Thesis (M. Ed.)--University of Hong Kong, 2001. / Includes bibliographical references (leaves 27-31).

This dissertation addresses three diverse research problems pertaining to rigid body attitude stabilization and control. The problems addressed result in theoretical development for the topics of cooperative control, delayed feedback, and state estimation, through the formulation of a novel class of switching observers. In the area of consensus management for cooperative control, the problem of designing torque control laws that synchronize the attitude of a team of rigid bodies under constant, unknown communication time delays is addressed. Directed communication graphs are considered, which encompass both leader-follower and leaderless architectures. A feedback linearization result involving the Modified Rodrigues parameter (MRP) representation of attitude kinematics reduces the attitude dynamics equations to double integrator agents and the remainder of the control effort achieves position consensus. New necessary and sufficient delay dependent stability conditions for the system of double integrator agents are presented. This dissertation also considers the problem of stabilizing attitude dynamics with unknown piecewise-constant delayed feedback. The problem is addressed through stability analysis of switched linear time-invariant and nonlinear timedelay systems. In the case of linear systems with switched delay feedback, a new sufficiency condition for average dwell time result is presented using a complete type Lyapunov-Krasovskii (L-K) functional approach. Further, the corresponding switched system with nonlinear perturbations is proven to be exponentially stable inside a well characterized region of attraction for an appropriately chosen average dwell time. Finally, this dissertation provides a new switching angular velocity observer formulation to the classical problem of rigid body attitude tracking in the absence of angular rate measurements. Exponential convergence of the angular velocity state estimation errors is proven independent of control design by using a novel error signal definition through this switching-type observer. The switching ensures C0 continuity for all the estimated states. Further, the maximum number of switches required by the observer is shown to be finite and that zeno-type behavior cannot occur. A “separation property” type result in the absence of actual angular rate measurements is established, wherein a linear and nonlinear controller utilizes angular velocity estimates from the proposed observer to achieve attitude tracking. / text

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published_or_final_version / Mathematics / Master / Master of Philosophy

The objective of this research is to demonstrate experimentally the feasibility of using the Internet for a Distributed Control System (DCS). An algorithm has been designed and implemented to ensure stability of the system in the presence of upper bounded time-varying delays. A single actuator magnetic ball levitation system has been used as a test bed to validate the proposed algorithm. Experiments were performed to obtain the round-trip time delay between the host PC and the client PC under varying network loads and at different times. A digital real-time lead-lag controller was implemented for the magnetic levitation system. Upper bounds for the artificial and experimental round-trip time delay that can be accommodated in the control loop for the maglev system were estimated. The artificial time delay was based on various probabilistic distributions and was generated through MATLAB. To accommodate sporadic surges in time delays that are more than these upper bounds, a timeout algorithm with sensor data prediction was developed. Experiments were performed to validate the satisfactory performance of this algorithm in the presence of the bonded sporadic excessive time delays.

With the advancement of communication technology, more and more control processes happen in networked environment. This makes it possible for us to deploy multiple systems in a spatially distributed way such that they could finish certain tasks collaboratively. While it brings about numerous advantages over conventional control, challenges arise in the mean time due to the imperfection of communication. This thesis is aimed to solve some problems in cooperative control involving multiple agents in the presence of communication constraints. Overall, it is comprised of two main parts: Distributed consensus in multi-agent systems and bilateral teleoperation. Chapter 2 to Chapter 4 deal with the consensus problem in multi-agent systems. Our goal is to design appropriate control protocols such that the states of a group of agents will converge to a common value eventually. The robustness of multi-agent systems against various adverse factors in communication is our central concern. Chapter 5 copes with bilateral teleoperation with time delays. The task is to design control laws such that synchronization is reached between the master plant and slave plant. Meanwhile, transparency should be maintained within an acceptable level. Chapter 2 investigates the consensus problem in a multi-agent system with directed communication topology. The time delays are modeled as a Markov chain, thus more characteristics of delays are taken into account. A delay-dependent approach has been proposed to design the Laplacian matrix such that the system is robust against stochastic delays. The consensus problem is converted into stabilization of its equivalent error dynamics, and the mean square stability is employed to characterize its convergence property. One feature of Chapter 2 is redesign of the adjacency matrix, which makes it possible to adjust communication weights dynamically. In Chapter 3, average consensus in single-integrator agents with time-varying delays and random data losses is studied. The interaction topology is assumed to be undirected. The communication constraints lie in two aspects: 1) time-varying delays that are non-uniform and bounded; 2) data losses governed by Bernoulli processes with non-uniform probabilities. By considering the upper bounds of delays and probabilities of packet dropouts, sufficient conditions are developed to guarantee that the multi-agent system will achieve consensus. Chapter 4 is concerned with the consensus problem with double-integrator dynamics and non-uniform sampling. The communication topology is assumed to be fixed and directed. With the adoption of time-varying control gains and the theory on stochastic matrices, we prove that when the graph has a directed spanning tree and the control gains are properly selected, consensus will be reached. Chapter 5 deals with bilateral teleoperation with probabilistic time delays. The delays are from a finite set and each element in the set has a probability of occurrence. After defining the tracking error between the master and slave, the input-to-state stability is used to characterize the system performance. By taking into account the probabilistic information in time delays and using the pole placement technique, the teleoperation system has achieved better position tracking and enhanced transparency. / Graduate

Consensus is a central issue in designing multi-agent systems (MASs). How to design control protocols under certain communication topologies is the key for solving consensus problems. This thesis is focusing on investigating the consensus protocols under different scenarios: (1) The second-order system dynamics with Markov time delays; (2) The Euler-Lagrange dynamics with uniform and nonuniform sampling strategies and the event-based control strategy. Chapter 2 is focused on the consensus problem of the multi-agent systems with random delays governed by a Markov chain. For second-order dynamics under the sampled-data setting, we first convert the consensus problem to the stability analysis of the equivalent error system dynamics. By designing a suitable Lyapunov function and deriving a set of linear matrix inequalities (LMIs), we analyze the mean square stability of the error system dynamics with fixed communication topology. Since the transition probabilities in a Markov chain are sometimes partially unknown, we propose a method of estimating the delay for the next sampling time instant. We explicitly give a lower bound of the probability for the delay estimation which can ensure the stability of the error system dynamics. Finally, by applying an augmentation technique, we convert the error system dynamics to a delay-free stochastic system. A sufficient condition is established to guarantee the consensus of the networked multi-agent systems with switching topologies. Simulation studies for a fleet of unmanned vehicles verify the theoretical results. In Chapter 3, we propose the consensus control protocols involving both position and velocity information of the MASs with the linearized Euler-Lagrange dynamics, under uniform sampling and nonuniform sampling schemes, respectively. Then we extend the results to the case of applying the centralized event-triggered strategy, and accordingly analyze the consensus property. Simulation examples and comparisons verify the effectiveness of the proposed methods. / Graduate / 0548

Thesis (Ph. D.)--University of Hong Kong, 2008. / Includes bibliographical references (leaf 238-259) Also available in print.

Thesis (M.Sc)(Chemical Technology, Engineering and Technology Management)--University of Pretoria, 2005. / Includes summary. Includes bibliographical references (leaves 75-80).

Thesis (Ph. D.)--Ohio State University, 2004. / Title from first page of PDF file. Document formatted into pages; contains xiii, 96 p.; also includes graphics Includes bibliographical references (p. 92-96). Available online via OhioLINK's ETD Center