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In this paper, we consider the problem of coordinating traffic light systems and connected automated vehicles (CAVs) in mixed-traffic intersections. We aim to develop an optimization-based control framework that leverages both the coordination capabilities of CAVs at higher penetration rates and intelligent traffic management using traffic lights at lower penetration rates. Since the resulting optimization problem is a multi-agent mixed-integer quadratic program, we propose a penalization-enhanced maximum block improvement algorithm to solve the problem in a distributed manner. The proposed algorithm, under certain mild conditions, yields a feasible person-by-person optimal solution of the centralized problem. The performance of the control framework and the distributed algorithm is validated through simulations across various penetration rates and traffic volumes., Comment: accepted to lcss

This paper introduces a mobility equity metric (MEM) for evaluating fairness and accessibility in multi-modal intelligent transportation systems. The MEM simultaneously accounts for service accessibility and transportation costs across different modes of transportation and social demographics. We provide a data-driven validation of the proposed MEM to characterize the impact of various parameters in the metric across cities in the U.S. We subsequently develop a routing framework that aims to optimize MEM within a transportation network containing both public transit and private vehicles. Within this framework, a system planner provides routing suggestions to vehicles across all modes of transportation to maximize MEM. We evaluate our approach through numerical simulations, analyzing the impact of travel demands and compliance of private vehicles. This work provides insights into designing transportation systems that are not only efficient but also equitable, ensuring fair access to essential services across diverse populations., Comment: 14 pages, 15 figures

The rapid evolution of Cyber-Physical Systems (CPS) across various domains like mobility systems, networked control systems, sustainable manufacturing, smart power grids, and the Internet of Things necessitates innovative solutions that merge control and learning [1]. Traditional model-based control methodologies often fail to adapt to the dynamism and complexity of modern CPS. This report outlines a comprehensive approach undertaken by the Information and Decision Science (IDS) Lab, focusing on integrating data-driven techniques with control strategies to enhance CPS performance, particularly in the context of energy efficiency and environmental impact. CPS are intricate networks where physical and software components are deeply intertwined, operating as systems of systems. These systems are characterized by their informationally decentralized nature, posing significant challenges in optimization and control. Classical control methods depend heavily on precise models, which often do not capture the full complexity of real-world CPS. As these systems generate large volumes of real-time data, there is a growing need for control algorithms that can leverage this data effectively. The IDS Lab is at the forefront of developing such data-driven approaches for CPS., Comment: 13 pages

In this paper, we introduce a metric to evaluate the equity in mobility and a routing framework to enhance the metric within multi-modal intelligent transportation systems. The mobility equity metric (MEM) simultaneously accounts for service accessibility and transportation costs to quantify the equity and fairness in a transportation network. Finally, we develop a system planner integrated with MEM that aims to distribute travel demand for the transportation network, resulting in a socially optimal mobility system. Our framework results in a transportation network that is efficient in terms of travel time, improves accessibility, and ensures equity in transportation., Comment: 6 pages, 7 figures

In this letter, we present an approach for learning human driving behavior, without relying on specific model structures or prior distributions, in a mixed-traffic environment where connected and automated vehicles (CAVs) coexist with human-driven vehicles (HDVs). We employ conformal prediction to obtain theoretical safety guarantees and use real-world traffic data to validate our approach. Then, we design a controller that ensures effective merging of CAVs with HDVs with safety guarantees. We provide numerical simulations to illustrate the efficacy of the control approach., Comment: 6 pages, 5 figures

In this letter, we address the problem of improving the feasible domain of the solution of a decentralized control framework for coordinating connected and automated vehicles (CAVs) at signal-free intersections as the traffic volume increases. The framework provides the optimal trajectories of CAVs to cross the intersection safely without stop-and-go driving. However, as the traffic volume increases, the domain of the feasible trajectories decreases. We use concepts of numerical interpolation to identify appropriate polynomials that can serve as alternative trajectories of the CAVs, expanding the domain of the feasible CAV trajectories. We provide the conditions under which such polynomials exist. Finally, we demonstrate the efficacy of our approach through numerical simulations.

