Adaptive Control For Uncertain Nonlinear Systems With Constraints

In real physical systems,a large number of plants are intrinsically nonlinear and commonly affected by uncertain parameters and unknown disturbances.As the system complexities increase,some existing theories and research methods of nonlinear systems are not available.On the other hand,due to the physical properties,runtime environ-ments and other factors,the control objects are inevitably limited by various constraints.If these constraints are neglected,system performance may be deteriorated,and even system instability may happen.Therefore,studying the control problems for nonlinear systems with constraints is a research topic of great theoretical significance and practical interest.Based on the existing work,the control theory of the nonlinear systems and neural networks,the control problems are studied for nonlinear systems with input sat-uration,output constraints,state constraints,unknown disturbances,unknown control gain signs and prescribed performance,respectively;and in the controller design process,some control methods are utilized,such as backstepping,surface dynamic control,mini-mal learning parameters,barrier Lyapunov function,Nussbaum function,etc.The main contents can be summarized as follows:1.An adaptive dynamic surface control approach using neural networks approxima-tion and nonlinear disturbance observer for uncertain nonlinear systems in the presence of input saturation,output constraint and unknown external disturbances is proposed.The issue of input saturation is addressed by introducing an upper bound assumption on the approximation function of saturation.The output constraint is handled by introducing an appropriate barrier Lyapunov function.The nonlinear disturbance observer is employed to estimate the unknown unmatched disturbances.It is manifested that the ultimately bounded convergence of all the variables in the closed-loop system is guaranteed and the tracking error can be made fairly small by tuning the design parameters.Finally,two simulation examples illustrate the effectiveness and feasibility of the proposed approach.2.Incorporating dynamic surface control and the neural networks(NNs)approxima-tion with the minimization parameter method,a neural adaptive controller is designed for a class of nonlinear systems in the case of full-state constraints and unknown disturbances.By introducing a novel barrier Lyapunov function(BLF)in the design steps,the issue of full-state constraints existing in the system can be solved.The highlighting features of the proposed control method are that only one online estimation parameter should be updated,and the same stability property as the conventional backstepping method can be reserved.The transgressions of full state constraints never occur in the case of un-known disturbances.By the Lyapunov stability analysis,all the signals of the closed-loop system are ultimately bounded.Finally,a numerical example and a Brusselaror chemical model display the effectiveness of the proposed approach.3.A composite neural dynamic surface control(DSC)method is designed for a class of pure-feedback nonlinear systems in the case of unknown control gain signs and full-state constraints.In the recursive design process,neural networks are utilized to approximate the compound unknown functions,and the approximation errors of neural networks are applied in the design of updated adaptation laws.Comparing the pro-posed composite approximation method with the conventional ones,a faster and better approximation performance result can be obtained.Combining the composite neural net-works approximation with the DSC technique,an improved composite neural adaptive control approach is designed for the considered nonlinear system.Then,together with the Lyapunov stability theory,all the variables of the closed-loop system are semi-global uniformly ultimately bounded.The infringements of full state constraints can be avoided in the case of unknown control gain signs as well as unknown disturbances.Finally,two simulation examples show the effectiveness and feasibility of the proposed results.4.The prescribed performance adaptive control problems are investigated for non-linear systems with partial state constraints and full state constraints.First,we consider the control problem for nonlinear systems in pure feedback form with partial state con-straints.Combining the neural networks approximation,dynamic surface control with the funnel prescribed performance control method,a neural adaptive control scheme is proposed.With the proposed controller,the tracking error satisfies the conditions of prescribed error performance.By the Lyapunov stability analysis,all the signals of the closed-loop system are ultimately bounded,and the partial state constraints are not vi-olated.Second,we consider the control problem for nonlinear systems in pure feedback form with full state constraints,and a new assumption is proposed to avoid the circular design problem.Incorporating dynamic surface control and the funnel prescribed perfor-mance control with minimum parameter method,a different control approach is designed for nonlinear systems with full state constraints.Only one adaptation parameter is need to be updated online,which alleviates the computation burden of the control system.Then,together with the Lyapunov stability theory,all the variables of the closed-loop system are uniformly ultimately bounded.The prescribed steady and transient perfor-mance of the control aims can be satisfied without infringements the full state constraints of the considered system.Finally,simulation examples are used to illustrate the validity of the proposed control method.