Approximation to the Optimal Strategy in the Mozart Café Problem by Simultaneous Perturbation Stochastic Approximation

The rendezvous search problem is an old and classic problem in operations research. In this problem, two agents with unit speed are placed in some common region and they try to find each other in the least expected time with the assumption that they neither have devices for communication nor necessarily share the same coordinates/directions. In this thesis, we focus on one specific problem in this field, called the “Mozart Café problem,” in which two agents search for each other among n discrete locations (cafés). They can go to any café each day and will stay there the whole day waiting for the other to come, and they wish to minimize the expected time to rendezvous. Previous researchers have found and shown the optimal strategies for n = 2, 3 cases. In this study, we first present some preliminary work on a variant of the general Mozart Café problem on the n = 4 case in which each agent can leave a token in the initial café he visits saying that he would never come back. The optimal strategy on this variant provides a lower bound for the optimal expected rendezvous time in the general n = 4 case. Then we propose a novel modelling technique named k-Markovian modelling where the model parameters can be optimized by stochastic optimization algorithms. This also parameterizes this problem. The aims of this work are to provide a parameterization method and demonstrate the potential to approximate the optimal rendezvous search strategy

Allocating patrolling resources to effectively thwart intelligent attackers

This thesis considers the allocation of patrolling resources deployed in an effort to thwart intelligent attackers, who are committing malicious acts at unknown locations which take a specified length of time to complete. This thesis considers patrolling games which depend on three parameters; a graph, a game length and an attack length. For patrolling games, the graph models the locations and how they are connected, the game length corresponds to the time-horizon in which two players, known as the patroller and attacker, act and the attack length is the time it takes an attacker to complete their malicious act. This thesis defines patrolling games (as first seen in [16]) and explains its known properties and how such games are solved. While any patrolling game can be solved by a linear program (LP) when the number of locations or game length is small, this becomes infeasible when either of these parameters are of moderate size. Therefore, strategies are often evaluated by knowing an opponent’s response and with this, patroller and attacker strategies give lower and upper bounds on the optimal value. Moreover, when tight bounds are given by strategies these are optimal strategies. This thesis states known strategies giving these bounds and classes for which patrolling games have been solved. Firstly, this thesis introduces new techniques which can be used to evaluate strategies, by reducing the strategy space for best responses from an opponent. Extensions to known strategies are developed and their respective bounds are given using known results. In addition we develop a patroller improvement program (PIP) which improves current patroller strategies by considering which locations are currently under performing. Secondly, these general techniques and strategies are applied to find solutions to a certain class of patrolling games which are not previously solved. In particular, classes of the patrolling game are solved when the graph is multipartite or is an extension of a star graph. Thirdly, this thesis conjectures that a developed patroller strategy known as the random minimal full-node cycle is optimal for a large class of patrolling games, when the graph is a tree. Intuitive reasoning behind the conjecture is given along with computational evidence, showing the conjecture holds when the number of locations in the graph is less than 9. Finally, this thesis looks at three extensions to the scenario modelled by the patrolling game. One extension models varying distances between locations rather than assuming locations are a unitary distance apart. Another extension allows the time needed for an attacker to complete their malicious act to vary depending on the vulnerability of the location. For the final extension of multiple players we look at four variants depending on how multiple attackers succeed in the extension. In each extension we find some properties of the game and show that it possible to relate # extensions to the classic patrolling game in order to find the value and optimal strategies for certain classes of such games

