Ultra-Wideband technology has attracted interests of the researchers and commercial groups due to its advantage of high data rate, low complexity and low power consumption. The direct-sequence code division multiple access ultra wideband system (DS-CDMA UWB) is one of the proposal of IEEE 802.15.3a standard. By combing the power of both UWB and DS-CDMA techniques, the system could construct multiple access architecture using direct sequence method. In multi-user environment, the major problem of the receiver designing of conventional DS-CDMA system is multiple access interference(MAI). In DS-CDMA UWB system, the transmitted signal were interfered by inter-symbol interference(ISI) and neighbor symbol interference because of the multi-path channel characteristic. In this thesis, we use the training method to get the spreading waveform influenced by multi-path. Based on the information of spreading waveform, we use the block method to reformulate the received signal. We can separate the interference into multiple access interference and neighbor symbol interference. With Combining the interference cancellation, probabilistic data association (PDA) filter and sliding window techniques, we could eliminate the interference. In the computer simulation section, we compare the detection performance of sliding window PDA detector with conventional detector, and the simulation result shows that the improved PDA detector has better performance than others.

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.

Given a string S = {a1, a2, a3, ..., an}, the longest increasing subsequence (LIS) problem is to find a subsequence of the given string such that the subsequence is increasing and its length is maximal. In a previous result, to find the longest increasing subsequences of each sliding window with a fixed size w of a given string with length n can be solved in O(w log log n+OUTPUT) time, where O(w log log n+ w^2) time is taken for preprocessing and OUTPUT is the sum of all output lengths. In this thesis, we solve the problem for finding the longest increasing subsequence of every substring of S. With the straightforward implementation of the previous result, the time required for the preprocessing would be O(n^3). We modify the data structure used in the algorithm, hence the required preprocessing time is improved to O(n^2). The time required for the report stage is linear to the size of the output. In other words, our algorithm can find the LIS of every substring in O(n^2+OUTPUT) time. If the LIS's of all substrings are desired to be reported, since there are O(n^2) substrings totally in a given string with length n, our algorithm is optimal.

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.

In this thesis a model reference adaptive sliding mode control scheme is proposed for a class of linear time-invariant MIMO systems with unstructured and input, output uncertainties to solve the robust tracking problems. The designing of the proposed control scheme is divided into three steps. The first step is to design the sliding functions, the second step is to construct the estimators of the lumped perturbation. These estimators are able to estimate the derivatives of the tracking errors. The third step is to design the adaptive sliding mode controller. The proposed control scheme is designed without requiring the information of the upper bound of perturbations, and guarantee the stability of the controlled system. In fact the asymptotical stability can be achieved for some special cases. Finally, three numerical examples are presented to demonstrate the feasibility of the proposed control scheme.

Abstract In this dissertation, four variable structure controllers are proposed for four different class of systems subjected to uncertainties and time varying delays respectively. In most cases, the variable structure control is incorporated with an adaptive law to drive the tracking error between the desired model and the controlled plant to zero. By using the Lyapunov stability theorem, the adaptive law is utilized for adapting the unknown upper bounds of the lumped perturbations so that the objective of asymptotical stability is achieved, and the variable structure control scheme is used for enhancing the robustness of stability of the controlled systems. Once the system enters the sliding region, the dynamics of controlled systems are insensitive to matching perturbations. It also shows that the proposed methodologies ensure the property of the globally uniformly ultimate boundness for the overall controlled system. Finally, four numerical examples are given for demonstrating the feasibility of the proposed control schemes.

Two different perturbation estimation methodologies are compared in this thesis. One is time delay method (TDM), the other is sliding mode techniqueli (SMT). When analyzing the TDM, Pade approximation is used to approximate a function with time-delay argument. The comparisons of perturbation estimation accuracy resulted from TDM and SMT both in time domain and frequency domain are addressed, and two numerical examples are also given for demonstration.

In position control systems like linear motor, friction is a key factor to influence the control performance when micron or sub-micron meter accuracy is required. To overcome the effect of the friction, besides a general model of the linear motor system, past researches have shown an additional static friction model of the system is necessary for a better control performance when the motor move into the micro region of the system (usually <100£gm). Two models, macro and micro model of the system have been well constructed by two different identification methods. After model construction, two different controllers are also designed for each model. A traditional pole-placement PID controller can be easily obtained for the macro model to move into the micro region quickly and stably. Then in micro model design, from the experiments, it is found that system parameter varies and thus degrades the positioning performance of the system. So, a Sliding-Mode Controller is designed to improve these problems. With a two step control strategy, macro and micro step, the linear motor positioning system can achieve a 0.1£gm accuracy within 0.2 sec.

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.