Research On Constrained Control Problems For Two Classes Of High-Order Nonlinear Systems

In many practical systems,due to equipment limitations,performance specifications,safety considerations and so on,systems are often restricted during the process of operation,that is,some constraint conditions need to be satisfied.Notably,violation of constraints may lead to system instability,system performance degeneration and even safety accidents.At the same time,the existence of constraints makes the control design more complex for nonlinear systems.In recent years,the research on constrained control for high-order nonlinear systems has attracted the attention of many scholars and made significant progress.However,the powers of considered systems are known constants in most previous works,while the constrained control for high-order nonlinear systems with unknown time-varying powers is rarely studied.Based on the existing literature,the following two control problems are investigated for a class of high-order nonlinear systems with state constraints and prescribed performance in this thesis.1.Asymptotic Tracking Control of State-Constrained Nonlinear Systems with Unknown Time-Varying PowersIn this chapter,the asymptotic tracking control problem is studied for fullstate constrained nonlinear systems with unknown time-varying powers.Different from the traditional barrier Lyapunov function-based methods,a nonlinear statedependent mapping is constructed to convert the full-state constrained problem into the boundedness problem of transformed states after mapping.Then,based on the adding a power integrator technique,a state feedback tracking control method is proposed by introducing a continuous bounded scalar function as well as lower and higher powers into control design.Under this control method,it is proved that without the frequently-used feasibility conditions,full-state constraints aren’t transgressed,all the closed-loop signals are bounded,and the output of the system asymptotically tracks the reference signal.The effectiveness of the proposed control method is illustrated by a simulation example.2.Adaptive Neural Network Preassigned Finite-Time Control of State-Constrained Nonlinear Systems with Unknown Time-Varying PowersFor full-state constrained nonlinear systems with unknown time-varying powers,the adaptive neural network preassigned finite-time control problem is studied in this chapter without feasibility conditions.To this end,radial basis function neural networks are used to approximate the unknown nonlinearities of the system.Then,lower and higher powers as well as nonlinear mapping based on finite-time performance functions are introduced into dynamic surface control design,an adaptive neural network state-feedback control method is proposed,while avoiding both the repeated differentiations of virtual controllers and the restrictive growth conditions imposed on the system nonlinearities.It is shown that all the closed-loop system signals are semi-globally bounded,and steady-state performances and transient performances of system states can be prescribed without violating full-state constraints by this method.Particularly,the prescribed performance function constructed in this chapter has the property of preassigned finite-time convergence,which guarantees that system states converge to a prescribed small region around zero after a preassigned setting time.In addition,the states of neural networks stay in a specific compact set,on which neural network approximation is valid.The feasibility and superiority of the control method are verified by two simulation examples,respectively.