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This paper deals with the efficient on-line calculation of supervisory controls for discrete event systems (DES's) in the framework of limited lookahead control policies (or LLPs) that we introduced in previous papers. In the LLP scheme, the control action after a given trace of events has been executed is calculated on-line on the basis of an N-step ahead projection of the behavior of the DES. To compute these controls, one must calculate after the execution of each event the supremal controllable sublanguage of a finite language with respect to another finite larger language. In our previous work, we showed how the required supremal controllable sublanguage calculation can be performed by using a backward dynamic programming algorithm over the nodes of the tree representation of these two languages. In this paper, we pursue the same approach for the calculation of LLP controls, but instead we adopt a forward calculation procedure over the N-level tree of interest. This forward procedure improves upon previous work by avoiding the explicit consideration of all the nodes of the N-level tree, while still permitting tree-to-tree recursiveness as enabled events are executed by the system. The forward search ends whenever a control decision can be made unambiguously or whenever the boundary of the N-level tree is reached, whichever comes first. This motivates the name "Variable Lookahead Policy" (or VLP) for this implementation of the LLP supervisory control scheme. This paper presents a general VLP algorithm and studies the properties of several special cases of it. The paper also discusses the implementation of the VLP algorithms and presents computational results regarding the application of these algorithms to a "time-varying" DES. This paper deals with the efficient on-line calculation of supervisory controls for discrete event systems (DES's) in the framework of limited lookahead control policies that we introduced in Chung, Lafortune, and Lin (1992). It builds upon the results presented in Chung, Lin (1992, 1993a) concerning this framework.Consider a DES that is being controlled by dynamically disabling/enabling events after the execution of each event by the controlled system. In supervisory control with limited lookahead policies (or LLPs), the control action after a given trace of events has been executed is calculated on-line on the basis of an N-step ahead projection of the behavior of 238 CHUNG, LAFORTUNE, AND LIN the DES under consideration; this procedure is repeated after the system executes any one of the enabled events. This is in contrast with the "conventional" supervisory control paradigm (cf. Wonham 1988, Ramadge and where the complete control policy is calculated off-line using automaton models of the DES and of the legal behavior. As discussed in Chung, Lafortune, and Lin (1992), LLPs allow to control certain classes of "time-varying" DES's and they also provide a means for dealing with the computational complexity of supervisor synthesis for DES's with large state spaces.Chung, Lafortune, a...

SUMMARYIn this paper, a fast and automated method of counting pedestrians in crowded areas is proposed along with three contributions. We firstly propose Local Empirical Templates (LET), which are able to outline the foregrounds, typically made by single pedestrians in a scene. LET are extracted by clustering foregrounds of single pedestrians with similar features in silhouettes. This process is done automatically for unknown scenes. Secondly, comparing the size of group foreground made by a group of pedestrians to that of appropriate LET captured in the same image patch with the group foreground produces the density ratio. Because of the local scale normalization between sizes, the density ratio appears to have a bound closely related to the number of pedestrians who induce the group foreground. Finally, to extract the bounds of density ratios for groups of different number of pedestrians, we propose a 3D human models based simulation in which camera viewpoints and pedestrians' proximity are easily manipulated. We collect hundreds of typical occluded-people patterns with distinct degrees of human proximity and under a variety of camera viewpoints. Distributions of density ratios with respect to the number of pedestrians are built based on the computed density ratios of these patterns for extracting density ratio bounds. The simulation is performed in the offline learning phase to extract the bounds from the distributions, which are used to count pedestrians in online settings. We reveal that the bounds seem to be invariant to camera viewpoints and humans' proximity. The performance of our proposed method is evaluated with our collected videos and PETS 2009's datasets. For our collected videos with the resolution of 320x240, our method runs in real-time with good accuracy and frame rate of around 30 fps, and consumes a small amount of computing resources. For PETS 2009's datasets, our proposed method achieves competitive results with other methods tested on the same datasets [1], [2]. key words: local empirical templates, local density ratios, density ratio bounds, and people counting

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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."