A Genetically Evolved Solution to the Firing Squad Problem

In 1957, J. Myhill presented the firing squad problem. A special case of k-color cellular automata (CA) synchronization, the firing squad problem offers more stringent rules allowing for a provable minimal running time. To date, CA solutions have been found that run in minimal time using as many as sixteen states and as few as six [5]. There have also been arguments against the existence of solutions using only 4 states [11]. Due to the extremely large search space involved with such problems, the existing solutions have all been analytic in nature. We attempt to apply genetic algorithms and genetic programming to create transition tables that solve the firing squad problem. Ideally, the solutions would run in minimal time. No generalized solutions were found, but progress was made towards determining the best strategies for an evolved solution

Distributed Cooperative Control of Multi-Agent Systems Under Detectability and Communication Constraints

Cooperative control of multi-agent systems has recently gained widespread attention from the scientific communities due to numerous applications in areas such as the formation control in unmanned vehicles, cooperative attitude control of spacecrafts, clustering of micro-satellites, environmental monitoring and exploration by mobile sensor networks, etc. The primary goal of a cooperative control problem for multi-agent systems is to design a decentralized control algorithm for each agent, relying on the local coordination of their actions to exhibit a collective behavior. Common challenges encountered in the study of cooperative control problems are unavailable group-level information, and limited bandwidth of the shared communication. In this dissertation, we investigate one of such cooperative control problems, namely cooperative output regulation, under various local and global level constraints coming from physical and communication limitations. The objective of the cooperative output regulation problem (CORP) for multi-agent systems is to design a distributed control strategy for the agents to synchronize their state with an external system, called the leader, in the presence of disturbance inputs. For the problem at hand, we additionally consider the scenario in which none of the agents can independently access the synchronization signal from their view of the leader, and therefore it is not possible for the agents to achieve the group objective by themselves unless they cooperate among members. To this end, we devise a novel distributed estimation algorithm to collectively gather the leader states under the discussed detectability constraint, and then use this estimation to synthesize a distributed control solution to the problem. Next, we extend our results in CORP to the case with uncertain agent dynamics arising from modeling errors. In addition to the detectability constraint, we also assumed that the local regulated error signals are not available to the agents for feedback, and thus none of the agents have all the required measurements to independently synthesize a control solution. By combining the distributed observer and a control law based on the internal model principle for the agents, we offer a solution to the robust CORP under these added constraints. In practical applications of multi-agent systems, it is difficult to consistently maintain a reliable communication between the agents. By considering such challenge in the communication, we study the CORP for the case when agents are connected through a time-varying communication topology. Due to the presence of the detectability constraint that none of the agents can independently access all the leader states at any switching instant, we devise a distributed estimation algorithm for the agents to collectively reconstruct the leader states. Then by using this estimation, a distributed dynamic control solution is offered to solve the CORP under the added communication constraint. Since the fixed communication network is a special case of this time-varying counterpart, the offered control solution can be viewed as a generalization of the former results. For effective validation of previous theoretical results, we apply the control algorithms to a practical case study problem on synchronizing the position of networked motors under time-varying communication. Based on our experimental results, we also demonstrate the uniqueness of derived control solutions. Another communication constraint affecting the cooperative control performance is the presence of network delays. To this regard, first we study the distributed state estimation problem of an autonomous plant by a network of observers under heterogeneous time-invariant delays and then extend to the time-varying counterpart. With the use of a low gain based estimation technique, we derive a sufficient stability condition in terms of the upper bound of the low gain parameter or the time delay to guarantee the convergence of estimation errors. Additionally, when the plant measurements are subject to bounded disturbances, we find that that the local estimation errors also remain bounded. Lastly, by using this estimation, we present a distributed control solution for a leader-follower synchronization problem of a multi-agent system. Next, we present another case study concerning a synchronization control problem of a group of distributed generators in an islanded microgrid under unknown time-varying latency. Similar to the case of delayed communication in aforementioned works, we offer a low gain based distributed control protocol to synchronize the terminal voltage and inverter operating frequency

Timetable synchronization for mass transit.

