Research On Output Regulation Problem Of Nonlinear Normal Form Systems

The output regulation problem (or servocompensation) of nonlinear normal form system is an important branch of control theory that has received widely con-cern. The inclusion of servocompensator (or internal model unit) can render the system to be asymptotic stable, and hence it has been considered as the most effec-tive and applicable method to solve the output regulation problem. This dissertation adopts internal model method to study the practical regulation of minimum-phase system under output feedback, adaptive regulation, the output regulation of non-minimum phase system and high-gain observer-based separation principle. The main contributions of the dissertation are as follows:1. For a class of minimum-phase normal form system with internal model per-turbation, a vector Lyapunov function method is proposed to solve practical output regulation problem. The proposed vector Lyapunov function method can ensure that the upper bound of the steady state regulation error is the lin-ear type function of internal model perturbation. Hence the conservativeness of the steady state regulation error is decreased significantly in contrast to the scalar quadratic Lyapunov function. Furthermore the system design param-eter can be tuned as a tuning parameter that solves the practical regulation problem of the system.2. For a class of minimum-phase nonlinear normal form system with exosystem with uncertain parameters, a novel adaptive regulator is proposed to achieve semiglobally asymptotic regulation. The proposed adaptive internal model does not only apply in balanced realization internal model but also in con-trollable canonical form. When the controllable canonical form internal model is applied, the number of the online estimated parameters can be reduced by half, the scaling factor is used to rescale the range of the estimated parameters and the numerical stability is increased. Moreover the semiglobally asymptotic regulation is achieved under the case that the PE (Persistent Excitation) con-dition is absent when the parameters are adaptively estimated. When the PE condition is present, the origin of the system is semiglobally asymptotic stable and locally exponential stable. 3. For the adaptive system in the absence of PE condition, a novel high-gain ob-server based separation principle is proposed. The existing high-gain observer based separation principle requires that there exist a asymptotically stable invariant set for the closed-loop system under state feedback. However such invariant set does not exist when only the partial modes of internal model are excited(or the PE condition is not satisfied in adaptive system). The dissertation firstly establishes the high-gain observer based non-local nonlin-ear separation principle. Through tuning the parameters of output feedback adaptive regulator, the trajectories of the system state can be tuned to be close to that shaped by the ideal state feedback sliding model controller.4. For the proposed adaptive regulator, in the presence of internal model pertur-bation, a three-time scale method is constructed to achieve adaptive practical regulation. This required all the modes of internal model be excited. More-over the one restriction on the observability of internal model is required. This point is a new application of multi-time scale method in nonlinear practical regulation problem.5. For a class of non-minimum phase nonlinear normal form system, the disser-tation proposes conditional integrator to achieve semiglobal asymptotic regu-lation. The dissertation casts the problem as two auxiliary problems, and uses the singular perturbation method to arrive at that the two auxiliary problems can be solved simultaneously. Moreover, in the derivation of output regula-tion of non-minimum phase system, the choosing of auxiliary controller can be independent of internal model parameter, the result facilitates the solution of output regulation of non-minimum phase system.6. Extends the conditional servocompensator that dealing with minimum phase system to the non-minimum normal form case. It is different from minimum phase system in that an auxiliary controller is proposed to stabilize the zero dynamics. Moreover through the proposed vector Lyapunov function method, the ultimate bound of the steady state error is the linear function of the upper bound of the internal model perturbation.