On Adaptive Optimal Control For Nonlinear Systems With Output Constraints In Strict-Feedback Form

In practical systems of engineering,output constraints and unmodeled dynamics are essential factors that affect the dynamic performances while optimizations are pursued to achieve specific performance indexes.If output constraints under actual backgrounds are not obeyed,the consequences include performance reduction and even instability.Due to modeling error and immeasurability,unmodeled dynamics affect stability of the system.At the same time,real systems may possess the optimization requirement to reach particular performance index.At present,there were many achievements on output constraints and unmodeled dynamics,but they were rarely combined with optimization.Thus,three adaptive optimal control schemes are proposed for three classes of systems with output constraints.The main contents of this paper are organized as follows:Firstly,an adaptive optimal control strategy is proposed for nonlinear systems with output constraints in strict-feedback form by using dynamic surface control(DSC)?The controller design procedure is divided into two parts.One is the·design of feedforward controller and the other is the optimal controller.To guarantee the satisfaction of output constraint,it is removed by nonlinear mapping(NM).Neural-network based adaptive dynamic programming(ADP)algorithm is employed to get the estimation of the cost function and the optimal control law.By theoretical analysis,all the signals in the closed-loop system are proved to be semi-globally uniformly ultimately bounded and the output constraint is not violated.A numerical example illustrates the effectiveness of the proposed scheme.Secondly,adaptive optimal control is proposed for a class of strict-feedback nonlinear systems with unmodeled dynamics and output constraints.The controller design procedure contains two parts.In the first part,to satisfy output constraint,nonlinear mapping is used to transform constrained system into a novel one without output constraints.A dynamical signal is utilized to deal with unmodeled dynamics.In the second part,an auxiliary dynamical system is introduced to optimize cost function,where neural-network based adaptive dynamic programming is employed to approximate the optimal cost function and the optimal control law.It is proved that the closed-loop system is semi-globally uniformly ultimately bounded and the output constraints are not violated by theoretical analysis.A simulation example illustrates the effectiveness of the proposed scheme.Thirdly,the problem of adaptive optimal control for constrained nonlinear systems with unmodeled dynamics and time-varying output constraints is investigated.The controller consist of the feedforward part and the optimal part.In the feedforward controller part,the constraint of the time-varying constrained system is canceled by nonlinear mapping,where unmodeled dynamics is dealt with by a dynamical signal.In the optimal controller part,by introducing an auxiliary dynamical system,neural-network based adaptive dynamic programming is employed to approximate the optimal cost function and the optimal control law.The proposed method is able to guarantee semi-globally uniformly ultimately boundedness of all the signals in the closed-loop system by theoretical analysis.Meanwhile,the output constraint is not violated.Several simulation examples illustrate the effectiveness of the proposed scheme.