Many cyber-physical-human systems (CPHS) involve a human decision-maker who may receive recommendations from an artificial intelligence (AI) platform while holding the ultimate responsibility of making decisions. In such CPHS applications, the human decision-maker may depart from an optimal recommended decision and instead implement a different one for various reasons. In this letter, we develop a rigorous framework to overcome this challenge. In our framework, we consider that humans may deviate from AI recommendations as they perceive and interpret the system's state in a different way than the AI platform. We establish the structural properties of optimal recommendation strategies and develop an approximate human model (AHM) used by the AI. We provide theoretical bounds on the optimality gap that arises from an AHM and illustrate the efficacy of our results in a numerical example.

In this work, we propose a framework for adapting the controller's parameters based on learning optimal solutions from contextual black-box optimization problems. We consider a class of control design problems for dynamical systems operating in different environments or conditions represented by contextual parameters. The overarching goal is to identify the controller parameters that maximize the controlled system's performance, given different realizations of the contextual parameters.We formulate a contextual Bayesian optimization problem in which the solution is actively learned using Gaussian processes to approximate the controller adaptation strategy. We demonstrate the efficacy of the proposed framework with a sim-to-real example. We learn the optimal weighting strategy of a model predictive control for connected and automated vehicles interacting with human-driven vehicles from simulations and then deploy it in a real-time experiment., Comment: submission to RAL, 8 pages

In this paper, we introduce a hierarchical decision-making framework for emerging mobility systems. Despite numerous studies focusing on optimizing vehicle flow, practical feasibility has often been overlooked. To address this gap, we present a route-recovery method and energy-optimal trajectory planning tailored for connected and automated vehicles (CAVs) to ensure the realization of optimal flow. Our approach identifies the optimal vehicle flow to minimize total travel time while considering consistent mobility demands in urban settings. We deploy a heuristic route-recovery algorithm that assigns routes to CAVs and departure/arrival time at each road segment. Furthermore, we propose an efficient coordination method that rapidly solves constrained optimization problems by flexibly piecing together unconstrained energy-optimal trajectories. The proposed method has the potential to effectively generate optimal vehicle flow, contributing to the reduction of travel time and energy consumption in urban areas., Comment: 17 pages, 11 figures

In this paper, we investigate the control of a cyber-physical system (CPS) while accounting for its vulnerability to external attacks. We formulate a constrained stochastic problem with a robust constraint to ensure robust operation against potential attacks. We seek to minimize the expected cost subject to a constraint limiting the worst-case expected damage an attacker can impose on the CPS. We present a dynamic programming decomposition to compute the optimal control strategy in this robust-constrained formulation and prove its recursive feasibility. We also illustrate the utility of our results by applying them to a numerical simulation., Comment: 8 pages, 2 Figures with 3 sub-figures each, submitted to the ECC 2024 conference for review

Addressing safe and efficient interaction between connected and automated vehicles (CAVs) and human-driven vehicles in a mixed-traffic environment has attracted considerable attention. In this paper, we develop a framework for stochastic time-optimal trajectory planning for coordinating multiple CAVs in mixed-traffic merging scenarios. We present a data-driven model, combining Newell's car-following model with Bayesian linear regression, for efficiently learning the driving behavior of human drivers online. Using the prediction model and uncertainty quantification, a stochastic time-optimal control problem is formulated to find robust trajectories for CAVs. We also integrate a replanning mechanism that determines when deriving new trajectories for CAVs is needed based on the accuracy of the Bayesian linear regression predictions. Finally, we demonstrate the performance of our proposed framework using a realistic simulation environment., Comment: first submission 15 pages

In this paper, we provide a theoretical framework that separates the control and learning tasks in a linear system. This separation allows us to combine offline model-based control with online learning approaches and thus circumvent current challenges in deriving optimal control strategies in applications where a large volume of data is added to the system gradually in real time and not altogether in advance. We provide an analytical example to illustrate the framework., Comment: 6 pages, 1 figure. arXiv admin note: text overlap with arXiv:2211.14972

In this paper, we develop a control framework for the coordination of multiple robots as they navigate through crowded environments. Our framework comprises of a local model predictive control (MPC) for each robot and a social long short-term memory model that forecasts pedestrians' trajectories. We formulate the local MPC formulation for each individual robot that includes both individual and shared objectives, in which the latter encourages the emergence of coordination among robots. Next, we consider the multi-robot navigation and human-robot interaction, respectively, as a potential game and a two-player game, then employ an iterative best response approach to solve the resulting optimization problems in a centralized and distributed fashion. Finally, we demonstrate the effectiveness of coordination among robots in simulated crowd navigation.

