UC Santa Cruz

Clock synchronization over networks is a nontrivial problem that has long been an important topic in the fields of computer science and engineering as it pertains to digital networks and distributed systems. Recently, clock synchronization has received much attention in the study of networked control theory due to the importance of consensus on time in distributed control and estimation settings.This dissertation addresses the need for new clock synchronization schemes with the presentation of several hybrid based approach to clock synchronization problem.

To motivate this work, the problem of a hybrid observer, with a clock synchronization scheme, that receives information sporadically over a network is presented. Through an attractivity result on the convergence properties of the observer system, sufficient conditions on the convergence properties of the accompanying clock synchronization scheme demonstrate the need for clock synchronization algorithms with performance guarantees.

In one of the solutions to the problem, a distributed hybrid algorithm that synchronizes the time and rate of a set of clocks connected over a network is presented. Clock measurements of the nodes are given at aperiodic time instants and the controller at each node uses these measurements to achieve synchronization. Due to the continuous and impulsive nature of the clocks and the network, a hybrid system model to effectively capture the dynamics of the system and proposed hybrid algorithm is introduced. Moreover, the hybrid algorithm allows each agent to estimate the skew of its internal clock in order to allow for synchronization to a common timer rate. Sufficient conditions guaranteeing synchronization of the timers, exponentially fast are provided. Numerical results illustrate the synchronization property induced by the proposed algorithm as well as robustness to communication noise.

Next, an innovative hybrid systems approach to the sender-receiver synchronization of timers is presented. Via the hybrid systems framework, the traditional sender-receiver algorithm for clock synchronization is united with an online, adaptive strategy to achieve synchronization of the clock rates to exponentially synchronize a pair of clocks connected over a network. Following the conventions of the algorithm, clock measurements of the nodes are given at periodic time instants, and each node uses these measurements to achieve synchronization. For this purpose, a hybrid system model of a network with continuous and impulsive dynamics that captures the sender-receiver algorithm as a state-feedback controller to synchronize the network clocks is introduced. Moreover, sufficient design conditions that ensure attractivity of the synchronization set are provided with numerical examples to validate the theoretical results.

Finally, a general approach and framework to modeling clock synchronization protocols using hybrid systems is presented. Using the general framework, several existing algorithms from the literature are modeled. The models are then simulated numerically to demonstrate the feasibility of the proposed modeling framework.