Based on the Lyapunov stability theorem, two design methodologies of adaptive block backstepping controller is proposed in this thesis for a class of multi-input systems with matched and mismatched perturbations to solve regulation problems. The main difference between these two method is that perturbation estimations are only employed in each virtual control input in the second method, whereas in the first method, the perturbation estimation is only employed in the last block. According to the number of block (m) in the dynamic equations of plant to be controlled, m-1 virtual input controllers are designed from the first block to the (m-1)th block, and the proposed robust controller is designed from the last block. Adaptive mechanisms are employed in each of the virtual input controllers as well as the robust controller, so that the least upper bounds of perturbations and perturbation estimation errors are not required. Furthermore, the dynamic equations of the plant do not need to satisfy the block strict feedback form, and the resultant control system can achieve asymptotic stability or uniformly ultimately boundedness. Finally, a numerical example and a practical example are given for demonstrating the feasibility of the proposed control schemes.

Based on the Lyapunov stability theorem, a design methodology of adaptive block backstepping decentralized controller is proposed in this thesis for a class of large-scale systems with interconnections to solve regulation problems. Each subsystem contains m blocks¡¦ state variables, and m- 1 virtual input controllers are designed from the first block to the (m - 1)th block. Then the proposed robust controller is designed in accordance with the last block. Some adaptive mechanisms are embedded in the backstepping controllers as well as virtual input controllers in each subsystem, so that the upper bounds of interconnections as well as perturbations are not required. Furthermore, the dynamic equations of each subsystem do not need to strictly satisfy the block strict feedback form, and the resultant controlled system can achieve asymptotic stability. Finally, a numerical and a practical examples are given for demonstrating the feasibility of the proposed control scheme.

In this thesis an adaptive backstepping control scheme is proposed for a class of multi-input perturbed systems with time-varying delays to solve regulation problems. The systems to be controlled contain n blocks¡¦ dynamic equations, hence n-1 virtual input controllers are designed from the first block to the (n-1)th block, and the backstepping controller is designed from the last block. In addition, adaptive mechanisms are embedded in each virtual input controllers and proposed controller, so that the least upper bounds of perturbations are not required to be known beforehand. Furthermore, the dynamic equations of the systems to be controlled need not satisfy strict-feedback form, and the upper bounds of the time delays as well as their derivatives need not to be known in advance either. The resultant controlled systems guarantee asymptotic stability in accordance with the Lyapunov stability theorem. Finally, a numerical example and a practical application are given for demonstrating the feasibility of the proposed control scheme.

Based on the Lyapunov stability theorem, a decentralized adaptive backstepping tracking control scheme for a class of perturbed large-scale systems with non-strict feedback form is presented in this thesis to solve tracking problems. First of all, the dynamic equations of the plant to be controlled are transformed into other equations with semi-strict feedback form. Then a decentralized tracking controller is designed based on the backstepping control methodology so that the outputs of controlled system are capable of tracking the desired signals generated from a reference model. In addition, by utilizing adaptive mechanisms embedded in the backstepping controller, one need not acquire the upper bounds of the perturbations and the interconnections in advance. The resultant control scheme is able to guarantee the stability of the whole large-scale systems, and the tracking precision may be adjusted through the design parameters. Finally, one numerical and one practical examples are demonstrated for showing the applicability of the proposed design technique.

Based on the Lyapunov stability theorem, a design methodology of adaptive block backstepping control scheme is proposed in this thesis for a class of multi-input perturbed nonlinear systems with input nonlinearities to solve regulation problems. Fuzzy control method is utilized to estimate the unknown inverse input functions in order to facilitate the design of the proposed control scheme, so that the sector condition need not to be satisfied. According to the number of block m in the plant to be controlled, m−1 virtual input controllers are designed from the first block to the (m−1)th block. Then the proposed robust controller is designed from the last block. Adaptive mechanisms are also employed in the virtual input controllers as well as the robust controller, so that the least upper bounds of perturbations and estimation errors of inverse input functions are not required. The resultant control system is able to achieve asymptotic stability. Finally, a numerical example and a practical example are given for demonstrating the feasibility of the proposed control scheme.