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

On tolerable and desirable behaviors in supervisory control of discrete event systems

We formulate and solve a new supervisory control problem for discrete event systems. The objective is to design a logical controller—or supervisor—such that the discrete event system satisfies a given set of requirements that involve event ordering. The controller must deal with a limited amount of controllability in the form of uncontrollable events. Our problem formulation considers that the requirements for the behavior (i.e., set of traces) of the controlled system are specified in terms of a “desired” behavior and a larger “tolerated” behavior. Due to the uncontrollable events, one may wish to tolerate behavior that sometimes exceeds the ideal desired behavior if overall this results in achieving more of the desired behavior. The general solution of our problem is completely characterized. The nonblocking solution is also analyzed in detail. This solution requires the study of a new class of controllable languages. Several results are proved about this class of languages. Algorithms to compute certain languages of interest within this class are also presented.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45034/1/10626_2005_Article_BF01797143.pd

Randomness for Free

We consider two-player zero-sum games on graphs. These games can be classified on the basis of the information of the players and on the mode of interaction between them. On the basis of information the classification is as follows: (a) partial-observation (both players have partial view of the game); (b) one-sided complete-observation (one player has complete observation); and (c) complete-observation (both players have complete view of the game). On the basis of mode of interaction we have the following classification: (a) concurrent (both players interact simultaneously); and (b) turn-based (both players interact in turn). The two sources of randomness in these games are randomness in transition function and randomness in strategies. In general, randomized strategies are more powerful than deterministic strategies, and randomness in transitions gives more general classes of games. In this work we present a complete characterization for the classes of games where randomness is not helpful in: (a) the transition function probabilistic transition can be simulated by deterministic transition); and (b) strategies (pure strategies are as powerful as randomized strategies). As consequence of our characterization we obtain new undecidability results for these games

Towards Efficient Exact Synthesis for Linear Hybrid Systems

We study the problem of automatically computing the controllable region of a Linear Hybrid Automaton, with respect to a safety objective. We describe the techniques that are needed to effectively and efficiently implement a recently-proposed solution procedure, based on polyhedral abstractions of the state space. Supporting experimental results are presented, based on an implementation of the proposed techniques on top of the tool PHAVer.Comment: In Proceedings GandALF 2011, arXiv:1106.081

Recursive computation of limited lookahead supervisory controls for discrete event systems

We continue the study of limited lookahead policies in supervisory control of discrete event systems undertaken in a previous paper. On-line control of discrete event systems using limited lookahead policies requires, after the execution of each event, the calculation of the supremal controllable sublanguage of a given language with respect to another larger language. These two languages are finite and represented by their tree generators, where one tree is a subtree of the other. These trees change dynamically from step to step, where one step is the execution of one event by the system. We show in this paper how to perform this calculation in a recursive manner, in the sense that the calculation for a new pair of trees can make use of the calculation for the preceding pair, thus substantially reducing the amount of computation that has to be done on-line. In order to make such a recursive procedure possible from step to step, we show how the calculation for a single step (i.e., for a given pair of trees) can itself be performed recursively by means of a backward dynamic programming algorithm on the vertices of the larger tree. These two nested recursive procedures are also extended to the limited lookahead version of the “supervisory control problem with tolerance.”Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45118/1/10626_2005_Article_BF01439177.pd

Semiperfect-Information Games

Abstract. Much recent research has focused on the applications of games with!-regular objectives in the control and verication of reactive systems. However, many of the game-based models are ill-suited for these applications, because they assume that each player has complete infor-mation about the state of the system (they are \perfect-information" games). This is because in many situations, a controller does not see the private state of the plant. Such scenarios are naturally modeled by \partial-information " games. On the other hand, these games are in-tractable; for example, partial-information games with simple reachabil-ity objectives are 2EXPTIME-complete. We study the intermediate case of \semiperfect-information " games, where one player has complete knowledge of the state, while the other player has only partial knowledge. This model is appropriate in con-trol situations where a controller must cope with plant behavior that is as adversarial as possible, i.e., the controller has partial informa-tion while the plant has perfect information. As is customary, we as-sume that the controller and plant take turns to make moves. We show that these semiperfect-information turn-based games are equiv-alent to perfect-information concurrent games, where the two play-ers choose their moves simultaneously and independently. Since the perfect-information concurrent games are well-understood, we obtain several results of how semiperfect-information turn-based games dif-fer from perfect-information turn-based games on one hand, and from partial-information turn-based games on the other hand. In particular, semiperfect-information turn-based games can benet from randomized strategies while the perfect-information variety cannot, and semiperfect-information turn-based games are in NP \ coNP for all parity objectives.

The 2-codeword screening test for lasso problems

Solving a lasso problem is a practical approach for acquiring a sparse representation of a signal with respect to a given dictionary. Driven by the demand for sparse representations over large-scale data in machine learning and statistics, we explore lasso screening tests. These enhance solution efficiency via the elimination of codewords absent in the optimal solution prior to detailed computation. On basis of the concept of a region test and the recently introduced dome test, we propose the 2-codeword test, which uses two codewords together in a correlation screening test. In addition to the rejection rate as the performance measure, we introduce an innovative way to access the performance of a screening test, called the uncertainty measure, via a comparison with the optimal test. © 2013 IEEE