Optimal Control Theory in Intelligent Transportation Systems Research - A Review <s> Categorize articles by ITS research objectives <s> Maintenance activities can be performed throughout the lifetime of a particular facility or piece of equipment, thereby affecting its quality in a continuous fashion. It is assumed in this paper that quality of a facility is determined by natural factors, rate of use and maintenance investments while demand for the facility is assumed to be a function of its quality. A dynamic optimization model in the form of a simple linear optimal control problem is then developed in order to determine optimal maintenance policies under these circumstances. Bang-bang and singular policies are derived and given economic interpretations. An algorithm is presented for numerical solution of the Pontryagin necessary conditions. Finally, sufficiency conditions are obtained for the model structure considered. <s> BIB001 </s> Optimal Control Theory in Intelligent Transportation Systems Research - A Review <s> Categorize articles by ITS research objectives <s> The time staging of investment decisions for transportation facilities has generally been analyzed using models which assume a complete independence between transportation level of service and demand for the use of the facility considered. Through the use of a dynamic optimal control model, we analyze the implications of explicitly considering the interrelationship between level of service and demand on the time staging of optimal investment decisions. This analysis leads to a more general time staging decision rule than those previously proposed in the literature; an economic interpretation of that decision rule is given. Second order conditions are developed for various cases of practical significance. Finally, a numerical example is introduced to illustrate the dramatic effect that demand-quality interrelationships can have on the optimal time staging policy. <s> BIB002 </s> Optimal Control Theory in Intelligent Transportation Systems Research - A Review <s> Categorize articles by ITS research objectives <s> This paper presents a control theoretic dynamic model for optimizing the timing and intensity of major highway pavement maintenance actions. The solution procedure is demonstrated through a simple case study, and the worthiness as a problem-solving tool is discussed through a systematic evaluation of the solutions. <s> BIB003 </s> Optimal Control Theory in Intelligent Transportation Systems Research - A Review <s> Categorize articles by ITS research objectives <s> In this paper, we set forth certain axioms for a positive theory of dynamic urban network flows. We then show that mathematical models which fulfill these axioms may be created by adapting and extending certain fundamental notions from microeconomics and nonlinear systems theory. We further show that models created in this fashion, using concepts of fast and slow dynamic processes, may be manipulated into a variety of mathematical forms, thereby providing a synthesis of dynamic systems, variational inequality and control theoretic perspectives for predicting dynamic urban network flows. We close with a discussion of the implications of this synthesis for route guidance and intelligent vehicle infrastructure. Throughout, our presentation is at a conceptual level; the mathematical arguments are purposely not rigorous to embrace the widest possible readership. <s> BIB004 </s> Optimal Control Theory in Intelligent Transportation Systems Research - A Review <s> Categorize articles by ITS research objectives <s> In this paper we develop two types of dynamic congestion pricing model, based on the theory of marginal cost pricing. The first model is appropriate for situations where commuters have the ability to learn the best route choices through day-to-day explorations on a network with arc capacities and travel demands that are stable from day to day. The second model is appropriate for situations where commuters optimize their routing decisions each day on a network with arc capacities and travel demands that fluctuate significantly from day to day. We show that two types of time-varying congestion tolls can be determined by solving a convex control formulation of the dynamic system optimal traffic assignment problem on a network with many origins and many destinations. We also show that the dynamic system optimal traffic assignment is an equilibrium for commuters under the tolls in both cases. <s> BIB005 </s> Optimal Control Theory in Intelligent Transportation Systems Research - A Review <s> Categorize articles by ITS research objectives <s> A collision avoidance/conflict resolution model for aircraft traversing planar intersecting trajectories is developed based on the actual flight dynamics of each aircraft and the criteria that a flight regime correction is optimal if it represents a minimum-time safe deviation from a preassigned flight program. The formulation of the model leads to a singular optimal control problem where the control variable constraint is the maximum acceptable aircraft turn rate for passenger comfort and safety and the state variable constraint is defined in terms of the radius of the protected zone about a potentially conflicting aircraft. A robust, accurate real-time solution procedure is derived for computing the steering program for the execution of the optimal safe avoidance maneuver. Several representative