Wong Chi Wing.Thesis (M.Phil.)--Chinese University of Hong Kong, 2004.Includes bibliographical references (leaves 105-106).Abstracts in English and Chinese.Abstract --- p.iAcknowledgement --- p.ivChapter 1 --- Introduction --- p.1Chapter 1.1 --- Motivation --- p.1Chapter 1.2 --- Literature Review --- p.3Chapter 1.3 --- Thesis Outline --- p.5Chapter 2 --- The Timetable Synchronization Problem --- p.7Chapter 2.1 --- Underlying Assumptions --- p.7Chapter 2.2 --- The Timetable Synchronization Problem (TTSP) --- p.10Chapter 2.2.1 --- Time-Horizon Boundary Concerns --- p.10Chapter 2.2.2 --- Transfer Waiting-times Declaration --- p.11Chapter 2.2.3 --- Set Declarations --- p.13Chapter 2.2.4 --- Parameter Declarations --- p.14Chapter 2.2.5 --- Variable Declarations --- p.16Chapter 2.2.6 --- Model Description --- p.17Chapter 2.3 --- Alternative Formulation --- p.22Chapter 2.4 --- Summary --- p.24Chapter 3 --- Solution Approach --- p.25Chapter 3.1 --- Computation Comparison of the Two Formulation --- p.25Chapter 3.2 --- CPLEX Parameter Settings --- p.26Chapter 3.3 --- Optimization-based Heuristic Method (OHM) --- p.26Chapter 3.3.1 --- Why Modify? - Sharper LP-Relaxation --- p.28Chapter 3.3.2 --- How to Predict and Release --- p.30Chapter 3.4 --- Performance of the OHM --- p.31Chapter 3.5 --- Summary --- p.32Chapter 4 --- Case Study of the MTR in HK --- p.33Chapter 4.1 --- Problem Settings --- p.33Chapter 4.1.1 --- Train Routes --- p.33Chapter 4.1.2 --- Cross-platform Times --- p.34Chapter 4.1.3 --- Testing Horizon --- p.35Chapter 4.1.4 --- Number of Trains --- p.35Chapter 4.1.5 --- Allowable Adjustments to Operational Parameters --- p.36Chapter 4.2 --- Solution Quality --- p.37Chapter 4.2.1 --- Average Transfer Waiting-times --- p.37Chapter 4.2.2 --- Possible Maximum Transfer Waiting-times --- p.37Chapter 4.2.3 --- """Just Miss""" --- p.38Chapter 4.3 --- Summary --- p.39Chapter 5 --- Solution Quality in Different Settings --- p.40Chapter 5.1 --- Optional Operational Constraints I - Improve Regularity --- p.41Chapter 5.1.1 --- Regularity of Dwell-times --- p.41Chapter 5.1.2 --- Regularity of Headway --- p.43Chapter 5.2 --- Cases Analysis I --- p.44Chapter 5.2.1 --- Case Analysis 1 - l Steps to Use the System --- p.45Chapter 5.2.2 --- Case Analysis 2 - Varying Run-times --- p.47Chapter 5.2.3 --- Case Analysis 3 - Non-rush Hour --- p.49Chapter 5.2.4 --- Case Analysis 4 - Varying Regularity of Dwell-times . . --- p.52Chapter 5.3 --- Cases Analysis II --- p.55Chapter 5.3.1 --- Optional Operational Constraints II - Increasing Dwell-times (1) --- p.55Chapter 5.3.2 --- Case Analysis 5 - Adding Special Dwell-times Bounds . --- p.56Chapter 5.4 --- Case Analysis III --- p.58Chapter 5.4.1 --- Optional Operational Constraints III - Increasing Dwell-times (2) --- p.58Chapter 5.4.2 --- Case Analysis 6 - Adding Modified Special Dwell-times Bounds --- p.59Chapter 5.5 --- Future Work --- p.61Chapter 6 --- Timetable-Synchronization System --- p.62Chapter 6.1 --- Hierarchy of the Timetable-Synchronization System --- p.64Chapter 6.2 --- Use of the Component Software Tools --- p.66Chapter 6.2.1 --- ILOG CPLEX 7.5 --- p.66Chapter 6.2.2 --- Microsoft Visual Basic. Net 2003 --- p.66Chapter 6.2.3 --- Microsoft Office XP - Excel --- p.67Chapter 6.2.4 --- Microsoft Office XP - Access --- p.68Chapter 6.3 --- Summary --- p.69Chapter 7 --- Conclusions --- p.70Chapter 7.1 --- Summary and Further Studies --- p.70Appendix --- p.72Chapter A --- The MTR System in HK --- p.73Chapter B --- Abbreviation of Routes --- p.74Chapter C --- Abbreviation of Interchange Stations --- p.75Chapter D --- Passenger Groups --- p.76Chapter E --- Average Transfer Waiting-times (08:00-ج09:00) --- p.78Chapter F --- Maximum Transfer Waiting-times (08:00-ج09:00) --- p.79Chapter G --- Using the Timetable-Synchronization System --- p.80Chapter G.l --- Steps to Use the System --- p.82Chapter H --- Timetable-Synchronization System Problem Generator --- p.85Chapter H.1 --- "Use of the ""Timetable-Synchronization System Problem Gen- erator""" --- p.85Chapter H.2 --- "Hierarchy of the ""Timetable-Synchronization System Problem Generator""" --- p.86Chapter H.3 --- "Using the ""Timetable-Synchronization System Problem Gen- erator""" --- p.87Chapter I --- Transfer Waiting-time Calculator --- p.94Chapter I.1 --- Use of Transfer Waiting-time Calculator --- p.94Chapter I.2 --- Using the Transfer Waiting-time Calculator --- p.95Chapter J --- Database Structure in Microsoft Access --- p.97Chapter J.1 --- Operational Parameters --- p.98Chapter J.1.1 --- Use of Operational Parameters --- p.98Chapter J.1.2 --- Structure of the Tables --- p.98Chapter J.2 --- Current Timetable --- p.102Chapter J.2.1 --- Use of Current Timetable --- p.102Chapter J.2.2 --- Structure of the Tables --- p.102Chapter J.3 --- Patronage --- p.103Chapter J.3.1 --- Structure of the Table --- p.104Bibliography --- p.10