Connected and automated vehicles (CAVs) provide the most intriguing opportunity for enabling users to better monitor transportation network conditions and make better operating decisions to improve safety and reduce pollution, energy consumption, and travel delays. While several studies have shown the benefits of CAVs in reducing energy and alleviating traffic congestion in specific traffic scenarios, e.g., crossing signal-free intersections, merging at roadways and roundabouts, cruising in congested traffic, passing through speed reduction zones, and lane-merging or passing maneuvers, most of these efforts have focused on 100% CAV penetration rates without considering human-driven vehicles (HDVs). One key question that still remains unanswered is ``how can CAVs and HDVs be coordinated safely?'' In this paper, we report on an optimal control framework to coordinate CAVs and HDVs at any traffic scenario. The idea is to directly control the CAVs to force the trailing HDVs to form platoons. Thus, we indirectly control the HDVs by coordinating the platoon of HDVs led by CAVs., Comment: 20 pages, 7 figures. arXiv admin note: substantial text overlap with arXiv:2003.12183, arXiv:2103.03393

In many real-world scenarios involving high-stakes and safety implications, a human decision-maker (HDM) may receive recommendations from an artificial intelligence while holding the ultimate responsibility of making decisions. In this letter, we develop an "adherence-aware Q-learning" algorithm to address this problem. The algorithm learns the "adherence level" that captures the frequency with which an HDM follows the recommended actions and derives the best recommendation policy in real time. We prove the convergence of the proposed Q-learning algorithm to the optimal value and evaluate its performance across various scenarios.

This letter proposes a routing framework in mixed transportation systems for improving mobility equity. We present a strategic routing game that governs interactions between compliant and noncompliant vehicles, where noncompliant vehicles are modeled with cognitive hierarchy theory. Then, we introduce a mobility equity metric (MEM) to quantify the accessibility and fairness in the transportation network. We integrate the MEM into the routing framework to optimize it with adjustable weights for different transportation modes. The proposed approach bridges the gap between technological advancements and societal goals in mixed transportation systems to enhance efficiency and equity. We provide numerical examples and analysis of the results., Comment: 6 pages, 5 figures

Connected and automated vehicles (CAVs) provide the most intriguing opportunity for enabling users to monitor transportation network conditions and make better decisions for improving safety and transportation efficiency. In this paper, we address the problem of effectively coordinating CAVs on lane-based roadways. Our approach utilizes potential functions to generate repulsive forces between CAVs that ensure collision avoidance. However, such potential functions can lead to unrealistic acceleration profiles and large inter-vehicle distances. The primary contribution of this work is the introduction of performance-sensitive potential functions to address these challenges. In our approach, the parameters of a potential function are determined through an optimization problem aiming to reduce both acceleration and inter-vehicle distances. To circumvent the computational implications due to the complexity of the resulting optimization problem that prevents the derivation of a real-time solution, we train a neural network model to learn the mapping of initial conditions to optimal parameters derived offline. Then, we prove sufficient criteria for the sampled-data model to ensure that the neural network output does not activate any of the state and safety constraints. Finally, we provide simulation results to demonstrate the effectiveness of the proposed approach.

Vehicle automation technology has made significant progress, laying the groundwork for a future of fully automated vehicles. This paper delves into the operation of connected and automated vehicles (CAVs). In prior work, we developed a controller that includes a tunable gain whose value significantly influences CAV performance and, in particular, its acceleration. By varying this gain, CAV acceleration is associated with different values depending on some initial conditions. Thus, our goal in this paper is to identify the optimal value of this gain in terms of acceleration for any group of initial conditions. To this end, we formulate an optimization problem where the decision variable is the gain value, and the objective function includes the acceleration of the vehicles. The complexity of this problem prohibits real-time solutions. To address this challenge, we train a neural network to map different initial conditions to the optimal gain values efficiently. We showcase the proposed approach to deriving the optimal gains in a merging scenario with an on-ramp.