examples of pairwise trajectory conflicts are analysed in detail. A brief discussion of how the model might be generalized to incorporate changes in airspeed and altitude as well as more comprehensive dynamics is included. <s> BIB006 </s> Optimal Control Theory in Intelligent Transportation Systems Research - A Review <s> Categorize articles by ITS research objectives <s> The fleet replacement problem of a profit-maximizing manager is examined using an optimal control model that captures both utilization and replacement decisions. Conditions for optimal utilization of each vessel in the fleet and optimal vessel acquisition and retirement strategies are discussed. The results indicate that the optimal replacement schedule and fleet size are influenced by utilization schedules, and vice versa. Thus, replacement and utilization strategies should be determined jointly. We develop a numerical example to illustrate the model's potential as a practical management decision tool and the procedures to solve it. <s> BIB007 </s> Optimal Control Theory in Intelligent Transportation Systems Research - A Review <s> Categorize articles by ITS research objectives <s> We consider optimal resolution of air traffic (AT) conflicts. Aircraft are assumed to cruise within a given altitude layer and are modeled as a kinematic system with constant velocity and curvature bounds. Aircraft cannot get closer to each other than a predefined safety distance. For such a system of multiple aircraft, we consider the problem of planning optimal paths among given waypoints. Necessary conditions for optimality of solutions are derived and used to devise a parametrization of possible trajectories that turns into efficient numerical solutions to the problem. Simulation results for a realistic aircraft conflict scenario are provided. A decentralized implementation of the optimal conflict resolution scheme is introduced that may allow free-flight coordination in a cooperative airspace management scheme. Impact of decentralization on performance and safety is finally discussed with the help of extensive simulations. <s> BIB008 </s> Optimal Control Theory in Intelligent Transportation Systems Research - A Review <s> Categorize articles by ITS research objectives <s> Real-time, incident-responsive traffic control and management is vital to development of advanced incident management systems in ITS. More importantly, it provides, from an academic point of view, the linkages between incident detection, incident management, and traffic signal control. This study explores the application of a stochastic optimal control approach to real-time, incident-responsive traffic control at isolated intersections. In the methodology development, time-varying lane traffic state variables and control variables are specified to characterize sectionwide interlane and intralane traffic states under conditions of lane-blocking incidents. Following specification of system states, we formulated a discrete-time nonlinear stochastic model that comprises four types of equations, namely (1) recursive equations, (2) measurement equations, (3) incident-induced delay equations, and (4) boundary constraints. From the proposed stochastic model we then developed a stochastic optimal control algorithm to update the time-varying control variables and lane traffic state variables in real-time with lane-blocking incidents at isolated intersections. To generate traffic data used in model tests efficiently, we employed an advanced microscopic traffic simulator, Paramics, Version 3.0, which is developed to model and analyze ITS traffic flow conditions. The preliminary test results indicate that the proposed method can accomplish the goal of real-time, incident-responsive traffic signal control. In addition to proposing a new methodology, we hope that this study can initiate investigation into real-time, incident-responsive traffic control and management to achieve the final goal of networkwide incident-responsive, traffic-optimal control for incident management. <s> BIB009 </s> Optimal Control Theory in Intelligent Transportation Systems Research - A Review <s> Categorize articles by ITS research objectives <s> This paper presents a mathematical programming model for optimal highway pavement rehabilitation planning which minimizes the life-cycle cost for a finite horizon. It extends previous researches in this area by solving the problem of multiple rehabilitation activities on multiple facilities, with realistic empirical models of deterioration and rehabilitation effectiveness. The formulation is based on discrete control theory. A nonlinear pavement performance model and integer decision variables are incorporated into a mixed-integer nonlinear programming (MINLP). Two solution approaches, a branch-and-bound algorithm and a greedy heuristic, are proposed for this model. It is shown that the heuristic results provide a good approximation to the exact optima, but with much lower computational costs. <s> BIB010 </s> Optimal Control Theory in Intelligent Transportation Systems Research - A Review <s> Categorize articles by ITS research objectives <s> In this paper we consider the infinite dimensional variational inequality (VI) formulation of dynamic user equilibrium (DUE) put forward by Friesz et al. (1993) [A variational inequality formulation of the dynamic network user equilibrium problem. Operations Research 41, 179-191] as well as the