Verification of the observer property in discrete event systems

The observer property is an important condition to be satisfied by abstractions of Discrete Event System (DES) models. This technical note presents a new algorithm that tests if an abstraction of a DES obtained through natural projection has the observer property. The procedure, called OP-Verifier, can be applied to (potentially nondeterministic) automata, with no restriction on the existence of cycles of 'non-relevant' events. This procedure has quadratic complexity in the number of states. The performance of the algorithm is illustrated by a set of experiments

Constructing Integrable Third Order Systems:The Gambier Approach

We present a systematic construction of integrable third order systems based on the coupling of an integrable second order equation and a Riccati equation. This approach is the extension of the Gambier method that led to the equation that bears his name. Our study is carried through for both continuous and discrete systems. In both cases the investigation is based on the study of the singularities of the system (the Painlev\'e method for ODE's and the singularity confinement method for mappings).Comment: 14 pages, TEX FIL

A graph-theoretic optimal control problem for terminating discrete event processes

Most of the results to date in discrete event supervisory control assume a “zero-or-infinity” structure for the cost of controlling a discrete event system, in the sense that it costs nothing to disable controllable events while uncontrollable events cannot be disabled (i.e., their disablement entails infinite cost). In several applications however, a more refined structure of the control cost becomes necessary in order to quantify the tradeoffs between candidate supervisors. In this paper, we formulate and solve a new optimal control problem for a class of discrete event systems. We assume that the system can be modeled as a finite acylic directed graph, i.e., the system process has a finite set of event trajectories and thus is “terminating.” The optimal control problem explicitly considers the cost of control in the objective function. In general terms, this problem involves a tradeoff between the cost of system evolution, which is quantified in terms of a path cost on the event trajectories generated by the system, and the cost of impacting on the external environment, which is quantified as a dynamic cost on control. We also seek a least restrictive solution. An algorithm based on dynamic programming is developed for the solution of this problem. This algorithm is based on a graph-theoretic formulation of the problem. The use of dynamic programming allows for the efficient construction of an “optimal subgraph” (i.e., optimal supervisor) of the given graph (i.e., discrete event system) with respect to the cost structure imposed. We show that this algorithm is of polynomial complexity in the number of vertices of the graph of the system.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45109/1/10626_2005_Article_BF01797725.pd

Linearisable Mappings and the Low-Growth Criterion

We examine a family of discrete second-order systems which are integrable through reduction to a linear system. These systems were previously identified using the singularity confinement criterion. Here we analyse them using the more stringent criterion of nonexponential growth of the degrees of the iterates. We show that the linearisable mappings are characterised by a very special degree growth. The ones linearisable by reduction to projective systems exhibit zero growth, i.e. they behave like linear systems, while the remaining ones (derivatives of Riccati, Gambier mapping) lead to linear growth. This feature may well serve as a detector of integrability through linearisation.Comment: 9 pages, no figur

Kinematic characteristics of elite men's 50 km race walking.

Race walking is an endurance event which also requires great technical ability, particularly with respect to its two distinguishing rules. The 50 km race walk is the longest event in the athletics programme at the Olympic Games. The aims of this observational study were to identify the important kinematic variables in elite men's 50 km race walking, and to measure variation in those variables at different distances. Thirty men were analysed from video data recorded during a World Race Walking Cup competition. Video data were also recorded at four distances during the European Cup Race Walking and 12 men analysed from these data. Two camcorders (50 Hz) recorded at each race for 3D analysis. The results of this study showed that walking speed was associated with both step length (r=0.54,P=0.002) and cadence (r=0.58,P=0.001). While placing the foot further ahead of the body at heel strike was associated with greater step lengths (r=0.45,P=0.013), it was also negatively associated with cadence (r= -0.62,P<0.001). In the World Cup, knee angles ranged between 175 and 186° at initial contact and between 180 and 195° at midstance. During the European Cup, walking speed decreased significantly (F=9.35,P=0.002), mostly due to a decrease in step length between 38.5 and 48.5 km (t=8.59,P=0.014). From this study, it would appear that the key areas a 50 km race walker must develop and coordinate are step length and cadence, although it is also important to ensure legal walking technique is maintained with the onset of fatigue

Dynamic system-optimal traffic assignment using a state space model

We propose a new mathematical formulation for the problem of optimal traffic assignment in dynamic networks with multiple origins and destinations. This problem is motivated by route guidance issues that arise in an Intelligent Vehicle-Highway Systems (IVHS) environment. We assume that the network is subject to known time-varying demands for travel between its origins and destinations during a given time horizon. The objective is to assign the vehicles to links over time so as to minimize the total travel time experienced by all the vehicles using the network. We model the traffic network over the time horizon as a discrete-time dynamical system. The system state at each time instant is defined in a way that, without loss of optimality, avoids complete microscopic detail by grouping vehicles into platoons irrespective of origin node and time of entry to network. Moreover, the formulation contains no explicit path enumeration. The state transition function can model link travel times by either impedance functions, link outflow functions, or by a combination of both. Two versions (with different boundary conditions) of the problem of optimal traffic assignment are studied in the context of this model. These optimization problems are optimal control problems for nonlinear discrete-time dynamical systems, and thus they are amenable to algorithmic solutions based on dynamic programming. The computational challenges associated with the exact solution of these problems are discussed and some heuristics are proposed.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/30420/1/0000041.pd

Removing Orbital Debris with Lasers

Orbital debris in low Earth orbit (LEO) are now sufficiently dense that the use of LEO space is threatened by runaway collisional cascading. A problem predicted more than thirty years ago, the threat from debris larger than about 1 cm demands serious attention. A promising proposed solution uses a high power pulsed laser system on the Earth to make plasma jets on the objects, slowing them slightly, and causing them to re-enter and burn up in the atmosphere. In this paper, we reassess this approach in light of recent advances in low-cost, light-weight modular design for large mirrors, calculations of laser-induced orbit changes and in design of repetitive, multi-kilojoule lasers, that build on inertial fusion research. These advances now suggest that laser orbital debris removal (LODR) is the most cost-effective way to mitigate the debris problem. No other solutions have been proposed that address the whole problem of large and small debris. A LODR system will have multiple uses beyond debris removal. International cooperation will be essential for building and operating such a system.Comment: 37 pages, 15 figures, in preparation for submission to Advances in Space Researc