In this paper, we present an optimal control framework to address motion coordination of connected automated vehicles (CAVs) in the presence of human-driven vehicles (HDVs) in merging scenarios. Our framework combines an unconstrained trajectory solution of a low-level energy-optimal control problem with an upper-level optimization problem that yields the minimum travel time for CAVs. We predict the future trajectories of the HDVs using Newell's car-following model. To handle potential deviations of HDVs' actual behavior from the predicted one, we design a safety filter for CAVs based on control barrier functions. The effectiveness of the proposed control framework is demonstrated via simulations with heterogeneous human driving behaviors., Comment: final CDC manuscript, 6 pages

Highway merging scenarios featuring mixed traffic conditions pose significant modeling and control challenges for connected and automated vehicles (CAVs) interacting with incoming on-ramp human-driven vehicles (HDVs). In this paper, we present an approach to learn an approximate information state model of CAV-HDV interactions for a CAV to maneuver safely during highway merging. In our approach, the CAV learns the behavior of an incoming HDV using approximate information states before generating a control strategy to facilitate merging. First, we validate the efficacy of this framework on real-world data by using it to predict the behavior of an HDV in mixed traffic situations extracted from the Next-Generation Simulation repository. Then, we generate simulation data for HDV-CAV interactions in a highway merging scenario using a standard inverse reinforcement learning approach. Without assuming a prior knowledge of the generating model, we show that our approximate information state model learns to predict the future trajectory of the HDV using only observations. Subsequently, we generate safe control policies for a CAV while merging with HDVs, demonstrating a spectrum of driving behaviors, from aggressive to conservative. We demonstrate the effectiveness of the proposed approach by performing numerical simulations.

In this paper, we present a study of a mobility game with uncertainty in the decision-making of travelers and incorporate prospect theory to model travel behavior. We formulate a mobility game that models how travelers distribute their traffic flows in a transportation network with splittable traffic, utilizing the Bureau of Public Roads function to establish the relationship between traffic flow and travel time cost. Given the inherent non-linearities and complexity introduced by the uncertainties, we propose a smooth approximation function to estimate the prospect-theoretic cost functions. As part of our analysis, we characterize the best-fit parameters and derive an upper bound for the error. We then show the existence of an equilibrium and its its best-possible approximation., Comment: arXiv admin note: text overlap with arXiv:2202.07691

This paper addresses the challenge of generating optimal vehicle flow at the macroscopic level. Although several studies have focused on optimizing vehicle flow, little attention has been given to ensuring it can be practically achieved. To overcome this issue, we propose a route-recovery and eco-driving strategy for connected and automated vehicles (CAVs) that guarantees optimal flow generation. Our approach involves identifying the optimal vehicle flow that minimizes total travel time, given the constant travel demands in urban areas. We then develop a heuristic route-recovery algorithm to assign routes to CAVs. Finally, we present an efficient coordination framework to minimize the energy consumption of CAVs while safely crossing intersections. The proposed method can effectively generate optimal vehicle flow and potentially reduce travel time and energy consumption in urban areas., Comment: 6 pages, 5 figures

Safety-critical cyber-physical systems require control strategies whose worst-case performance is robust against adversarial disturbances and modeling uncertainties. In this paper, we present a framework for approximate control and learning in partially observed systems to minimize the worst-case discounted cost over an infinite time horizon. We model disturbances to the system as finite-valued uncertain variables with unknown probability distributions. For problems with known system dynamics, we construct a dynamic programming (DP) decomposition to compute the optimal control strategy. Our first contribution is to define information states that improve the computational tractability of this DP without loss of optimality. Then, we describe a simplification for a class of problems where the incurred cost is observable at each time instance. Our second contribution is defining an approximate information state that can be constructed or learned directly from observed data for problems with observable costs. We derive bounds on the performance loss of the resulting approximate control strategy and illustrate the effectiveness of our approach in partially observed decision-making problems with a numerical example.

