Optimal Control Theory in Intelligent Transportation Systems Research - A Review <s> Categorize articles by research methods of reducing traffic congestion <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 research methods of reducing traffic congestion <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 research methods of reducing traffic congestion <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 research methods of reducing traffic congestion <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> BIB004 </s> Optimal Control Theory in Intelligent Transportation Systems Research - A Review <s> Categorize articles by research methods of reducing traffic congestion <s> The problem of clearing congestion situations in freeway traffic is addressed for both an N-stage and an infinite-stage control horizon (in the latter case, a receding-horizon control mechanism is used). Traffic is controlled by regulating the vehicle access to the freeway and by limiting the vehicle speed by means of variable message signs. To describe the traffic behavior, a "classical" macroscopic model, first proposed by Payne (1971), is adapted. Even though the problem is stated within a deterministic context, an optimal control law in feedback form is sought to react to unpredictable events. The resulting functional optimization problem is reduced to a nonlinear programming problem by constraining the control law to take on a fixed structure in which free parameters have to be optimized. For such a structure, a multilayer feedforward neural mapping is chosen. Simulation results show the effectiveness of the proposed method in two different case studies. For the simulation of the second case study, real traffic data are used, which allows one to very well represent critical traffic conditions on freeways. <s> BIB005 </s> Optimal Control Theory in Intelligent Transportation Systems Research - A Review <s> Categorize articles by research methods of reducing traffic congestion <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> BIB006 </s> Optimal Control Theory in Intelligent Transportation Systems Research - A Review <s> Categorize articles by research methods of reducing traffic congestion <s> The problem of designing integrated traffic control strategies for motorway networks with the use of ramp metering, route guidance, and motorway-to-motorway control measures is considered in this paper. A generic problem formulation is presented in the format of a discrete-time optimal control problem whose numerical solution is achieved by use of a feasible-direction algorithm. As an illustrative example, a relatively simple motorway network is considered under different control scenarios. In each case the optimal control strategy is discussed along with its effect on the traffic flow process. The results demonstrate the efficiency of the proposed approach as well as the genuinely intelligent behaviour of the designed control strategy. <s> BIB007 </s> Optimal Control Theory in Intelligent Transportation Systems Research - A Review <s> Categorize articles by research methods of reducing traffic congestion <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> BIB008 </s> Optimal Control Theory in Intelligent Transportation Systems Research - A Review <s> Categorize articles by research methods of reducing traffic congestion <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> BIB009 </s> Optimal Control Theory in Intelligent Transportation Systems Research - A Review <s> Categorize articles by research methods of reducing traffic congestion <s> Summary form only given. The continuously increasing daily traffic congestions on motorway networks around the world call for innovative control measures that would drastically improve the current traffic conditions. Mainstream traffic flow control (MTFC) is proposed as a novel and efficient motorway traffic management tool, and its possible implementation and principal impact on traffic flow efficiency is analysed. Variable speed limits, suitably operated and enforced, are considered as one (out of several possible) way(s) for MTFC realisation, either as a stand-alone measure or in combination with ramp metering. A computationally efficient software tool for optimal integrated motorway network traffic control including MTFC is applied to a large-scale motorway ring-road. It is demonstrated via several investigated control scenarios that traffic flow can be substantially improved via MTFC with or without integration with coordinated ramp metering actions. <s> BIB010
It's important to gain more insights on reducing traffic congestion by using OCT because congestion reduction is essential to ITS  . Moreover, there is a considerable body of optimal control based studies within the scope of this subject. This section reveals what underlying techniques are adopted in the literature to reduce traffic congestion in which optimal control theory was used as the fundamental enabler of such techniques. Table 4 summarizes the literatures. We found there are five methods in ITS to mitigate traffic congestion problems, they are dynamic pricing, ramp metering, variable speed limits, traffic light control and the combination of different methods, namely the integrated control approach. We can observe from table 4 that research articles we reviewed distribute to these categories pretty well. In addition, it's not difficult to see that more researchers are interested in using optimal control to address ramp metering problems. This implies that more papers were devoted to congestion reduction on highways, freeways and motorways. This makes sense, because on one hand the phenomenon of traffic congestion on highways is indeed quite serious in many places, on the other hand highways, freeways and motorways are relatively easier to model than regular roads in urban areas. This largely makes the optimal control problem more tractable and more realistic  BIB010 . BIB008 BIB009 BIB002 BIB001 BIB004 BIB003 It's also worth pointing out that though there are not as many studies as that in addressing congestion reduction on highways, studies in reducing traffic congestion in urban roads should not be neglected. There are two main optimal control based methods in these studies, namely dynamic pricing and traffic light control in this area. An integrated approach prevails in such studies by considering two or even three of these methods simultaneously to get a better result. For instance, Carlson et al. BIB010 combines the factors of ramp metering and variable speed limits and proposed mainstream traffic flow control method to improve traffic flow efficiency. They published another research article at the same year aiming to reduce the congestion in the bottleneck of highways by using a similar approach BIB006 . Other studies using the integrating approach can also be found in the literatures BIB005  BIB007 .