IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS, VOL. 12, NO. 4, DECEMBER 2011 1167 Optimization-Based Feedback Control for Pedestrian Evacuation From an Exit Corridor Apoorva Shende, Mahendra P. Singh, and Pushkin Kachroo Abstract—The evacuation of pedestrians is the most important task when a building is subjected to a significant level of threat that compromises occupant safety. However, very few studies have dealt with the problem of controlling pedestrian evacuation in real time. Due to modern developments in sensor technology and computational facilities, it now seems possible to attempt a real-time controlled evacuation by instructing pedestrians to adjust their velocities according to an algorithm to effect an efficient evacuation. This paper deals with the development of such a control algorithm for an exit corridor where high congestion can be expected during evacuation. To accommodate the possible variation in the pedestrian density along the length, the corridor is divided into several sections. Using the conservation of pedestrian mass, ordinary differential equations that define the pedestrian flow in all sections are developed. For the system of state-space equations that define the flow in all the sections of the corridor, an optimization-based feedback control scheme is developed, which ensures the maximum input discharge subject to tracking the critical state and boundedness of the control variables. Simulation results are obtained, which indicate the superior performance of the controlled flow over the uncontrolled flow. The proposed flow control is also applicable to the regulation of vehicular traffic on a long section of a freeway in urban areas that receives input at several ramps along its length. Index Terms—Conservation of mass, feedback linearization, linear programming, pedestrian evacuation, traffic flow models. I. I NTRODUCTION T HE EVACUATION of occupants is of primary concern when a building is engulfed in an emergency situation caused by fire, an earthquake, or a terrorist attack. In such situations, an organized evacuation of the occupants from the building is most desired. To accomplish such an efficient evac- uation of pedestrians, we propose a feedback control algorithm for pedestrian evacuation from an exit corridor. Exit corridors will have high usage demand during an evacuation, because all the pedestrians in the building will have to use one exit Manuscript received August 11, 2009; revised July 31, 2010 and February 20, 2011; accepted April 10, 2011. Date of publication May 27, 2011; date of current version December 5, 2011. This work was supported in part by the National Science Foundation (with Dr. S. C. Liu as the Program Director) under Grant CMS-0428196. Any opinion, findings, and conclusions or recommendations expressed in this paper are those of the authors and do not necessarily reflect the views of the National Science Foundation. The Associate Editor for this paper was Z. Li. A. Shende and M. P. Singh are with the Department of Engineering Science and Mechanics, Virginia Polytechnic Institute and State University (Virginia Tech), Blacksburg, VA 24060 USA (e-mail: apoorva@vt.edu; mpsingh@ vt.edu). P. Kachroo is with the Transportation Research Center and the De- partment of Electrical and Computer Engineering, University of Nevada, Las Vegas, NV 89154 USA (e-mail: pushkin@unlv.edu). Digital Object Identifier 10.1109/TITS.2011.2146251 corridor or another to finally exit the building in a relatively short span of time. Pedestrians would enter such a corridor from its back end and adjacent rooms and exit from the front end into the free space. The broad objective of control here is to achieve a smooth flow of pedestrians without the development of any congestion that leads to stoppage. This paper must, of course, be complimented with the development of sensors (e.g., cameras) to sense the pedestrian congestion level and actuators (e.g., video displays, light arrays, and speakers) to convey the desired control actions to the pedestrians. In addition, a study of human responses to the signals from actuators is required for implementation in a real building. These issues, however, are not a part of this paper. This paper assumes that the pedestrian flow in an evacuation scenario is directional, i.e., it is only in the direction toward the exit. For such situations, it is possible to use the techniques of the control theory to improve the flow characteristics. The pedestrian flow will, indeed, be directional in an evacuation scenario, because all pedestrians share the common objective of leaving the building through the exit closest to them. This paper identifies the parameters that can be used to control the pedestrian motion during evacuation and develops a model- based control algorithm to adjust these parameters to reach a desired outcome. In the study of pedestrian flow, both microscopic and macro- scopic flow models have been considered. In microscopic flow models, the flow dynamics are based on the motion of individ- ual pedestrians, which results from their purpose of performing the motion and their interactions with other pedestrians and sur- rounding influences. These models are best suited for including the behavioral aspects of pedestrians in flow modeling, thus generating detailed simulations. More details with regard to microscopic modeling can be found in [1]–[12]. A macroscopic model, on the other hand, gives a big-picture averaged view of the pedestrian flow situation. It is based on the assumption that the pedestrian flow can be treated as a continuum. This assumption directly results in the use of conservation equa- tions in flow modeling. The detailed interactions of pedestrians are overlooked to attain the global flow scenario in terms of relatively fewer and simpler equations. Various macroscopic models that address different aspects of pedestrian flow can be found in [13]–[19]. In this paper, we adopt a macroscopic model to represent the pedestrian flow similar to the vehicular traffic flow model [20]. Although microscopic models may more accurately predict the pedestrian motion, they are typically rule based, and with a large number of people involved in an evacuation, they can be computationally intensive and, hence, unsuitable for real-time 1524-9050/$26.00 © 2011 IEEE