In this paper, we address the vehicle scheduling problem for improving passenger safety in bus rapid transit systems. Our focus is on passengers waiting at street stops to enter terminal stations. To enhance their safety, we minimize deviations from the proposed timetable, thereby minimizing passengers' initial waiting time. We formulate an optimization problem considering the position, speed deviation, and passenger count at each stop, solved using dynamic programming. Numerical simulations validate the effectiveness of our approach in enhancing passenger safety. Our work is the first attempt to minimize waiting time for improved safety and the first to utilize position tracking for departure time matching., Comment: 6 pages, 5 figures, 7th IEEE Conference on Control Technology and Applications (CCTA) 2023

In this paper, we investigate discrete-time decision-making problems in uncertain systems with partially observed states. We consider a non-stochastic model, where uncontrolled disturbances acting on the system take values in bounded sets with unknown distributions. We present a general framework for decision-making in such problems by using the notion of the information state and approximate information state, and introduce conditions to identify an uncertain variable that can be used to compute an optimal strategy through a dynamic program (DP). Next, we relax these conditions and define approximate information states that can be learned from output data without knowledge of system dynamics. We use approximate information states to formulate a DP that yields a strategy with a bounded performance loss. Finally, we illustrate the application of our results in control and reinforcement learning using numerical examples., Comment: Preliminary results related to this article were reported in arXiv:2203.15271

Connected and automated vehicles (CAVs) provide the most intriguing opportunity for enabling users to significantly improve safety and transportation efficiency by monitoring network conditions and making better operating decisions. CAVs, however, could alter the tendency to travel, eventually leading to a high traffic demand and causing rebound effects (e.g., increasing vehicle miles traveled). This chapter provides a control framework to distribute travel demand in a given transportation network, resulting in a socially optimal mobility system that travelers would be willing to accept. A "socially optimal mobility system" implies a mobility system that (1) is efficient (in terms of energy consumption and travel time), (2) mitigates rebound effects, and (3) ensures equity in transportation., Comment: 17 pages, 6 figures. arXiv admin note: text overlap with arXiv:2011.14399

This article provides an introduction to the theory of mechanism design and its application to engineering problems. Our aim is to provide the fundamental principles of the theory of mechanism design for control engineers and theorists along with the state-of-the-art methods in engineering applications. We start our exposition with a brief overview of game theory highlighting the key notions that are necessary to introduce mechanism design, and then we offer a comprehensive discussion of the principles in mechanism design. Finally, we explore four key applications of mechanism design in engineering, i.e., communication networks, power grids, transportation, and security systems.

Cyber-physical systems (CPS) encounter a large volume of data which is added to the system gradually in real time and not altogether in advance. As the volume of data increases, the domain of the control strategies also increases, and thus it becomes challenging to search for an optimal strategy. Even if an optimal control strategy is found, implementing such strategies with increasing domains is burdensome. To derive an optimal control strategy in CPS, we typically assume an ideal model of the system. Such model-based control approaches cannot effectively facilitate optimal solutions with performance guarantees due to the discrepancy between the model and the actual CPS. Alternatively, traditional supervised learning approaches cannot always facilitate robust solutions using data derived offline. Similarly, applying reinforcement learning approaches directly to the actual CPS might impose significant implications on safety and robust operation of the system. The goal of this chapter is to provide a theoretical framework that aims at separating the control and learning tasks which allows us to combine offline model-based control with online learning approaches, and thus circumvent the challenges in deriving optimal control strategies for CPS., Comment: 18 pages, 5 figures. arXiv admin note: text overlap with arXiv:2101.10992

The article provides an overview of the latest developments on control approaches for connected and automated vehicles along with their effectiveness on energy and transportation efficiency., Comment: 9 pagers, 3 figures

In this paper, we develop an optimal weight adaptation strategy of model predictive control (MPC) for connected and automated vehicles (CAVs) in mixed traffic. We model the interaction between a CAV and a human-driven vehicle (HDV) as a simultaneous game and formulate a game-theoretic MPC problem to find a Nash equilibrium of the game. In the MPC problem, the weights in the HDV's objective function can be learned online using moving horizon inverse reinforcement learning. Using Bayesian optimization, we propose a strategy to optimally adapt the weights in the CAV's objective function so that the expected true cost when using MPC in simulations can be minimized. We validate the effectiveness of the optimal strategy by numerical simulations of a vehicle crossing example at an unsignalized intersection., Comment: accepted to ACC 2023