Scheduling Models with Additional Features: Synchronization, Pliability and Resiliency

In this thesis we study three new extensions of scheduling models with both practical and theoretical relevance, namely synchronization, pliability and resiliency. Synchronization has previously been studied for flow shop scheduling and we now apply the concept to open shop models for the first time. Here, as opposed to the traditional models, operations that are processed together all have to be started at the same time. Operations that are completed are not removed from the machines until the longest operation in their group is finished. Pliability is a new approach to model flexibility in flow shops and open shops. In scheduling with pliability, parts of the processing load of the jobs can be re-distributed between the machines in order to achieve better schedules. This is applicable, for example, if the machines represent cross-trained workers. Resiliency is a new measure for the quality of a given solution if the input data are uncertain. A resilient solution remains better than some given bound, even if the original input data are changed. The more we can perturb the input data without the solution losing too much quality, the more resilient the solution is. We also consider the assignment problem, as it is the traditional combinatorial optimization problem underlying many scheduling problems. Particularly, we study a version of the assignment problem with a special cost structure derived from the synchronous open shop model and obtain new structural and complexity results. Furthermore we study resiliency for the assignment problem. The main focus of this thesis is the study of structural properties, algorithm development and complexity. For synchronous open shop we show that for a fixed number of machines the makespan can be minimized in polynomial time. All other traditional scheduling objectives are at least as hard to optimize as in the traditional open shop model. Starting out research in pliability we focus on the most general case of the model as well as two relevant special cases. We deliver a fairly complete complexity study for all three versions of the model. Finally, for resiliency, we investigate two different questions: `how to compute the resiliency of a given solution?' and `how to find a most resilient solution?'. We focus on the assignment problem and single machine scheduling to minimize the total sum of completion times and present a number of positive results for both questions. The main goal is to make a case that the concept deserves further study

Relativity and Accelerator Engineering

From a geometrical viewpoint, according to the theory of relativity, space and time constitute a four-dimensional continuum with pseudo-Euclidean structure. This has recently begun to be a practically important statement in accelerator physics. An X-ray Free Electron Laser (XFEL) is in fact the best, exciting example of an engineering system where improvements in accelerator technology makes it possible to develop ultrarelativistic macroscopic objects with an internal fine structure, and the theory of relativity plays an essential role in their description. An ultrarelativistic electron bunch modulated at nanometer-scale in XFELs has indeed a macroscopic finite-size of order of 10 $\mu$m. Its internal, collective structure is characterized in terms of a wave number vector. Here we will show that a four-dimensional geometrical approach, unusual in accelerator physics, is needed to solve problems involving the emission of radiation from an ultrarelativistic modulated electron beam accelerating along a curved trajectory. We will see that relativistic kinematics enters XFEL physics in a most fundamental way through the so-called Wigner rotation of the modulation wave number vector, which is closely associated to the relativity of simultaneity. If not taken into account, relativistic kinematics effects would lead to a strong qualitative disagreement between theory and experiments. In this paper, several examples of relativistic kinematics effects, which are important for current and future XFEL operation, are studied. The theory of relativity is applied by providing details of the clock synchronization procedure within the laboratory frame. This approach, exploited here but unusual in literature, is rather "practical", and should be acceptable to accelerator physicists

A characteristic particle method for traffic flow simulations on highway networks

A characteristic particle method for the simulation of first order macroscopic traffic models on road networks is presented. The approach is based on the method "particleclaw", which solves scalar one dimensional hyperbolic conservations laws exactly, except for a small error right around shocks. The method is generalized to nonlinear network flows, where particle approximations on the edges are suitably coupled together at the network nodes. It is demonstrated in numerical examples that the resulting particle method can approximate traffic jams accurately, while only devoting a few degrees of freedom to each edge of the network.Comment: 15 pages, 5 figures. Accepted to the proceedings of the Sixth International Workshop Meshfree Methods for PDE 201

Robust Rotation Synchronization via Low-rank and Sparse Matrix Decomposition

This paper deals with the rotation synchronization problem, which arises in global registration of 3D point-sets and in structure from motion. The problem is formulated in an unprecedented way as a "low-rank and sparse" matrix decomposition that handles both outliers and missing data. A minimization strategy, dubbed R-GoDec, is also proposed and evaluated experimentally against state-of-the-art algorithms on simulated and real data. The results show that R-GoDec is the fastest among the robust algorithms.Comment: The material contained in this paper is part of a manuscript submitted to CVI