Adaptive Approximation Control Techniques For Noncanonical Form Nonlinear Systems

This dissertation presents a new study on adaptive control problem of noncanonical form nonlinear systems with unparametrizable uncertainties,for which new adaptive approximation control techniques for noncanonical form nonlinear systems are developed.Existing adaptive approximation control designs are developed mostly based on certain canonical-form nonlinear systems.Consider a canonical-form nonlinear system:???₁=x₂+f₁?x₁?,???₂=f₂?x₁,x₂?+u with unparametrizable uncertain functions f₁andf₂.Using approximation techniques?T-S fuzzy systems or neural networks?,an approximation system can be constructed as???₁=???₂+?₁^*T?₁?x₁?+?₁,???₂=?₂^*T?₂?x₁,x₂?+u+?₂for some known basis functions?₁and?₂and un-known parameter vectors?₁^*and?₂^*of appropriate dimensions,where?₁and?₂are approximation errors.Then,an adaptive control algorithm can be designed directly based on the approximation system model to achieve desired system performance,using backstepping technique.Such approximation con-trol designs and analysis of canonical-form nonlinear systems have solved significant theoretical and practical problems.However,there are many applications of which the system models are in noncanonical forms.Aircraft flight control systems are a typical class of non-canonical practical systems.Canonical-form systems have explicit structure features such as explicit relative degree structures,infinite zero struc-tures and multivariable coupling structures,etc.,and so do their approximation systems,which is crucial for adaptive control law designs.Whereas,noncanonical form nonlinear systems of the form???_i=f_i?x₁,x₂,...,x_n,u?,i=1,2,...,n,with uncertain unparametrizable functions f_i,do not have such features,neither do their approximation systems.Existing control methods of canonical-form sys-tems are not applicable for control of noncanonical systems.Adaptive approximation control of non-canonical form nonlinear systems with unparametrizable uncertainties faces new technical problems including how to employ adaptive feedback linearization and adaptive backstepping control techniques to noncanonical form approximation system models.It motivates our research on developing new solu-tions for adaptive approximation control approaches and algorithms,to meet the urgent need of control of noncanonical form nonlinear systems with unparametrizable uncertainties.The main work in this dissertation is establishing a fairly complete parametrized adaptive control framework of uncertain noncanonical form approximation system models.The fundamental techni-cal developments include adaptive control designs of uncertain noncanonical form continuous-time T-S fuzzy systems and uncertain noncanonical form continuous-time neural network systems covering SISO case and MIMO case,and feedback control design of noncanonical form SISO discrete-time neural net-work systems.The new study extends the system relative degree concept,commonly used for control of nonlinear systems,to noncanonical form T-S fuzzy systems and noncanonical form neural network systems,derives various relative degree conditions for such systems,and establishes the relative degree dependent normal forms.A new adaptive feedback linearization based control design framework is developed for such systems using their normal forms,to achieve closed-loop stability and asymptotic output tracking under relaxed design conditions,with complete control designs and stability analysis.In such a control framework,new technical methods are developed to handle the new technical problems encountered in the control schemes,including a new matrix decomposition and parametrization inte-gration based method is developed to handle the singularity problem of control gain matrices of MIMO neural network systems,a new implicit function theory and numerical solution technique integration based method is developed to achieve stable output tracking of noncanonical form discrete-time neu-ral network systems,etc..Some extensions of relative degrees and their applications to robust adaptive control of noncanonical form T-S fuzzy systems and noncanonical form neural network systems are also studied.A class of aircraft mathematical models and various numerical models are used for simulation study,and the simulation results verify the effectiveness of the proposed control methods.In this dissertation,the proposed adaptive approximation control techniques for noncanonical form nonlinear systems provide a new research idea for adaptive control of nonlinear systems,expands the applicable range of adaptive control,and provides effective control theory foundations and design ref-erences for control of noncanonical form practical systems with large unparametrizable uncertainties.