In this paper, we propose a re-routing strategy for connected and automated vehicles (CAVs), considering coordination and control of all the CAVs in the network. The objective for each CAV is to find the route that minimizes the total travel time of all CAVs. We coordinate CAVs at signal-free intersections to accurately predict the travel time for the routing problem. While it is possible to find a system-optimal solution by comparing all the possible combinations of the routes, this may impose a computational burden. Thus, we instead find a person-by-person optimal solution to reduce computational time while still deriving a better solution than selfish routing. We validate our framework through simulations in a grid network., Comment: 6 pages, 4 figures

In this paper, we consider the problem of optimizing the worst-case behavior of a partially observed system. All uncontrolled disturbances are modeled as finite-valued uncertain variables. Using the theory of cost distributions, we present a dynamic programming (DP) approach to compute a control strategy that minimizes the maximum possible total cost over a given time horizon. To improve the computational efficiency of the optimal DP, we introduce a general definition for information states and show that many information states constructed in previous research efforts are special cases of ours. Additionally, we define approximate information states and an approximate DP that can further improve computational tractability by conceding a bounded performance loss. We illustrate the utility of these results using a numerical example., Comment: This article is specializes to additive cost problems the theory and results presented for terminal cost problems in arXiv:2203.15271

The study of robotic flocking has received significant attention in the past twenty years. In this article, we present a constraint-driven control algorithm that minimizes the energy consumption of individual agents and yields an emergent V formation. As the formation emerges from the decentralized interaction between agents, our approach is robust to the spontaneous addition or removal of agents to the system. First, we present an analytical model for the trailing upwash behind a fixed-wing UAV, and we derive the optimal air speed for trailing UAVs to maximize their travel endurance. Next, we prove that simply flying at the optimal airspeed will never lead to emergent flocking behavior, and we propose a new decentralized "anseroid" behavior that yields emergent V formations. We encode these behaviors in a constraint-driven control algorithm that minimizes the locomotive power of each UAV. Finally, we prove that UAVs initialized in an approximate V or echelon formation will converge under our proposed control law, and we demonstrate this emergence occurs in real-time in simulation and in physical experiments with a fleet of Crazyflie quadrotors., Comment: 12 pages, 7 figures

Platoon formation with connected and automated vehicles (CAVs) in a mixed traffic environment poses significant challenges due to the presence of human-driven vehicles (HDVs) with unknown dynamics and control actions. In this paper, we develop a safety-prioritized receding horizon control framework for creating platoons of HDVs preceded by a CAV. Our framework ensures indirect control of the following HDVs by directly controlling the leading CAV given the safety constraints. The framework utilizes a data-driven prediction model that is based on the recursive least squares algorithm and the constant time headway relative velocity car-following model to predict future trajectories of human-driven vehicles. To demonstrate the efficacy of the proposed framework, we conduct numerical simulations and provide the associated scalability, robustness, and performance analyses.

In this paper, we develop a socially cooperative optimal control framework to address the motion planning problem for connected and automated vehicles (CAVs) in mixed traffic using social value orientation (SVO) and a potential game approach. In the proposed framework, we formulate the interaction between a CAV and a human-driven vehicle (HDV) as a simultaneous game where each vehicle minimizes a weighted sum of its egoistic objective and a cooperative objective. The SVO angles are used to quantify preferences of the vehicles toward the egoistic and cooperative objectives. Using the potential game approach, we propose a single objective function for the optimal control problem whose weighting factors are chosen based on the SVOs of the vehicles. We prove that a Nash equilibrium can be obtained by minimizing the proposed objective function. To estimate the SVO angle of the HDV, we develop a moving horizon estimation algorithm based on maximum entropy inverse reinforcement learning. The effectiveness of the proposed approach is demonstrated by numerical simulations of a vehicle merging scenario., Comment: final version to CDC2022

In this paper, we extend a framework that we developed earlier for coordination of connected and automated vehicles (CAVs) at a signal-free intersection by integrating a safety layer using control barrier functions. First, in our motion planning module, each CAV computes the optimal control trajectory using simple vehicle dynamics. The trajectory does not make any of the state, control, and safety constraints active. A vehicle-level tracking controller employs a combined feedforward-feedback control law to track the resulting optimal trajectory from the motion planning module. Then, a barrier-certificate module, acting as a middle layer between the vehicle-level tracking controller and physical vehicle, receives the control law from the vehicle-level tracking controller and using realistic vehicle dynamics ensures that none of the state, control, and safety constraints becomes active. The latter is achieved through a quadratic program, which can be solved efficiently in real time. We demonstrate the effectiveness of our extended framework through a numerical simulation., Comment: 8 pages, 5 figures, 1 table

