Based on the Lyapunov stability theorem, an adaptive sliding mode control scheme is proposed in this thesis for a class of mismatched perturbed multi-input multi-output (MIMO) dynamic systems to solve regualtion problems. The sliding surface function is firstly designed by treating some state variables as a pseudo controllers through the usage of sliding function to stabilize the rest of state variables. In this thesis the number of these pseudo controllers is less than that of the state variables to be stabilized. The second step is to design the controllers so that the trajectories of the controlled systems are able to reach sliding surface in a finite time. Some adaptive mechanisms are embedded in the sliding surface function and sliding mode controllers, so that not only the mismatched perturbations can be suppressed during the sliding mode, but also the information of upper bounds of some perturbations are not required when designing the sliding surface function and controllers. Once the controlled system enters the sliding mode, the state trajectories can achieve asymptotical stability under certain conditions. A numerical example and a practical example are given to demonstrate the feasibility of the proposed design technique.

With the ability to generate fine displacements with a resolution down to sub-nanometers, piezoelectric actuators (PEAs) have found wide applications in various nano-positioning systems. However, existence of various effects in PEAs, such as hysteresis and creep, as well as dynamics can seriously degrade the PEA performance or even lead to instability. This raises a great need to model and control PEAs for improved performance, which have drawn remarkable attention in the literature. Sliding mode control (SMC) shows its potential to the control of PEA, by which the hysteresis and other nonlinear effects can be regard as disturbance to the dynamic model and thus rejected or compensated by its switching control. To implement SMC in digital computers, this research is aimed at developing novel discrete models and discrete SMC (DSMC)-based control schemes for PEAs, along with their experimental validation. The first part of this thesis concerns with the modeling and control of one-degree of freedom (DOF) PEA, which can be treated as a single-input-single-output (SISO) system. Specifically, a novel discrete model based on the concept of auto-regressive moving average (ARMA) was developed for the PEA hysteresis; and to compensate for the PEA hysteresis and improve its dynamics, an output tracking integrated discrete proportional-integral-derivative-based SMC (PID-SMC) was developed. On this basis, by making use of the availability of PEA hysteresis models, two control schemes, named “the discrete inversion feedforward based PID-SMC” and “the discrete disturbance observer (DOB)-based PID-SMC”, were further developed. To illustrate the effectiveness of the developed models and control schemes, experiments were designed and conducted on a commercially available one-DOF PEA, as compared with the existing ones. The second part of the thesis presents the extension of the developed modeling and control methods to multi-DOF PEAs. Given the fact that details with regard to the PEA internal configurations is not typically provided by the manufacturer, a state space model based on the black box system identification was developed for the three-DOF PEA. The developed model was then integrated in the output tracking based discrete PID-SMC, with its effectiveness verified through the experiments on a commercially available three-DOF PEA. The superiority of the proposed control method over the conventional PID controller was also experimentally investigated and demonstrated. Finally, by integrating with a DOB in the discrete PID-based SMC, a novel control scheme is resulted to compensate for the nonlinearities of the three-DOF PEA. To verify its effectiveness, the discrete DOB based PID-SMC was applied in the control experiments and compared with the existing SMC. The significance of this research lies in the development of the discrete models and PID-based SMC for PEAs, which is of great help to improve their performance. The successful application of the proposed method in the control of multi-DOF PEA allows the application of SMC to the control of complicated multi-inputs-multi-outputs (MIMO) systems without details regarding the internal configuration. Also, integration of the inversion based feedforward control and the DOB in the SMC design has been proven effective for the tracking control of PEAs.

Based on the Lyapunov stability theorem, a modified stability analysis as well as a modified observer is proposed in this thesis for a class of uncertain nonlinear systems with an existent high gain observer. By assuming that the first two state variables are indirectly measurable, reanalyzing the stability of the error dynamics is presented first. The advantage of this modified analytic method is that the upper bound of the disturbance distribution functions is not required to be known in advance, and the asymptotic stability is still guaranteed. Next, based on this existent observer, a slightly modified observer is presented for systems with disturbances whose upper bound is unknown. An adaptive mechanism is embedded in the proposed observer, so that the upper bound of perturbations is not required to be known beforehand. The resultant dynamics of estimation errors can be driven into the sliding surface in a finite time, and guarantee asymptotic stability. A numerical example and a practical example are given to demonstrate the feasibility of the proposed observer.

Synchronization of two identical chaotic systems with matched and mismatched perturbations by utilizing adaptive sliding mode control (ASMC) technique is presented in this thesis. The sliding surface function is designed based on Lyapunov stability theorem and linear matrix inequality (LMI) optimization technique. Adaptive mechanisms embedded in the proposed control scheme are used to adapt the unknown upper bounds of the perturbations. The designed tracking controller can not only suppress the mismatched perturbations when the controlled dynamics (master-slave) are in the sliding mode, but also drive the trajectories of synchronization errors into a small bounded region whose size can be adjusted through the designed parameters. The stability of overall controlled synchronization systems is guaranteed. Application of proposed chaotic synchronization technique to secure communication as well as several numerical examples are given to demonstrate the feasibility of the proposed design technique.