Allocating patrolling resources to effectively thwart intelligent attackers

This thesis considers the allocation of patrolling resources deployed in an effort to thwart intelligent attackers, who are committing malicious acts at unknown locations which take a specified length of time to complete. This thesis considers patrolling games which depend on three parameters; a graph, a game length and an attack length. For patrolling games, the graph models the locations and how they are connected, the game length corresponds to the time-horizon in which two players, known as the patroller and attacker, act and the attack length is the time it takes an attacker to complete their malicious act. This thesis defines patrolling games (as first seen in [16]) and explains its known properties and how such games are solved. While any patrolling game can be solved by a linear program (LP) when the number of locations or game length is small, this becomes infeasible when either of these parameters are of moderate size. Therefore, strategies are often evaluated by knowing an opponent’s response and with this, patroller and attacker strategies give lower and upper bounds on the optimal value. Moreover, when tight bounds are given by strategies these are optimal strategies. This thesis states known strategies giving these bounds and classes for which patrolling games have been solved. Firstly, this thesis introduces new techniques which can be used to evaluate strategies, by reducing the strategy space for best responses from an opponent. Extensions to known strategies are developed and their respective bounds are given using known results. In addition we develop a patroller improvement program (PIP) which improves current patroller strategies by considering which locations are currently under performing. Secondly, these general techniques and strategies are applied to find solutions to a certain class of patrolling games which are not previously solved. In particular, classes of the patrolling game are solved when the graph is multipartite or is an extension of a star graph. Thirdly, this thesis conjectures that a developed patroller strategy known as the random minimal full-node cycle is optimal for a large class of patrolling games, when the graph is a tree. Intuitive reasoning behind the conjecture is given along with computational evidence, showing the conjecture holds when the number of locations in the graph is less than 9. Finally, this thesis looks at three extensions to the scenario modelled by the patrolling game. One extension models varying distances between locations rather than assuming locations are a unitary distance apart. Another extension allows the time needed for an attacker to complete their malicious act to vary depending on the vulnerability of the location. For the final extension of multiple players we look at four variants depending on how multiple attackers succeed in the extension. In each extension we find some properties of the game and show that it possible to relate # extensions to the classic patrolling game in order to find the value and optimal strategies for certain classes of such games

Nonlinear Control Strategies for Cooperative Control of Multi-Robot Systems

This thesis deals with distributed control strategies for cooperative control of multi-robot systems. Specifically, distributed coordination strategies are presented for groups of mobile robots. The formation control problem is initially solved exploiting artificial potential fields. The purpose of the presented formation control algorithm is to drive a group of mobile robots to create a completely arbitrarily shaped formation. Robots are initially controlled to create a regular polygon formation. A bijective coordinate transformation is then exploited to extend the scope of this strategy, to obtain arbitrarily shaped formations. For this purpose, artificial potential fields are specifically designed, and robots are driven to follow their negative gradient. Artificial potential fields are then subsequently exploited to solve the coordinated path tracking problem, thus making the robots autonomously spread along predefined paths, and move along them in a coordinated way. Formation control problem is then solved exploiting a consensus based approach. Specifically, weighted graphs are used both to define the desired formation, and to implement collision avoidance. As expected for consensus based algorithms, this control strategy is experimentally shown to be robust to the presence of communication delays. The global connectivity maintenance issue is then considered. Specifically, an estimation procedure is introduced to allow each agent to compute its own estimate of the algebraic connectivity of the communication graph, in a distributed manner. This estimate is then exploited to develop a gradient based control strategy that ensures that the communication graph remains connected, as the system evolves. The proposed control strategy is developed initially for single-integrator kinematic agents, and is then extended to Lagrangian dynamical systems

Computer algebra and transputers applied to the finite element method

Recent developments in computing technology have opened new prospects for computationally intensive numerical methods such as the finite element method. More complex and refined problems can be solved, for example increased number and order of the elements improving accuracy. The power of Computer Algebra systems and parallel processing techniques is expected to bring significant improvement in such methods. The main objective of this work has been to assess the use of these techniques in the finite element method. The generation of interpolation functions and element matrices has been investigated using Computer Algebra. Symbolic expressions were obtained automatically and efficiently converted into FORTRAN routines. Shape functions based on Lagrange polynomials and mapping functions for infinite elements were considered. One and two dimensional element matrices for bending problems based on Hermite polynomials were also derived. Parallel solvers for systems of linear equations have been developed since such systems often arise in numerical methods. Both symmetric and asymmetric solvers have been considered. The implementation was on Transputer-based machines. The speed-ups obtained are good. An analysis by finite element method of a free surface flow over a spillway has been carried out. Computer Algebra was used to derive the integrand of the element matrices and their numerical evaluation was done in parallel on a Transputer-based machine. A graphical interface was developed to enable the visualisation of the free surface and the influence of the parameters. The speed- ups obtained were good. Convergence of the iterative solution method used was good for gated spillways. Some problems experienced with the non-gated spillways have lead to a discussion and tests of the potential factors of instability