In this paper, we investigate a worst-case-scenario control problem with a partially observed state. We consider a non-stochastic formulation, where noises and disturbances in our dynamics are uncertain variables which take values in finite sets. In such problems, the optimal control strategy can be derived using a dynamic program (DP) with respect to the memory. The computational complexity of this DP can be improved using a conditional range of the state instead of the memory. We present a more general definition of an information state which is sufficient to construct a DP without loss of optimality, and show that the conditional range is an example of an information state. Next, we extend this notion to define an approximate information state and an approximate DP. We also bound the maximum loss of optimality when using an approximate DP to derive the control strategy. Finally, we illustrate our results in a numerical example.

In this paper, we consider a multi-modal mobility system of travelers each with an individual travel budget, and propose a game-theoretic framework to assign each traveler to a ``mobility service" (each one representing a different mode of transportation). We are interested in equity and sustainability, thus we maximize the worst-case revenue of the mobility system while ensuring ``mobility equity," which we define it in terms of accessibility. In the proposed framework, we ensure that all travelers are truthful and voluntarily participate under informational asymmetry, and the solution respects the individual budget of each traveler. Each traveler may seek to travel using multiple services (e.g., car, bus, train, bike). The services are capacitated and can serve up to a fixed number of travelers at any instant of time. Thus, our problem falls under the category of many-to-one assignment problems, where the goal is to find the conditions that guarantee the stability of assignments. We formulate a linear program of maximizing worst-case revenue under the constraints of mobility equity, and we fully characterize the optimal solution., Comment: arXiv admin note: text overlap with arXiv:2110.06403

In this letter, we consider a transportation network with a 100\% penetration rate of connected and automated vehicles (CAVs) and present an optimal routing approach that takes into account the efficiency achieved in the network by coordinating the CAVs at specific traffic scenarios, e.g., intersections, merging roadways, and roundabouts. To derive the optimal route of a travel request, we use the information of the CAVs that have already received a routing solution. This enables each CAV to consider the traffic conditions on the roads. The solution of any new travel request determines the optimal travel time at each traffic scenario while satisfying all state, control, and safety constraints. We validate the performance of our framework through numerical simulations. To the best of our knowledge, this is the first attempt to consider the coordination of CAVs in a routing problem., Comment: 6 pages, 5 figures

In this letter, we present a constraint-driven optimal control framework that achieves emergent cluster flocking within a constrained 2D environment. We formulate a decentralized optimal control problem that includes safety, flocking, and predator avoidance constraints. We explicitly derive conditions for constraint compatibility and propose an event-driven constraint relaxation scheme, which we map to an equivalent finite state machine that intuitively describes the behavior of each agent in the system. Instead of minimizing control effort, as it is common in the ecologically-inspired robotics literature, in our approach, we minimize each agent's deviation from their most efficient locomotion speed. Finally, we demonstrate our approach in simulation both with and without the presence of a predator., Comment: 6 pages, 5 figures

A typical urban signalized intersection poses significant modeling and control challenges in a mixed traffic environment consisting of connected automated vehicles (CAVs) and human-driven vehicles (HDVs). In this paper, we address the problem of deriving safe trajectories for CAVs in a mixed traffic environment that prioritizes rear-end collision avoidance when the preceding HDVs approach the yellow and red signal phases of the intersection. We present a predictive control framework that employs a recursive least squares algorithm to approximate in real time the driving behavior of the preceding HDVs and then uses this approximation to derive safety-aware trajectory in a finite horizon. We validate the effectiveness of our proposed framework through numerical simulation and analyze the robustness of the control framework.