Based on the Lyapunov stability theorem, an adaptive sliding mode control scheme is proposed in this thesis for a class of mismatched perturbed multi-input multi-output (MIMO) dynamic systems to solve stabilization problems. In order to suppress the perturbations in the control systems, adaptive mechanisms are employed both in sliding function and control effort, so that the information of upperbound of some perturbations is not required when designing the proposed control scheme. Due to the novel design of sliding function, the state trajectories of this system can achieve asymptotical stability in the sliding mode even if mismatched perturbations exist. In addition, with an adaptive mechanism embedded in the proposed control scheme, the controller can drive the state's trajectory into the designated sliding surface in a finite time. A numerical example is demonstrated for showing the applicability of the proposed design technique.

Two robust control strategies are proposed in this dissertation for a class of multi-input multi-output dynamic systems with matched and mismatched perturbations. First of all, a novel design methodology of switching variables is proposed for solving the regulation problems. A serial state transformations are needed in order to design pseudo feedback gains and adaptive mechanisms. By utilizing the pseudo control input gain embedded in each of the switching variable, the proposed controller can not only suppress the mismatched perturbations when the controlled systems are in the sliding mode, but also attain locally asymptotic stability. The design of a robust output tracking controller is presented next for solving the tracking problems. Without utilizing the information of state variable, the proposed output feedback tracking controllers are capable of driving the state tracking errors into a small bounded region whose size can be adjusted through the designed parameters, and guarantee the stability of controlled systems. These two robust control schemes are designed by means of the variable structure control technique with sliding mode and Lyapunov stability theorem. Each controller contains three parts. The first part is for eliminating measurable feedback signals. The second part is used for adjusting the convergent rate of state variables (or tracking errors) of the controlled system. The third part is an adaptive control mechanism, which is to adapt some unknown constants of the least upper bounds of perturbations, so that the knowledge of the least upper bounds of matched and mismatched perturbations are not required. Several numerical examples and an application of controlling aircraft's velocity are demonstrated for showing the feasibility of the proposed control methodologies.

In this dissertation, four nonlinear controllers are proposed for different class of multi-input multi-output (MIMO) systems with matched and mismatched perturbations. All the plants to be controlled contains input uncertainty. The technique of the adaptive sliding mode control (ASMC) scheme is first introduced in order to solve the regulation or tracking problems. By applying adaptive techniques to the design of a novel sliding surface as well as to the design of sliding mode controller, one can not only enable the fulfillment of reaching mode in fi- nite time, but also suppress the mismatched perturbations when system is in the sliding mode. Secondly, the design methodology of block backstepping is proposed to solve the regulation problem in chapter 5. Some adaptive mechanisms are employed in the virtual input controller, so that the mismatched perturbations can be tackled and the proposed robust controller can guarantee stability of the controlled systems. All these control schemes are designed by means of Lyapunov stability theorem. Each robust controller contains two parts. The first part is for eliminating measurable feedback signals of the plant, and the second part is an adaptive control mechanism, which is capable of adapting some unknown constants embedded in the least upper bounds of perturbations, so that the knowledge of the least upper bounds of matched and mismatched perturbations is not required and can achieve asymptotic stability. Several numerical examples and industrial applications are demonstrated for showing the feasibility of the proposed control schemes.

The brightness variance, caused by relative velocity of the camera and environment in a sequence of images, is called optical flow. The advantage of the optical-flow-based visual servo method is that feature of the object dose not need to be known in advance. Therefore, it can be applied for positioning and tracking implement tasks. The purpose of this thesis is to implement the image servo technique and the sliding-mode control method to track an unknown image pattern in three dimensional motion. The goal of tracking is to maintain identical image captured by the camera based on the relative movement calculated from the optical flow.

In this dissertation three robust control strategies are proposed for a class of multi-input multi-output dynamic systems with matched or mismatched perturbations. Firstly, an adaptive variable structure observer and controller are introduced for solving the regulation problems, where some state variables are not measurable. By utilizing adaptive mechanisms in the design of sliding mode controller, one can enable the controlled systems not only to generate a reaching mode in finite time, but also to suppress the mismatched perturbations during the sliding mode. Secondly, the design of adaptive sliding mode controllers with application to robot manipulators is presented to solve the tracking problems. The dynamic equations of the controlled systems contain a perturbed leading coefficient matrix and can be either positive definite or negative definite. The asymptotical stability of the controlled systems will be attained if the proposed control scheme is employed. Thirdly, a design methodology of adaptive sliding mode controller based on T-S fuzzy model is proposed to solve tracking problems. It is shown that the trajectories of the controlled systems can be driven into a designated sliding surface in finite time, and the property of asymptotical stability is also guaranteed. All these three control schemes are designed by means of Lyapunov stability theorem. Each control scheme contains three parts. The first part is designed for eliminating measurable feedback signals. The second part is used for adjusting the convergent rate of state variables (or tracking errors) of the controlled system. The third part is the adaptive control mechanism, which is used to adapt some unknown constants of the least upper bounds of perturbations, so that the knowledge of the least upper bounds of matched or mismatched perturbations are not required. Several numerical examples and an application of controlling robot manipulator are demonstrated for showing the feasibility of the proposed control methodologies.

The main focus of about this thesis is to design an anti-interference depth controller for underwater remotely operated vehicles(ROV). Since the underwater remotely operated vehicle experiences combination effects of nonlinearities, uncertain and time-varying parameters, and unknown disturbances, demand of robustness for the controller needs to be extremely strict. Therefore, an anti-interference depth controller using PID control and Sliding-mode control is developed. The Matlab simulation tool is employed to simulate the depth control performance of the behavior of the ROV. The simulation is also considered about the model uncertainty of ROV.