Finite-time Preset Performance Optimization Control Design For Nonlinear System

Stability is one of the basic problems to be solved in controlled systems.On the basis of stability,the transient performance is often considered for the actual system.Prescribed performance control method controls the transient performance of the system by setting prescribed performance functions,which can meet the transient performance requirements of the system such as convergence speed and overshoot while ensuring the stability of the system.In addition,the practical systems are often constrained by various conditions.The system may become unstable and the control performance will be degraded if the constraints are not satisfied.Model predictive control has developed rapidly in recent years because of its ability to deal with system constraints.In practical industrial applications,many systems are required to satisfy both constraints and transient performance requirements.Therefore,it is meaningful to adopt predictive control method based on prescribed performance to study the stability of the system.In this paper,appropriate predictive control methods based on prescribed performance are proposed to stabilize the nonlinear systems with constraints and external disturbances,constrained switched nonlinear systems and constrained nonlinear systems with unmeasurable states.The work content of this paper is mainly summarized into the following three parts:Firstly,a finite time prescribed performance controller is designed for a class of constrained nonlinear systems with external disturbances.A homeomorphic mapping is used for error conversion to establish the equivalent error model of the system.A robust controller is designed when the initial state is in the stability region.A finite time optimization controller is designed to make the state reach the stability region when the initial state is outside the stability region.Based on the Lyapunov stability theory,it is proved that the system state can track the desired trajectory in a finite time and meet the prescribed performance conditions.The effectiveness of the proposed method is testified by two simulation examples.Secondly,the tracking control problem for a class of constrained nonlinear switched systems with external disturbances is studied.A homeomorphic mapping is used for error conversion to establish the equivalent error model of the system.The robust stability controller and model predictive controller are designed for each subsystem.Based on the selected Lyapunov function of the subsystem,a suitable switching law is designed.It is demonstrated that the tracking error of the system can converge to origin in a finite time and meet the given prescribed performance conditions by using the Lyapunov stability theory.Simulation results verify the effectiveness of the proposed control strategy.Thirdly,an output feedback control method based on event triggered strategy and prescribed performance is proposed for a class of constrained nonlinear systems with unmeasurable states.An observer is designed to observe the unmeasurable state of the system.The equivalent error model of the system is established through a homeomorphism mapping.When the initial state is in the stable region,a finite time output feedback controller is designed.When the system state is outside the stable region,a finite time optimal controller based on event triggered strategy is designed to reduce the computational complexity and make the system state reach the stable region.Based on the Lyapunov stability theory,it is proved that the output of the system can track the desired trajectory in a finite time and meet the prescribed performance conditions.The effectiveness of the method is verified by a simulation example.