonlinear Systems Under Different Constraints

Many practical systems can be modeled as strict-feedback systems,such as robot manipulators,chemical reaction systems,unmanned surface vehicles,etc.These systems are usually highly nonlinear and uncertain,so it is difficult to establish accurate mathematical models for them.Fortunately,adaptive neural control technology and deterministic learning theory provide an effective way to solve the control problem of such uncertain nonlinear systems.Furthermore,due to the physical limitations of system hardware,the influence of external environment or to meet some special performance indicators,most practical systems need to satisfy different constraints during the operation.For example,the state and tracking error of the system usually need to operate within a specific region.Transgression of those constraints may decrease control performance,and even cause safety accidents.However,the introduction of different constraints will bring great challenges to the controller design and stability analysis of the system.On the other hand,with the rapid development of networked control technology,more and more control systems are transmitting data through communication networks.The traditional time-triggered control method requires periodic data transmission,which inevitably leads to a large amount of redundant data transmission and can easily cause communication congestion in a network environment with limited bandwidth,thus affecting the system control performance.Event-triggered control strategy transmits data in an aperiodic manner,which can effectively save network resources and has received widespread attention.Therefore,the study of eventtriggered control and learning for strict-feedback nonlinear systems under different constraints has important theoretical significance and practical application value.In view of this,combined with barrier Lyapunov function,nonlinear transformed function,finite-time performance function,adaptive neural control technology and deterministic learning theory,this thesis studies the event-triggered control and learning problems for strict-feedback nonlinear systems under two different constraints,including state constraints and prescribed performance constraints.The main contents and innovations are shown as follows:1)The problem of event-triggered control is investigated for strict-feedback nonlinear systems with time-varying full state constraints based on the barrier Lyapunov function.Firstly,in order to remove the existing restrictions on a high power of barrier Lyapunov function and high-order differentiability of virtual controllers in traditional control schemes,a simple backstepping control framework is proposed based on a first-order sliding mode differentiator.Furthermore,the problem of time-varying full state constraints is solved by utilizing the lower-order barrier Lyapunov function,which simplifies the controller design and stability analysis process.Subsequently,an adaptive parameter updating law is designed to estimate the upper bound of the actual control gain function of the system.Then,the difficulty of compensating event-triggered measurement error caused by unknown control direction is effectively tackled by the combination of the Nussbaum function and such an adaptive parameter updating law.Finally,an event-triggered adaptive neural tracking control scheme is developed,which can not only ensure that the system output tracks the given reference signal well,but also ensure that the system states satisfy the prescribed state constraints,while greatly reducing the communication burden.2)The problem of event-triggered control is investigated for strict-feedback nonlinear systems with time-varying full state constraints based on the nonlinear transformed function.Firstly,to deal with the time-varying full state constraints problem,a novel nonlinear transformed function is designed,which converts the original state constraints problem into the stabilization problem of an unconstrained new system.Subsequently,an effectively event-triggered adaptive neural control scheme is proposed by combining the backstepping method,Nussbaum function and radial basis function neural network(NN).The proposed control scheme can not only tackle both situations with and without state constraints uniformly without redesigning the controller and readjusting the control parameters,but also save the network resources significantly.Finally,the developed state constrained control scheme is compared with some state constrained control schemes in the existing literature.Comparison results show that the developed state constrained control scheme can deal with more types of state constraint problems.3)The problem of event-triggered control is investigated for strict-feedback nonlinear systems with time-varying full state constraints based on the deterministic learning theory.Firstly,to simplify the recurrent verification process of NN input signals,an effective signal regression lemma is given.Then,a NN weight updating law is designed based on the state estimation error,which is beneficial to improve the learning ability of NNs.Subsequently,in the case of sufficient network resources,an adaptive neural control scheme is proposed,which ensures that the system output can well track the given recurrent reference signal.In the steadystate control process,with the aid of the presented signal regression lemma and the system state equation,all the NN input signals are verified to be recurrent,thereby ensuring the exponential convergence of the NN estimated weights.Furthermore,the converged NN estimated weights are stored as the experienced knowledge,which can accurately model the unknown system dynamics.Finally,considering the case of limited network resources,an event-triggered neural learning control scheme is designed by utilizing the stored knowledge,which can not only achieve time-varying full state constraints control,but also effectively improve the control performance,and reduce the online computational burden as well as the network communication burden.4)The problem of event-triggered control is investigated for strict-feedback nonlinear systems with prescribed performance constraints based on the deterministic learning theory.Firstly,to cope with the problem of prescribed performance constraints,a novel finite-time performance function is constructed to characterize the predefined performance constraints indicators.Then,coordinate transformation technology is employed to convert the original strict-feedback system into a system with normal form,which reduces the number of NN approximators used in the backstepping design process of high-order nonlinear systems,facilitates the acquisition and storage of the experienced knowledge,and thus helping to achieve learning control.Subsequently,in the case of sufficient network resources,an adaptive neural control scheme is designed for the system with normal form,which guarantees that the NNs can accurately approximate the unknown system dynamics and the neural estimated weights can exponentially converge to their ideal weights during the steady-state control process.And the converged NN estimated weights are stored as the experienced knowledge.Finally,considering the case of limited network resources,an event-triggered neural learning controller is constructed by utilizing the stored knowledge,which can not only guarantee that the tracking error satisfies the prescribed performance constraints,but also elevate the control performance,save the network resources and reduce the amount of online calculation.