This thesis is concerned with the designing of an nth order adaptive integral variable structure derivative estimator (AIVSDE). The proposed estimator's scheme is in fact a modified and extended version of the existing AIVSDE. The new proposed AIVSDE can be used as a direct nth differentiator for a smooth signal which has n continuous and bounded derivatives. The adaptive algorithm is utilized for the switching gain to remove the requirement for a priori knowledge about the upper bound of the derivative of the input signal. The stability of the redesigned first order, the second order, and the nth order derivative's estimation is guaranteed by the proposed scheme. An example is demonstrated for showing the applicability of the proposed AIVSDE.

By using Lyapunov stability theorem, a quasi-optimal model reference adaptive control (QOMRAC) scheme is presented in this thesis to stabilize a class of uncertain systems with input nonlinearity. This control scheme contains two main types of controllers. The first type is a linear feedback controller, which is an optimal controller if the controlled systems do not have any perturbations. The second type is an adaptive controller, which is used for adapting the unknown upper bound of perturbation or perturbation estimation error. The property of uniformly ultimately boundness is guaranteed when employing the proposed control scheme, and the effects of each design parameter on the dynamic performance are also analyzed. An example is demonstrated for showing the feasibility of the proposed control scheme.

The objective of this thesis is to solve the trajectory tracking control problems of the mobile manipulators in two stages. In the first stage, a desired velocity input function for a steering system is designed by using Lyapunov stability theorem so that the posture of the mobile manipulator can track the reference trajectory. Further analysis shows that the vehicle of the mobile manipulator will achieve better result of trajectory tracking than the existent methods if the reference trajectory of the vehicle is not assigned to be static condition. In the second stage, the torque controller of the dynamic equations of the mobile manipulator with perturbations and input uncertainty is designed by adaptive variable structure control (AVSC) methodology, so that the actual velocity can track the desired velocity input function designed in the first stage. In addition, this controller with an adaptive mechanism embedded is capable of suppressing the perturbations with unknown upper bound except that from the input channel, and achieve asymptotical stability under certain mild conditions. Finally, an example of a two-link wheeled mobile manipulator is presented to demonstrate the feasibility of the proposed control schemes.

A simple technique of designing a robust discrete-time variable structure output tracking controller for a class of perturbed MIMO linear and nonlinear systems is proposed in this thesis. For linear systems, a model reference scheme is employed. Both an adaptive mechanism and a perturbation estimation process are embedded in the proposed control scheme. The information of the upper bound of the perturbation estimation error is not required due to the usage of adaptive mechanism. It is shown that the dynamics of the controlled systems will be driven into the vicinity of the designed switching surface, therefore the tracking error will be constrained in a small bounded region. Furthermore, the stability of the overall controlled system is guaranteed, and one can increase the tracking accuracy by adjusting the controller's parameters or by employing the perturbation estimation process.

Based on the Lyapunov stability theorem, two different variable structure controllers are proposed in this thesis for two different classes of multi-variable descriptor systems subject to matched nonlinear perturbations. The integral variable structure controller is proposed first for solving the stabilization problems, and model reference variable structure controller is the second for solving the state tracking problems. Both proposed control schemes can guarantee the trajectories of the controlled systems to lie in the sliding surface from initial time, so that the properties of regularity, impulse free, and stability can be obtained. Two numerical examples are given for demonstrating the feasibility of the proposed control schemes.

Based on the Lyapunov stability theorem, a methodology of designing robust discrete-time model reference variable structure state tracking controller is proposed in this thesis for a class of multi-input multi-output (MIMO) discrete-time systems. This variable structure controller is composed of three types of controllers. The first one is the feedback control law, which can eliminate the nominal term in the derivative of a Lyapunov function. The second one is the switching control law, which can determine the decreasing rate of the Lyapunov function. The third one is the adaptive control law, which is used to overcome the perturbations. The resultant robust variable structure controllers are capable of driving all the trajectories of tracking errors toward a small bounded region. The information of upper bound of the perturbation, which is not a constant and is dependent on the norm of state variable, is not required beforehand due to some adaptive mechanisms are embedded in the proposed control scheme, and the stability of the overall controlled system is guaranteed. A numerical example and a practical example are given to demonstrate the feasibility of the proposed control scheme.

