On Adaptive Output Feedback Control For Nonlinear Systems With Output Constraint

In many practical nonlinear systems,the existence of unmodeled dynamics significantly reduces the closed-loop systems performance and even makes the systems unstable.Realizing the restraint and offset of unmodeled dynamics is a key to improve the system control performance.In addition,to ensure the high performance and security of the systems,most practical control systems are often subject to constraint on their manipulated outputs and state variables.Currently,the research of unconstrained systems is very mature,but the existence of various constraints makes it unsuitable for constrained systems,this makes the in-depth study of controller design of constrained systems more and more necessary.In this paper,based on barrier Lyapunov function(BLF),integral barrier Lyapunov function(iBLF)and nonlinear mapping(NM),four adaptive dynamic surface control schemes are proposed for several classes of nonlinear systems with unmodeled dynamics and output constraint.The main content of this paper are summarized as follows:Firstly,based on the assumption that the unmodeled dynamics is exponentially input state practically stable,an adaptive dynamic surface output feedback control scheme is proposed for a class of nonlinear systems with symmetric output constraint and state unmodeled dynamics by introducing BLF.The radial basis function neural networks(RBF NNs)are utilized to approximate unknown nonlinear continuous functions.By utilizing K-filters,the complex nonlinear system is transformed into lower order subsystems.A dynamic signal is introduced to compensate the effects of the dynamic uncertainties on the system.By ensuring boundedness of the BLF along the system trajectories,transgression of constraint is prevented.By theoretical analysis,the closed-loop control system is proved to be semi-globally uniformly ultimately bounded,while the output constraint is never violated.Finally,a numerical simulation example further validates the effectiveness of the proposed approach.Secondly,an adaptive dynamic surface output feedback control scheme is proposed for a class of nonlinear systems with symmetric output constraint and state unmodeled dynamics by introducing iBLF.To reduce the order of K-filters and the dimension of the corresponding parameter vector,unknown smooth nonlinear functions are not directly approximated by RBF NNs.By directly limiting the output of the system,the initial condition to ensure constraint satisfaction is relaxed.To reduce the complexity of controller design,dynamic surface control method is adopted to design controller,and the error terms which come from neural network approximation and unmodeled dynamics are handled efficiently by constructing unknown continuous functions in stability analysis.By theoretical analysis,the closed-loop control system is proved to be semi-globally uniformly ultimately bounded,while the output constraint is never violated.Finally,two numerical simulation examples further validate the effectiveness of the proposed approach.Thirdly,based on the assumption that the unmodeled dynamics is global exponential stability,an adaptive dynamic surface output feedback control scheme is proposed for a class of nonlinear systems with asymmetric output constraint and state unmodeled dynamics by introducing NM.Unmodeled dynamics is described by Lyapunov function.By introducing K-filters and NM,the complex nonlinear system is transformed into lower order system without constraint.By theoretical analysis,the closed-loop control system is proved to be semi-globally uniformly ultimately bounded,while the output constraint is never violated.Finally,two numerical simulation example further validate the effectiveness of the proposed approach.Fourth,the method of NM is utilized further to a class of strict-feedback nonlinear systems,and the influence of input unmodeled dynamics is considered.By theoretical analysis,the closed-loop control system is proved to be semi-globally uniformly ultimately bounded,while the output constraint is never violated.Finally,two numerical simulation example further validate the effectiveness of the proposed approach.