differential variational inequality (DVI) version reported in Friesz et al. (2001) [Dynamic network user equilibrium with state-dependent time lags. Networks and Spatial Economics 1, 319-347]. We show how the theory of optimal control and the theory of infinite dimensional variational inequalities may be combined to create a simple and effective fixed point algorithm for calculating DUE network flows that are solutions of both formulations. A numerical example is provided. <s> BIB011 </s> Optimal Control Theory in Intelligent Transportation Systems Research - A Review <s> Categorize articles by ITS research objectives <s> We present an integrated framework to address performance prediction and maintenance optimization for transportation infrastructure facilities. The framework is based on formulating the underlying resource allocation problem as discrete-time, stochastic optimal control problem with linear dynamics and a quadratic criterion. Facility deterioration is represented as a time series which provides an attractive and rigorous approach to specify and estimate performance models. The state and decision variables in the framework are continuous which allows the framework to overcome important computational and statistical limitations that do not allow existing optimization models to address various problems that arise the management of transportation infrastructure. To illustrate the advantages of the proposed approach, we conduct a numerical study where we examine the case of multiple technologies being used simultaneously to collect condition data. Specifically, we illustrate how the framework can be used to quantify the effect of the capabilities of inspection technologies, i.e., precision, accuracy and relationships, on life-cycle costs. This information can be used to compute the operational value of combining technologies, and thus, to guide in their selection based on economic criteria. <s> BIB012 </s> Optimal Control Theory in Intelligent Transportation Systems Research - A Review <s> Categorize articles by ITS research objectives <s> This paper presents a stochastic optimal-control-based approach to real-time incident-responsive coordinated ramp control. The proposed coordinated ramp-control methodology includes two major functions, i.e., 1) identification of control-zone-based congestion patterns using the modified generalized-sequential-probability-ratio-testing technology and 2) group-based ramp control using stochastic optimal control coupled with extended Kalman filtering technologies. With the aid of the Paramics microscopic traffic simulator, numerical studies under various simulated incident-induced congestion conditions were conducted. Corresponding numerical results indicate the feasibility of the proposed ramp-control method in responding to diverse lane-blocking incident-induced traffic-congestion conditions <s> BIB013 </s> Optimal Control Theory in Intelligent Transportation Systems Research - A Review <s> Categorize articles by ITS research objectives <s> Due to the loss of vehicle directional stability in emergency maneuvers, a new complete desired model for vehicle handling based on the linear two-degrees-of-freedom (2DOF) model and tire/road conditions is presented to be tracked by the direct yaw moment control (DYC) system. In order to maintain the vehicle actual motions, yaw rate and side-slip angle, close to the proposed desired responses without excessively large external yaw moment, a complete linear quadratic (LQ) optimal problem is formulated and its analytical solution is obtained. Here, the derived control law is evaluated and its different versions are discussed. It is shown that the side-slip tracking by DYC is more effective than the yaw rate control to stabilize vehicle motions in nonlinear regimes. Also, optimal property of the control law provides the possibility of reducing the external yaw moment as low as possible, at the cost of some admissible tracking errors. Simulation studies of vehicle handling, with and without control, have been conducted using a full nonlinear vehicle dynamic model. The results, obtained during various maneuvers, indicate that when the proposed optimal controller is engaged with the model, improvements in the handling performance through a reduced external yaw moment can be acquired. <s> BIB014 </s> Optimal Control Theory in Intelligent Transportation Systems Research - A Review <s> Categorize articles by ITS research objectives <s> This paper investigates a traffic volume control scheme for a dynamic traffic network model which aims to ensure that traffic volumes on specified links do not exceed preferred levels. The problem is formulated as a dynamic user equilibrium problem with side constraints (DUE-SC) in which the side constraints represent the restrictions on the traffic volumes. Travelers choose their departure times and routes to minimize their generalized travel costs, which include early/late arrival penalties. An infinite-dimensional variational inequality (VI) is formulated to model the DUE-SC. Based on this VI formulation, we establish an existence result for the DUE-SC by showing that the VI admits at least one solution. To analyze the necessary condition for the DUE-SC, we restate the VI as an equivalent optimal control problem. The Lagrange multipliers associated with the side constraints as derived from the optimality condition of the DUE-SC provide the traffic volume control