Artificial neural network (ANNs) is an information processing paradigm inspired by the human brain. ANNs have been used in numerous applications to provide complex nonlinear input-output mappings. They have the ability to adapt and learn from observed data. The training of neural networks is an important area of research and consideration. Training techniques have to provide high accuracy, fast speed of convergence, and avoid premature convergence to local minima. In this thesis, a novel training method is proposed. This method is based on the relatively new Smooth Variable Structure filter (SVSF) and is formulated for feedforward multilayer perceptron training. The SVSF is a state and parameter estimation that is based on the Sliding Mode Concept and works in a predictor-corrector fashion. The SVSF applies a discontinuous corrective term to estimate state and parameters. Its advantages include guaranteed stability, robustness, and fast speed of convergence. The proposed training technique is applied to three real-world benchmark problems and to a fault detection application in a Ford diesel engine. SVSF-based training technique shows an excellent generalization capability and a fast speed of convergence. / Artificial neural network (ANNs) is an information processing paradigm inspired by the human brain. ANNs have been used in numerous applications to provide complex nonlinear input-output mappings. They have the ability to adapt and learn from observed data. The training of neural networks is an important area of research and consideration. Training techniques have to provide high accuracy, fast speed of convergence, and avoid premature convergence to local minima. In this thesis, a novel training method is proposed. This method is based on the relatively new Smooth Variable Structure filter (SVSF) and is formulated for feedforward multilayer perceptron training. The SVSF is a state and parameter estimation that is based on the Sliding Mode Concept and works in a predictor-corrector fashion. The SVSF applies a discontinuous corrective term to estimate state and parameters. Its advantages include guaranteed stability, robustness, and fast speed of convergence. The proposed training technique is applied to three real-world benchmark problems and to a fault detection application in a Ford diesel engine. SVSF-based training technique shows an excellent generalization capability and a fast speed of convergence. / Thesis / Master of Applied Science (MASc)

An application of binary state latch device with proper real-time control algorithm for energy redistribution application is introduced in this thesis. Unlike traditional tuned vibration absorber, the latch device can be viewed as variable semi-active dampers such as magnetorheological (MR) and piezoelectric friction dampers. The distinct difference between other semi-active dampers and our latch device is that other semi-active dampers can provide continuous resistance according to the amount of input current, however, the binary latch device can only provide two different values of resistance - either the maximum or no resistance at all. This property brings the latch possibly having higher maximum and minimum ratio of resistance than MR dampers. As for the operating structure, the mechanism of latch element is nearly the same as the piezoelectric friction dampers which the resistance force is provided according to the normal force acting on two rough plates. Nonetheless, because of the characteristic of the binary states output of the latch element, this make it very different from the ordinary variable dampers. Since it is either being turned on or turned off, a novel control law is required for shifting energy. Also, because of the simplicity of the binary states output, it is very accessible to implement the controller on Field Programmable Gate Array (FPGA). With this accessibility, it is promising to apply plenty of latch elements in the same time for large scale application, such as multi-agent networks. In this thesis, an energy-based analytic solution is proposed to illustrate the universal latch-off condition. And a latch-on condition under ideal situations is discussed. At the end, a control law under nonideal condition is being suggested for real-time periodically excited system. We found that energy redistribution is achievable by using the proper control law under fairly broad conditions. / Master of Science

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.

Three robust tracking control design strategies are proposed in this dissertation for different classes of nonlinear MIMO dynamic systems with mismatched perturbations. The first controller design method is proposed for a class of nonlinear MIMO dynamic systems in canonical form. The second design procedure of controller is for the nonlinear MIMO dynamic systems without canonical form. A decentralized controller is presented in the last for perturbed large-scale systems with time-varying delay interconnections, where the knowledge of the exact function of time-delay is not required. These robust tracking controllers with a perturbation estimating scheme and an adaptive control mechanism embedded are designed by means of the variable structure control technique and Lyapunov stability theorem. The adaptive control mechanism is used to adapt the unknown upper-bound of perturbation estimation error, so that the knowledge of upper-bounds of perturbation as well as perturbation estimation error is not required. The chattering phenomenon is effectively alleviated, for the gain of the proposed controllers, which needs only to overcome the perturbation estimation error, is in general smaller than those of the traditional sliding mode controllers. Furthermore, the stability of the overall controlled systems is proved, and the desired tracking accuracy can be achieved by adjusting the design parameters of the proposed controller schemes. A numerical example for each controller's design is provided for demonstrating the feasibility of the proposed control schemes.