The Analysis And Synthesis Of The Domain Of Attraction For Nuonlinear Parameter-varying Systems

Problems of the analysis and synthesis of the domain of attraction(DA)for nonlinear systems are significantly important studying issues in the field of control science.For nonlinear time-varying(NTV)systems,there are still no available results in the literature for the analysis and synthesis of the DA.In view of this,under the novel nonlinear parameter-varying(NPV)framework,we propose methods for the estimation of the DA of a wide class of nonlinear polynomial systems and the local stabilization of NPV systems.The main contents of this dissertation are outlined as follows:1)Bisectional SOS programming(BiSOSP)algorithm.For nonlinear polynomial time-invariant systems,we put forward a relatively simple BiSOSP algorithm to estimate the DA.First,based on the given Lyapunov functional,the BiSOSP algorithm is used to compute the largest estimate of the DA.Furthermore,considering the complex system dynamics and high dimensions,we develop a computationally simple BiSOSP algorithm to search for a better Lyapunov functional,which is optimized with a specified simple shape.Those types of BiSOSP algorithms can be solved directly with free SOSTOOLS toolbox.As a result,the estimations are tight,and the computational burden is small.2)The estimate and the optimization of the DA for NPV systems.Under the NPV framework,this dissertation generalizes the definition of robust DA(RDA)to NPV systems,and to take into account the time-varying parameter,we propose the novel concept of parameter-dependent DA(PDA)for NPV systems,together with SOS-based conditions for their estimations.Differently from the existing DA-related works,the theoretical results in this paper can be applied to a large class of nonlinear polynomial systems including the time-invariant,the parameter-dependent and the uncertain ones.Moreover,the commonly bilinear problem is avoided,and hence the complicated iterative/coordinate-wise search is no longer needed.3)The local stabilization problem of NPV systems with RDA constraints.For a class of NTV systems,this dissertation provides the solvable SOS-based conditions to search a state-feedback controller using the SOS programming theory and the NPV modeling method.Differently from the traditional approaches,we can specify the RDA as the control performance index during the design process of controllers,such that the closed-loop system is at least locally asymptotically stable within the RDA.The NPV system has abundant connotations and extensions.Benefiting from those advantages,the proposed method for the estimate of the DA possesses general applicability;the given SOS conditions for the local stabilization of NPV systems,can be applied for stabilizing a class of NTV systems under the NPV modeling framework.Two simulation examples are given to validate the effectiveness of the proposed methods.