Optimal Control Theory in Intelligent Transportation Systems Research - A Review <s> Introduction <s> Abstract This study uses fuel consumption simulators for 15 late-model automobiles to determine how one ought to drive to maximize fuel economy. The simulation is based on extensive on-road and dynamometer testing of the 15 cars. Dynamic programming is used to determine the optimal way to accelerate from rest to cruising speed, to drive a block between stop signs, and to cruise on hilly terrain while maintaining a given average speed. The dependence of fuel economy on cruising speed is also characterized for various road grades. Findings include that optimal speeds are generally higher for larger cars and higher on downgrades than on upgrades, and that the relative fuel penalty for exceeding the speed limit is no worse for small cars than large cars. Optimal control for accelerate-and-cruise and for driving between stop signs varies considerably from car to car; in the latter case fuel economy is much improved by achieving a rather low peak speed. Optimal control on hills is consistent from car to car and can achieve fuel economy 7% to 30% better than that of constant-speed driving on 3% to 6% grades. Results that appear generalizable to other cars are reduced to advice for the fuel-conscious driver. <s> BIB001 </s> Optimal Control Theory in Intelligent Transportation Systems Research - A Review <s> Introduction <s> This paper examines the conditions for which ramp metering can be beneficial to the overall system in terms of travel time savings for a simple traffic corridor that consists of a freeway and a set of parallel arterials connected by entrance ramps. The focus is on analyzing state and control relationships to arrive at general analytical results regarding optimal metering policies, rather than on either developing specific control algorithms or solving a specific application. The analysis is concerned with the general behavior of the system under ramp control and traffic diversion. The analysis assumes that time-varying traffic demands that originate from various locations are destined for a single location and that the freeway is uniformly congested throughout the control period. Under these assumptions, some general results are obtained regarding the effectiveness of ramp metering for various traffic diversion propensities and differentials between freeway and arterial traffic conditions. It is shown that the optimal ramp control policies are determined by the magnitudes of two co-state vectors that depend on traffic conditions on the freeway and its alternative, and the drivers diversion propensity. The results of two limiting cases imply that when the freeway is uniformly congested ramp control is counter-productive unless diversion occurs, and where drivers have a high propensity to divert, the optimal policy is dependent on the travel speed on the freeway alternative and on the wave speed of backward propagating waves on the freeway. <s> BIB002 </s> Optimal Control Theory in Intelligent Transportation Systems Research - A Review <s> Introduction <s> Preface to First Edition.- Preface to Second Edition.- What is Optimal Control Theory?.- The Maximum Principle: Continuous Time.- The Maximum Principle: Mixed Inequality Constraints.- The Maximum Principle: General Inequality Constraints.- Applications to Finance.- Applications to Production and Inventory.- Applications to Marketing.- The Maximum Principle: Discrete Time.- Maintenance and Replacement.- Applications to Natural Resources.- Economic Applications.- Differential Games, Distributed Systems, and Impulse Control.- Stochastic Optimal Control.- Solutions of Linear Differential Equations.- Calculus of Variations and Optimal Control Theory.- An Alternative Derivation of the Maximum Principle.- Special Topics in Optimal Control.- Answers to Selected Exercises.- Bibliography.- Index.- List of Figures.- List of Tables. <s> BIB003 </s> Optimal Control Theory in Intelligent Transportation Systems Research - A Review <s> Introduction <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> BIB004 </s> Optimal Control Theory in Intelligent Transportation Systems Research - A Review <s> Introduction <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> BIB005 </s> Optimal Control Theory in Intelligent Transportation Systems Research - A Review <s> Introduction <s> This paper presents an arterial signal optimization model that features its effectiveness on: (1) explicitly modeling physical queue evolution on arterial links by lane-group to account for shared-lane traffic interactions; and (2) capturing the dynamic interactions of spillback queues among lane groups and between neighboring intersections due to high demand, geometric constraints, or signal settings. Depending on the detected traffic patterns, one can select the control objective to be either minimizing the total travel time or maximizing the total throughput over the target area. The solution procedures developed with the Genetic Algorithm (GA) have been tested with an example arterial of four intersections under different demand scenarios. Extensive experimental analyses in comparison with results from TRANSYT-7F (version 8) reveal that the proposed model and solution method are quite promising for use in design of arterial signals, especially under congested, high demand traffic conditions. <s> BIB006
Conventional transportation systems are experiencing significant and ever-growing pressure during the past several decades due to the continuous motorization and urbanization around the world. While continuous motorization and urbanization lead to the increase of urban population, demand for automobile is also growing rapidly. It is not uncommon that various traffic issues such as traffic congestion, traffic accident and environmental issues become much more serious in metropolises. In addition to the traditional methods of "solving" these problems, namely building more infrastructures, an emerging technology called Intelligent Transportation Systems (ITS) provides an alternative which is creating far-reaching impact on solving current transportation problems. ITS equips the elements within the transportation systems, such as vehicles, roads, traffic lights, traffic signs, etc. with information technology (IT), so that they would become more intelligent. IT also empowers these elements to communicate with each other to make more systematic decisions to reduce the potential conflict or error which may cause transportation problems. In many countries where embrace ITS, it has brought significant improvements in various ways including reduced congestion, enhanced safety and traveler satisfaction and convenience  . Due to the nature of ITS, a large number of research topics in this area could be formulated as problems of finding optimal operation policies. In other words, the underlying problem is how to find optimal policies to manage the transportation systems. For example, BIB002 provides an optimal policy to control the freeway ramp so that the goal of reducing traffic congestion is achieved. BIB006 manipulated the traffic signal timing policy to get the optimal result of congestion reduction. Similar examples can be found in more ITS research papers BIB005 BIB001 BIB004 . Many research topics in ITS share the same characteristic, namely the transportation systems act as a control system in which the inputs and the expected outputs can be clearly defined. It is of great value to find the optimal policies of operating the inputs to approach the expected output so that the whole system can be effectively managed. Not surprisingly, such problem domain fits nicely to the territory of optimal control theory (OCT), one of the most widely used research methodologies in addressing management issues in engineering. Optimal control theory deals with the problem of finding a control law for a given system such that a certain optimality criterion is achieved. It is a branch of mathematics based on calculus of variations developed to find optimal ways to control a dynamic system. It's widely used in engineering, information systems and management science to solve various types of management problems BIB003 . In addition to our previous discussion, many other evidences could be found in the literature to testify that optimal control is suitable to solve research problems in ITS area    . Since OCT fits the context of ITS research, we believe it is both important and interesting to gain insights of the current adoption of this methodology in the contemporary ITS research. We attempt to answer the following research questions in this paper. First of all, how does OCT contribute to ITS research objectives? In other words, is OCT widely used and what particular research problems does optimal control solve in ITS? Second, what are the current research gaps and possible future research directions in ITS in which OCT can be effectively used? To our knowledge, there is very little prior studies addressed these research questions in the extant literature though we believe answering these research questions is important. The rest of this paper is structured as the follows. Section two introduces the literature review methodology and categorizes the articles by 4 different ways so that our research questions can be properly addressed. Section three summarizes the findings and identified the current research gaps and points out the possible future research directions based on our review. Section four ends the paper with the concluding remarks.