Research Reports: 1984 NASA/ASEE Summer Faculty Fellowship Program

A NASA/ASEE Summer Faulty Fellowship Program was conducted at the Marshall Space Flight Center (MSFC). The basic objectives of the programs are: (1) to further the professional knowledge of qualified engineering and science faculty members; (2) to stimulate an exchange of ideas between participants and NASA; (3) to enrich and refresh the research and teaching activities of the participants' institutions; and (4) to contribute to the research objectives of the NASA Centers. The Faculty Fellows spent ten weeks at MSFC engaged in a research project compatible with their interests and background and worked in collaboration with a NASA/MSFC colleague. This document is a compilation of Fellows' reports on their research during the summer of 1984. Topics covered include: (1) data base management; (2) computational fluid dynamics; (3) space debris; (4) X-ray gratings; (5) atomic oxygen exposure; (6) protective coatings for SSME; (7) cryogenics; (8) thermal analysis measurements; (9) solar wind modelling; and (10) binary systems

Collaborative Communication And Storage In Energy-Synchronized Sensor Networks

In a battery-less sensor network, all the operation of sensor nodes are strictly constrained by and synchronized with the fluctuations of harvested energy, causing nodes to be disruptive from network and hence unstable network connectivity. Such wireless sensor network is named as energy-synchronized sensor networks. The unpredictable network disruptions and challenging communication environments make the traditional communication protocols inefficient and require a new paradigm-shift in design. In this thesis, I propose a set of algorithms on collaborative data communication and storage for energy-synchronized sensor networks. The solutions are based on erasure codes and probabilistic network codings. The proposed set of algorithms significantly improve the data communication throughput and persistency, and they are inherently amenable to probabilistic nature of transmission in wireless networks. The technical contributions explore collaborative communication with both no coding and network coding methods. First, I propose a collaborative data delivery protocol to exploit the optimal performance of multiple energy-synchronized paths without network coding, i.e. a new max-flow min-variance algorithm. In consort with this data delivery protocol, a localized TDMA MAC protocol is designed to synchronize nodes\u27 duty-cycles and mitigate media access contentions. However, the energy supply can change dynamically over time, making determined duty cycles synchronization difficult in practice. A probabilistic approach is investigated. Therefore, I present Opportunistic Network Erasure Coding protocol (ONEC), to collaboratively collect data. ONEC derives the probability distribution of coding degree in each node and enable opportunistic in-network recoding, and guarantee the recovery of original sensor data can be achieved with high probability upon receiving any sufficient amount of encoded packets. Next, OnCode, an opportunistic in-network data coding and delivery protocol is proposed to further improve data communication under the constraints of energy synchronization. It is resilient to packet loss and network disruptions, and does not require explicit end-to-end feedback message. Moreover, I present a network Erasure Coding with randomized Power Control (ECPC) mechanism for collaborative data storage in disruptive sensor networks. ECPC only requires each node to perform a single broadcast at each of its several randomly selected power levels. Thus it incurs very low communication overhead. Finally, I propose an integrated algorithm and middleware (Ravine Stream) to improve data delivery throughput as well as data persistency in energy-synchronized sensor network

Proceedings of the 22nd Conference on Formal Methods in Computer-Aided Design – FMCAD 2022

The Conference on Formal Methods in Computer-Aided Design (FMCAD) is an annual conference on the theory and applications of formal methods in hardware and system verification. FMCAD provides a leading forum to researchers in academia and industry for presenting and discussing groundbreaking methods, technologies, theoretical results, and tools for reasoning formally about computing systems. FMCAD covers formal aspects of computer-aided system design including verification, specification, synthesis, and testing