Research On Control And Its Applications Of Nonlinear Parameter-varying Systems With Constraints

Time-varying nature and nonlinearities are commonly existed in control systems.At present,there is a lack of general criteria for stability analysis and controller design of nonlinear time-varying(NTV)systems.This paper applies nonlinear parameter-varying(NPV)models to describe nonlinearities and time-varying characteristics of the controlled systems.Based on polynomial sum-of-squares techniques,this paper investigates the stability and control problems of NPV systems.These theorem results are applied to solve the mode conversion control of tilt-rotor aircraft and the steady-state control of turbofan engines,respectively.The main research contents of this paper are summarized as follows:1)Asymptotic stability and the stabilisation control problem of NPV systems.Based on SOS techniques and Lyapunov stability theory,the asymptotic stability control approaches of NPV systems are given.The results for input saturation are provided as well.These theorems are reduced to the corresponding solvable conditions in nonlinear systems and linear parameter varying(LPV)systems.Thus,the research of the analysis and synthesis problems can be regarded as a further extension and development of nonlinear systems and LPV systems to NPV systems.2)The guaranteed cost control problem of NPV systems.The guaranteed cost control problems of NPV systems are investigated.These solvability conditions are given in term of state-and-parameter-dependent(SAPD)linear matrix inequalities(LMIs).The results for input saturation are provided as well.By mathematical equivalence changes,the asymptotic stability guaranteed cost control approaches of NPV systems are given for input-constraint-free case and input-constraint case.These corresponding results are applied to the mode conversion control of tilt-rotor aircraft,which verifies the feasibility and effectiveness of the proposed method.3)Mixed H2/H_∞ guaranteed cost control problem of NPV systems.The mixed H2/H∞ guaranteed cost control problems are discussed.These solvability conditions are given.Mixed H2/H∞ robust guaranteed cost control problems are investigated in the presence of dynamic uncertainty of NPV systems.The corresponding results are applied to the mode transition control of tilt-rotor aircraft and a numerical example,which verifies the effectiveness of the proposed method.4)Prescribed performance control problem of NPV systems.The steady state performance and the transient performance of controlled systems are considered in practice.The prescribed performance control problems of NPV systems are investigated and these solvability conditions are given.The results for input saturation are provided as well.Finally,the corresponding results are applied to performance constraint control of turbofan engine5)Output feedback control problem of NPV systems.The output feedback control problem of NPV system is investigated.The SPAD controller and the SPAD observer gain matrices can be designed separately.And it is effectively reduced the computation complexity and the difficulty of constructing Lyapunov function.The results for input saturation are provided as well.The feasibility of the proposed method is verified by numerical examples.