Adaptive Neural Network Control Of Nonlinear Systems With State Constraint

In practical engineering,the majority of the systems are nonlinear and can be represented by the corresponding state space models.However,these systems will inevitably involve unknown nonlinearities,which may result in major difficulties in control design.Besides,due to the constraints of the operating environment or the requirements of the control task,the output or states of the system will always be constrained in some way,and this is reflected in the fact that the system states must remain within certain predefined limits during operation.Moreover,controlled systems are usually required to have a good transient response,namely,the system is able to reach a steady state rapidly from the initial state.Compared to time-independent control,finite-time control not only reduces convergence time but also improves error accuracy.Therefore,this paper investigates the finite-time(fixed-time)tracking control problem for several types of nonlinear systems with state(output)constraints,as follows.1.The tracking control problem for a class of nonlinear systems with constant output constraints is considered in the presence of known and unknown states,respectively.A new barrier Lyapunov function is constructed based on the defined performance function,and the corresponding prescribed finite-time adaptive neural control scheme is proposed by using state-feedback and output-feedback approaches.The designed state-feedback controller and output-feedback controller ensure that all closed-loop signals meet the boundedness requirement and the system output cannot violate the given constraint limits during the whole process,meanwhile,the tracking error can reach the pre-given accuracy requirement at the setting time.2.The fixed-time control problem for a class of nonlinear systems subject to time-varying output constraints and constant state constraints is investigated.First,a general fixed-time stability criterion is established.Next,a new virtual control signal is constructed by utilizing the properties of hyperbolic tangent functions to ensure that the virtual control signals satisfy the corresponding states constraints.Lastly,based on the established general fixed-time stability criterion,a novel fixed-time control strategy is developed by adopting the barrier Lyapunov function and neural network approximation approach to ensure that the output error can converge to a small neighborhood around the origin in the fixed time and the system states satisfy the corresponding constraint requirements.3.The tracking control problem of the time-varying state-constrained nonlinear system is investigated under the prerequisite that the system states already satisfy the specified constraint requirements.A asymmetric virtual control signal is first developed to ensure that the virtual control signal satisfies the time-varying constraint requirements of the corresponding state.In the framework of the backstepping design,a new barrier Lyapunov function is constructed based on the defined performance function and new error variables,and the prescribed finite-time control scheme is proposed by combining the adaptive neural network approximation approach.The designed controller can ensure that the system achieves the prescribed finite-time control task,namely,the tracking error meets the pre-given accuracy requirement within the preassigned time and the residual closed-loop signals remain bounded.