Constructive Nonlinear Systems Control Based On Dynamic State Feedback

In the field of nonlinear systems control,there are mainly two well-established method,that is,feedback linearization and backstepping approach.This thesis studies a class of nonlinear systems which cannot be stabilized by these two mentioned methods.This class of systems can be further classified into two cases:affine systems and nonaffine systems.Due to generality and complexity of the studied nonlinear systems,some related control methods are rarely seen in existing control literatures,and most of them focus on the state feedback stabilization problem provided that the model information is explicitly known.For the control of affine systems,there are mainly four methods:(1)Interconnection and Damping Assignment Passivity based Control(IDA-PBC),(2)Immersion and Invariance approach(I&I),(3)Contraction analysis based method,and(4)Gain scheduling based approach.The first three method all rely on solving partial differential equations(PDEs),which makes the control design not straightforward,and hinders the practical applications.The gain scheduling method does not require solving PDEs.However,since it is based on local linearization or linear parameter-varying system theory,the resulting control design cannot theo-retically guarantee the closed-loop stability or has huge computation complexity.For the control of nonaffine systems,most of the existing methods focus on the single input case,or require that the nonaffine input of the controlled systems has particular forms.Some other researchers seek to transform the controlled nonaffine systems into affine systems by directly designing the derivative of the control input.However,this design increases the relative degree of the controlled system and thus leads to deterioration of the control performance.In order to overcome the drawbacks of the aforementioned approaches,this thesis considers to investigate the constructive control of nonlinear systems by exploiting the dynamic state-feedback method.Specifically,it includes the following aspects:(1)A brief literature review on the background and development of nonlinear systems control is provided.For the convenience of the readers and to facilitate the related discussions,some basic definitions and theorems are given.(2)For a class of incrementally passive nonlinear systems,we propose a dynamic state-feedback controller which can ensure an asymptotic tracking result under the condition that the velocity of the target trajectory is unknown.Based on nonsmooth systems theory,zero-state detectability,and Lyapunov method,a rigorous stability analysis is provided for the closed-loop system.Simulation results are given to show that the proposed method can applied to the nonlinear systems which are not feedback linearizable nor in a strict-feedback form.Furthermore,it shows that the proposed method can achieve a better control performance compared to some existing approaches.(3)For a class of multi-input nonaffine nonlinear systems,an I&I based dynamic state-feedback controller is proposed,and it is also extended to adaptive stabilization of a class of nonaffine non-linear systems with linearly parametric uncertainty.Compared to other approach,the proposed method can deal with the multiple inputs case,and also does not require that the nonaffine input has particular forms.At the same time,the proposed method offers a simple and constructive de-sign.Simulation results are provided to show that the proposed method can achieve a better control performance compared to the dynamic inversion method.(4)The dynamic state-feedback method is applied to the fuel cell/battery hybrid power sys-tems,and an IDA-PBC based real-time power sharing strategy is proposed.Compared to the con-ventional IDA-PBC method,the problem of solving PDEs is avoided by introducing an extended state to increase the control degree of freedom.Furthermore,online parameter adaptation laws are design for unknown model parameters.Compared to other existing power sharing method for hybrid power systems,the proposed method has provable closed-loop stability.Simulation and experiment results are provided to validate the effectiveness of the proposed method.At the end of the thesis,some concluding remarks are provided.A list of the future research directions is given.