Guaranteed Performance Control Of Strict-feedback System With Prescribed Time

Practical engineering systems often have highly complex dynamic characteristics,and their control problems are extremely challenging.With the rapid development of artificial intelligence technology,people have higher and higher requirements on the performance of the controlled system,so the prescribed performance control for the complex nonlinear system is particularly important.At present,most of the prescribed performance control methods for this type of nonlinear system can only ensure that the tracking error converges to a certain predefined accuracy at infinite time,and the selection of design parameters depends on the initial conditions of the system.Due to safety or different mission requirements,the system often has a different initial state or a different desired trajectory each time it restarts.Therefore,traditional control methods that are dependent on specific initial conditions will be difficult to meet the requirements of complex nonlinear systems to achieve different tasks and operate safely and efficiently.How to ensure that complex nonlinear systems can guarantee some specific performance within a prescribed finite time under the conditions of various system uncertainties and even unknown initial conditions is the key point of the research on this dissertation.This dissertation mainly studies the two scenarios of known and unknown initial conditions of the system,focusing on the given performance control problem of complex nonlinear systems with a presettable time when the initial conditions of the system are known and the prescribed performance control of complex nonlinear systems within a preset time when the initial conditions are unknown.The innovative content has been accomplished as follows.(1)For the given performance tracking control of a class of multiple input and multiple output(MIMO)nonlinear strict-feedback systems with unknown time-varying control gain matrix,a neuroadaptive tracking control scheme is proposed by combining the error transformation based on speed function and the barrier Lyapunov function theory,which makes the tracking error converge to a predetermined accuracy at a pregiven convergence rate within a prescribed time chosen by the designer,and realizes that the convergence time and convergence speed as well as tracking accuracy can be predetermined.In addition,the introduction of matrix factorization technique eliminates the assumption that the control gain matrix itself is positive definite symmetric or its estimated value is nonsingular,thereby broadening the scope of application of the control algorithm,and the introduction of virtual parameters also reduces the number of parameters that need to be updated online,which reduces the computational burden significantly.(2)For a family of MIMO nonlinear normal form systems with actuator faults,the problem of given performance tracking control is studied.Firstly,the speed function is first introduced to make a nonlinear transformation of the error and virtual error variables,and then a nonlinear transformation is constructed for each element of the new transformed variable.Based on these two error transformation techniques,a neural network adaptive redundant fault-tolerant control strategy is proposed,so that the tracking error and virtual error can converge to an asymmetric and specifiable residual region at a pregiven decay rate within a prescribed time.It not only realizes the predetermining of convergence time and convergence speed as well as steady-state accuracy,but also solves the problem that conventional control methods generally cannot guarantee the asymmetric error constraints of MIMO systems.Besides,different from most existing methods that are upon partial loss of actuation effectiveness,this control strategy can handle extreme failures in which some actuators at some particular channel completely fail to work,and there is no need for hard switching of standby actuators nor additional fault detection and isolation devices during the entire control process,making it easier to implement the controller in real-time.(3)The problem of prescribed performance tracking control for a class of nonlinear strict-feedback systems under unknown initial conditions and external disturbances is investigated.Firstly,a transfer function is constructed to transform the error,and then a barrier Lyapunov function based on the transformation variable is established.With the help of the core function technology,a robust adaptive tracking control scheme is designed so that the tracking error from any bounded(possibly unknown)initial value converges to the prescribed performance region within a prescribed time,eliminating the initial error constraint limitation of the conventional prescribed performance control algorithm.(4)Regarding to the prescribed performance control problem of tracking error and virtual error of nonlinear strict-feedback system under unknown initial conditions,a robust adaptive control strategy is developed by constructing an error transfer transformation and a new asymmetric barrier Lyapunov function,which enables the tracking error and virtual error to converge from any bounded initial value to prescribed and asymmetrical performance region within a prescribed time.This control scheme not only eliminates the initial error constraint limitation of traditional prescribed performance control methods,but also greatly reduces the analysis complexity caused by the piecewise continuous asymmetric barrier Lyapunov function that is commonly used to deal with asymmetric error constraints.(5)The prescribed time practical tracking control problem for nonlinear strict-feedback systems subject to unknown initial conditions and unmeasurable states is investigated.First,a state observer with a simple structure is constructed with the aid of the neural network,and then a new type of transfer function is introduced to perform a nonlinear transformation on the tracking error.With the help of the barrier Lyapunov function theory,an output-feedback tracking control scheme with an event-triggered mechanism is proposed so that the tracking error with any bounded initial value can converge to the prescribed practical tracking accuracy within a prescribed time,which relaxes the constraints of the initial conditions of the system and reduces the communication burden.Besides,unlike the existing finite-time output-feedback control methods,the convergence time of the system is independent of the initial conditions of the system and other design parameters,and the scheme involves neither finite-time observer nor fractional power feedback of system states,which greatly reduces the complexity of controller design and analysis.