Probabilistic Language Framework for Stochastic Discrete Event Systems

We introduce the notion of probabilistic languages to describe the qualitative behavior of stochastic discrete event systems. Regular language operators such as choice, concatenation, and Kleene-closure have been defined in the setting of probabilistic language to allow modeling of complex systems in terms of simpler ones. The set of probabilistic languages is closed under such operators thus forming an algebra. It also is a complete partial order under a natural ordering in which the operators are continuous. Hence recursive equations can be solved in this algebra. This fact is alternatively derived by using contraction mapping theorem on the set of probabilistic languages which is shown to be a complete metric space. The notion of regularity of probabilistic languages has also been identified. We show that this formalism is also useful in describing system performances such as completion time, reliability, etc. and present techniques for computing them

Extension based limited lookahead supervision of discrete event systems

Abstract Supervisory control of discrete event systems using limited lookahead has been studied by Chung-Lafortune-Lin, where control is computed by truncating the plant behavior up to the limited lookahead window. We present a modification of this approach in which the control is computed by extending the plant behavior by arbitrary traces beyond the limited lookahead window. The proposed supervisor avoids the notion of pending traces. Consequently the need for considering either a conservative or an optimistic attitude regarding pending traces (as in the work of Chung-LafortuneLin) does not arise. It was shown that an optimistic attitude may result in violation of the desired specifications. We demonstrate here that a conservative attitude may result in a restrictive control policy by showing that in general the proposed supervisor is less restrictive than the conservative attitude based supervisor. Moreover, the proposed approach uses the notion of relative closure to construct the supervisor so that it is non-blocking even when the desired behavior is not relative closed (Chung-LafortuneLin assume relative closure). Finally, the proposed supervisor possesses all the desirable properties that a conservative attitude based supervisor of Chung-Lafortune-Lin possesses. We illustrate our approach by applying it to concurrency control in database management systems

Extension Based Limited Lookahead Supervision of Discrete Event Systems

Supervisory control of discrete event systems using limited lookahead has been studied by Chung-Lafortune-Lin, where control is computed by truncating the plant behavior up to the limited lookahead window. We present a different approach in which the control is computed by extending the plant behavior by arbitrary traces beyond the limited lookahead window. The proposed supervisor avoids the notion of pending traces. Consequently the need for considering either a conservative or an optimistic attitude regarding pending traces (as in the work of Chung- Lafortune-Lin) does not arise. It was shown that an optimistic attitude may result in violation of the desired specifications. We demonstrate here that a conservative attitude may result in a restrictive control policy by showing that in some cases the proposed supervisor is less restrictive than the conservative attitude-based supervisor. Moreover, the proposed approach uses the notion of relative closure to construct the supervisor so that it is non-blocking even when the desired behavior is not relative closed (Chung-Lafortune-Lin assume relative closure). Finally, the proposed supervisor possesses all the desirable properties that a conservative attitude based supervisor of Chung-Lafortune-Lin possesses. We illustrate our approach by applying it to concurrency control in database management systems

Fractional Calculus and the Future of Science

Newton foresaw the limitations of geometry’s description of planetary behavior and developed fluxions (differentials) as the new language for celestial mechanics and as the way to implement his laws of mechanics. Two hundred years later Mandelbrot introduced the notion of fractals into the scientific lexicon of geometry, dynamics, and statistics and in so doing suggested ways to see beyond the limitations of Newton’s laws. Mandelbrot’s mathematical essays suggest how fractals may lead to the understanding of turbulence, viscoelasticity, and ultimately to end of dominance of the Newton’s macroscopic world view.Fractional Calculus and the Future of Science examines the nexus of these two game-changing contributions to our scientific understanding of the world. It addresses how non-integer differential equations replace Newton’s laws to describe the many guises of complexity, most of which lay beyond Newton’s experience, and many had even eluded Mandelbrot’s powerful intuition. The book’s authors look behind the mathematics and examine what must be true about a phenomenon’s behavior to justify the replacement of an integer-order with a noninteger-order (fractional) derivative. This window into the future of specific science disciplines using the fractional calculus lens suggests how what is seen entails a difference in scientific thinking and understanding

Extremal Solutions of Inequations over Lattices with Applications to Supervisory Control

We study the existence and computation of extremal solutions of a system of inequations defined over lattices. Using the Knaster-Tarski fixed point theorem, we obtain sufficient conditions for the existence of supremal as well as infimal solution of a given system of inequations. Iterative techniques are presented for the computation of the extremal solutions whenever they exist, and conditions under which the termination occurs in a single iteration are provided. These results are then applied for obtaining extremal solutions of various inequations that arise in computation of maximally permissive supervisors in control of logical discrete event systems (DESs) first studied by Ramadge and Wonham. Thus our work presents a unifying approach for computation of supervisors in a variety of situations. Keywords: Fixed points, lattices, inequations, discrete event systems, supervisory control, language theory. 1 Introduction Given a set X and a function f : X ! X, x 2 X is called a fixed..

Optimization and Mathematical Modelling for Path Planning of Co-operative Intra-logistics Automated Vehicles

Small indoor Autonomous Vehicles have revolutionized the operation of pick-pack-and-ship warehouses. The challenges for path planning and co-operation in this domain stem from uncontrolled environments including workspaces shared with humans and human-operated vehicles. Solutions are needed which scale up to the largest existing sites with thousands of vehicles and beyond. These challenges might be familiar to anyone modelling road traffic control with the introduction of Autonomous Vehicles, but key differences in the level of decision autonomy lead to different approaches to conflict-resolution. This thesis proposes a decomposition of site-wide conflict-free motion planning into individual shortest paths though a roadmap representing the free space across the site, zone-based speed optimization to resolve conflicts in the vicinity of one intersection and individual path optimization for local obstacles. In numerical tests the individual path optimization based on clothoid basis functions created paths traversable by different vehicle configurations (steering rate limit, lateral acceleration limit and wheelbase) only by choosing an appropriate maximum longitudinal speed. Using two clothoid segments per convex region was sufficient to reach any goal, and the problem could be solved reliably and quickly with sequential quadratic programming due to the approximate graph method used to determine a good sequence of obstacle-free regions to the local goal. A design for zone-based intersection management, obtained by minimizing a linear objective subject to quadratic constraints was refined by the addition of a messaging interface compatible with the path adaptations based on clothoids. A new approximation of the differential constraints was evaluated in a multi-agent simulation of an elementary intersection layout. The proposed FIFO ordering heuristic converted the problem into a linear program. Interior point methods either found a solution quickly or showed that the problem was infeasible, unlike a quadratic constraint formulation with ordering flexibility. Subsequent tests on more complex multi-lane intersection geometries showed the quadratic constraint formulation converged to significantly better solutions than FIFO at the cost of longer and unpredictable search time. Both effects were magnified as the number of vehicles increased. To properly address site-wide conflict-free motion planning, it is essential that the local solutions are compatible with each other at the zone boundaries. The intersection management design was refined with new boundary constraints to ensure compatibility and smooth transitions without the need for a backup system. In numerical tests it was found that the additional boundary constraints were sufficient to ensure smooth transitions on an idealized map including two intersections