Trajectory planning of connected and automated vehicles (CAVs) poses significant challenges in a mixed traffic environment due to the presence of human-driven vehicles (HDVs). In this paper, we apply a framework that allows coordination of CAVs and HDVs traveling through a traffic corridor consisting of an on-ramp merging, a speed reduction zone, and a roundabout. We study the impact of different penetration rates of CAVs and traffic volumes on the efficiency of the corridor. We provide extensive simulation results and report on the benefits in terms of total travel time and fuel economy., Comment: 6 pages conference

In this paper, we study a routing and travel-mode choice problem for mobility systems with a multimodal transportation network as a ``mobility game" with coupled action sets. We develop a game-theoretic framework to study the impact on efficiency of the travelers' behavioral decision-making. In our framework, we introduce a mobility ``pricing mechanism," in which we model traffic congestion using linear cost functions while also considering the waiting times at different transport hubs. We show that the travelers' selfish actions lead to a pure-strategy Nash equilibrium. We then perform a Price of Anarchy analysis to establish that the mobility system's inefficiencies remain relatively low as the number of travelers increases. We deviate from the standard game-theoretic analysis of decision-making by extending our modeling framework to capture the subjective behavior of travelers using prospect theory. Finally, we provide a simulation study as a proof of concept for our proposed mobility game.

Vehicle platooning using connected and automated vehicles (CAVs) has attracted considerable attention. In this paper, we address the problem of optimal coordination of CAV platoons at a highway on-ramp merging. We present a single-level constrained optimal control framework that optimizes fuel economy and travel time of the platoons while satisfying the state, control, and safety constraints. We also explore the effect of delayed communication among the CAV platoons and propose a robust coordination framework to enforce lateral and rear-end collision avoidance constraints in the presence of bounded delays. We provide a closed-form analytical solution of the optimal control problem with safety guarantees that can be implemented in real time. Finally, we validate the effectiveness of the proposed control framework using a high-fidelity commercial simulation environment.

The control of swarm systems is relatively well understood for simple robotic platforms at the macro scale. However, there are still several unanswered questions about how similar results can be achieved for microrobots. In this paper, we propose a modeling framework based on a dynamic model of magnetized self-propelling Janus microrobots under a global magnetic field. We verify our model experimentally and provide methods that can aim at accurately describing the behavior of microrobots while modeling their simultaneous control. The model can be generalized to other microrobotic platforms in low Reynolds number environments., Comment: 7 pages, 2 figures

In this paper, we consider a mobility system of travelers and providers, and propose a "mobility game" to study when a traveler is matched to a provider. Each traveler seeks to travel using the services of only one provider, who manages one specific mode of transportation (e.g., car, bus, train, bike). The services of each provider are capacitated and can serve up to a fixed number of travelers at any instant of time. Thus, our problem falls under the category of many-to-one assignment problems, where the goal is to find the conditions that guarantee the stability of assignments. We formulate a linear program of maximizing the social welfare of travelers and providers and show how it is equivalent to the original problem and relate its solutions to stable assignments. We also investigate our results under informational asymmetry and provide a "mechanism" that elicits the information of travelers and providers. Finally, we investigate and validate the advantages of our method by providing a numerical simulation example.

In this paper, we investigate the problem of routing, rebalancing, and charging for electric autonomous mobility-on-demand systems concerning traffic congestion. We analyze the problem at the macroscopical level and use a volume-delay function to capture traffic congestion. To address this problem, we first formulate an optimization problem for routing and rebalancing. Then, we present heuristic algorithms to find the loop of the traffic flow and examine the energy constraints within the resulting loop. We impose charging constraints on the re-routing problem so that the new solution satisfies the energy constraint. Finally, we verify the effectiveness of our method through simulation., Comment: 6 pages, 2 figures

Coordination of connected and automated vehicles (CAVs) in a mixed traffic environment poses significant challenges due to the presence of human-driven vehicles (HDVs) with stochastic dynamics and driving behavior. In earlier work, we addressed the problem of platoon formation of HDVs led by a CAV using a model-dependent controller. In this paper, we develop a comprehensive model-agnostic, multi-objective optimal controller which ensures platoon formation by directly controlling the leading CAV without having explicit knowledge of the trailing HDV dynamics. We provide a detailed exposition of the control framework that uses instantaneous motion information from multiple successive HDVs to enforce safety while achieving the optimization objectives. To demonstrate the efficacy of the proposed control framework, we evaluate its performance using numerical simulation and provide associated sensitivity and robustness analysis., Comment: arXiv admin note: text overlap with arXiv:2103.03393