scheme. The control scheme can be interpreted as additional travel delays (either tolls or access delays) imposed upon drivers for using the controlled links. This additional delay term derived from the Lagrange multiplier is compared with its counterpart in a static user equilibrium assignment model. If the side constraint is chosen as the storage capacity of a link, the additional delay can be viewed as the effort needed to prevent the link from spillback. Under this circumstance, it is found that the flow is incompressible when the link traffic volume is equal to its storage capacity. An algorithm based on Euler's discretization scheme and nonlinear programming is proposed to solve the DUE-SC. Numerical examples are presented to illustrate the mechanism of the proposed traffic volume control scheme. <s> BIB015 </s> Optimal Control Theory in Intelligent Transportation Systems Research - A Review <s> Categorize articles by ITS research objectives <s> An urban rail-transit emergency response system is developed based on existing artificial systems by analyzing human behaviors from a pedestrian dynamics viewpoint. This enables necessary computational experiments on the systems that can ultimately lead to the establishment of a database of emergency response strategies and schemes. <s> BIB016 </s> Optimal Control Theory in Intelligent Transportation Systems Research - A Review <s> Categorize articles by ITS research objectives <s> Integrating artificial systems, computational experiments, and parallel execution (ACP) is an effective approach to modeling, simulating, and intervening real complex systems. Emergency response is an important issue in the operation of urban rail transport systems for ensuring the safety of people and property. Inspired by the ACP method, this paper introduces a basic framework of parallel control and management (PCM) for emergency response of urban rail transportation systems. The proposed framework is elaborated from three interdependent aspects: Points, Lines, and Networks. Points represent the modeling of urban rail stations, Lines describe the microscopic characteristics of urban rail connections between designated stations, and Networks present the macroscopic properties of all the urban rail connections. Based on the given framework, a series of parallel experiments, which were impossible to achieve in real systems, can now be conducted in the constructed artificial system. Furthermore, the constructed artificial system can be used to test and develop effective emergency control and management strategies for real rail transport systems. Therefore, this proposed framework will be able to enhance the reliability, security, robustness, and maneuverability of urban rail transport systems in case of an emergency. <s> BIB017
In the previous section, we not only categorized papers by traffic types, we also summarized different ITS research topics for each traffic type. It's worthwhile to point out that ITS research topics don't necessarily represent the research objectives of ITS. For instance, dynamic pricing is a typical ITS research topic (or called ITS methodology), however one of the most important research goals of doing dynamic pricing in ITS is to reduce traffic congestion. It is reducing congestion the ITS research objective, not dynamic pricing. It's important to distinguish these two concepts because when we say OCT contributes to ITS research, we need to make sure OCT contributes to ITS research objectives, not just to methodologies. As we mentioned previously, we are especially interested in the question "How does OCT contribute to ITS research objectives". In order to answer this question, we further examined the literature and categorized them by research objectives in the following table (table 3) . It's not difficult to observe that a large number of (15 out of 41) studies talked about mitigating traffic congestions. We may conclude from this finding that OCT contributes to ITS research objectives most by addressing the issue of traffic congestion. This finding is interesting because it indicates that OCT is the methodology which is widely used to solve one of the major problems in contemporary transportation, namely reducing traffic congestion. It further implies that the usage of OCT in the extant literature is consistent with one of the main management objectives of ITS  . The second largest body of research addresses efficiency improvement. We can see that this body of studies is growing rapidly in recent years since many of the papers were published very recently. Meanwhile, various maintenance issues in ITS were also addressed by OCT. In addition, it is also not uncommon for optimal control to solve traffic safety issues. Improve maintenance or construction BIB010 BIB012 BIB002 BIB001 BIB007 BIB003 Improve traffic forecasting and prediction BIB011 BIB004 BIB015 Improve safety BIB014 BIB009 BIB016 BIB017 BIB008 BIB006 In traffic congestion problem domain, various methods are used to solve the issue from different angles. For instance, BIB005 developed two types of dynamic congestion pricing models based on OCT to achieve equilibrium for commuters under the tolls. BIB013 presents a stochastic optimal control based approach to real-time incident responsive coordinated ramp control, etc. The next section discusses what detailed ITS methodologies are used to reduce traffic congestion in the extant literature by using OCT.