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In this study, we introduce a toll lane framework that optimizes the mixed flow of autonomous and high-occupancy vehicles on freeways, where human-driven and autonomous vehicles of varying commuter occupancy share a segment. Autonomous vehicles, with their ability to maintain shorter headways, boost traffic throughput. Our framework designates a toll lane for autonomous vehicles with high occupancy to use free of charge, while others pay a toll. We explore the lane choice equilibria when all vehicles minimize travel costs, and characterize the equilibria by ranking vehicles by their mobility enhancement potential, a concept we term the mobility degree. Through numerical examples, we demonstrate the framework's utility in addressing design challenges such as setting optimal tolls, determining occupancy thresholds, and designing lane policies, showing how it facilitates the integration of high-occupancy and autonomous vehicles. We also propose an algorithm for assigning rational tolls to decrease total commuter delay and examine the effects of toll non-compliance. Our findings suggest that self-interest-driven behavior mitigates moderate non-compliance impacts, highlighting the framework's resilience. This work presents a pioneering comprehensive analysis of a toll lane framework that emphasizes the coexistence of autonomous and high-occupancy vehicles, offering insights for traffic management improvements and the integration of autonomous vehicles into existing transportation infrastructures.

In this paper, a comparison analysis between geometric impedance controls (GICs) derived from two different potential functions on SE(3) for robotic manipulators is presented. The first potential function is defined on the Lie group, utilizing the Frobenius norm of the configuration error matrix. The second potential function is defined utilizing the Lie algebra, i.e., log-map of the configuration error. Using a differential geometric approach, the detailed derivation of the distance metric and potential function on SE(3) is introduced. The GIC laws are respectively derived from the two potential functions, followed by extensive comparison analyses. In the qualitative analysis, the properties of the error function and control laws are analyzed, while the performances of the controllers are quantitatively compared using numerical simulation., Comment: This paper is accepted to American Control Conference (ACC) 2024

In Robust Control and Data Driven Robust Control design methodologies, multiple plant transfer functions or a family of transfer functions are considered and a common controller is designed such that all the plants that fall into this family are stabilized. Though the plants are stabilized, the controller might be sub-optimal for each of the plants when the variations in the plants are large. This paper presents a way of clustering stable linear dynamical systems for the design of robust controllers within each of the clusters such that the controllers are optimal for each of the clusters. First a k-medoids algorithm for hard clustering will be presented for stable Linear Time Invariant (LTI) systems and then a Gaussian Mixture Models (GMM) clustering for a special class of LTI systems, common for Hard Disk Drive plants, will be presented., Comment: 6 pages, 4 figures

Diffusion models have risen as a powerful tool in robotics due to their flexibility and multi-modality. While some of these methods effectively address complex problems, they often depend heavily on inference-time obstacle detection and require additional equipment. Addressing these challenges, we present a method that, during inference time, simultaneously generates only reachable goals and plans motions that avoid obstacles, all from a single visual input. Central to our approach is the novel use of a collision-avoiding diffusion kernel for training. Through evaluations against behavior-cloning and classical diffusion models, our framework has proven its robustness. It is particularly effective in multi-modal environments, navigating toward goals and avoiding unreachable ones blocked by obstacles, while ensuring collision avoidance. Project Website: https://sites.google.com/view/denoising-heat-inspired, Comment: 9 pages, 6 figures

Recent studies have verified that equivariant methods can significantly improve the data efficiency, generalizability, and robustness in robot learning. Meanwhile, denoising diffusion-based generative modeling has recently gained significant attention as a promising approach for robotic manipulation learning from demonstrations with stochastic behaviors. In this paper, we present Diffusion-EDFs, a novel approach that incorporates spatial roto-translation equivariance, i.e., SE(3)-equivariance to diffusion generative modeling. By integrating SE(3)-equivariance into our model architectures, we demonstrate that our proposed method exhibits remarkable data efficiency, requiring only 5 to 10 task demonstrations for effective end-to-end training. Furthermore, our approach showcases superior generalizability compared to previous diffusion-based manipulation methods., Comment: 27 pages, 4 figures

This paper presents a differential geometric control approach that leverages SE(3) group invariance and equivariance to increase transferability in learning robot manipulation tasks that involve interaction with the environment. Specifically, we employ a control law and a learning representation framework that remain invariant under arbitrary SE(3) transformations of the manipulation task definition. Furthermore, the control law and learning representation framework are shown to be SE(3) equivariant when represented relative to the spatial frame. The proposed approach is based on utilizing a recently presented geometric impedance control (GIC) combined with a learning variable impedance control framework, where the gain scheduling policy is trained in a supervised learning fashion from expert demonstrations. A geometrically consistent error vector (GCEV) is fed to a neural network to achieve a gain scheduling policy that remains invariant to arbitrary translation and rotations. A comparison of our proposed control and learning framework with a well-known Cartesian space learning impedance control, equipped with a Cartesian error vector-based gain scheduling policy, confirms the significantly superior learning transferability of our proposed approach. A hardware implementation on a peg-in-hole task is conducted to validate the learning transferability and feasibility of the proposed approach.

In this paper, we present a frequency domain data-driven feedback control design methodology for the design of tracking controllers for hard disk drives with two-stage actuator as a part of the open invited track 'Benchmark Problem on Control System Design of Hard Disk Drive with a Dual-Stage Actuator' in the IFAC World Congress 2023 (Yokohoma, Japan). The benchmark models are Compared to the traditional controller design, we improve robustness and avoid model mismatch by using multiple frequency response plant measurements directly instead of plant models. Disturbance rejection and corresponding error minimization is posed as an H2 norm minimization problem with H infinity and H2 norm constraints. H infinity norm constraints are used to shape the closed loop transfer functions and ensure closed loop stability and H2 norm constraints are used to constrain and/or minimize the variance of relevant., Comment: 7 pages, 10 figures, IFAC World Congress, Yokohoma

After its introduction, impedance control has been utilized as a primary control scheme for robotic manipulation tasks that involve interaction with unknown environments. While impedance control has been extensively studied, the geometric structure of SE(3) for the robotic manipulator itself and its use in formulating a robotic task has not been adequately addressed. In this paper, we propose a differential geometric approach to impedance control. Given a left-invariant error metric in SE(3), the corresponding error vectors in position and velocity are first derived. We then propose the impedance control schemes that adequately account for the geometric structure of the manipulator in SE(3) based on a left-invariant potential function. The closed-loop stabilities for the proposed control schemes are verified using Lyapunov function-based analysis. The proposed control design clearly outperformed a conventional impedance control approach when tracking challenging trajectory profiles., Comment: Presented at IFAC World Congress 2023, Yokohama, Japan

Strictly Positive Real (SPR) transfer functions arise in many areas of engineering like passivity theory in circuit analysis and adaptive control to name a few. In many physical systems, it is possible to conclude that the system is Positive Real (PR) or SPR but system identification algorithms might produce estimates which are not SPR. In this paper, an algorithm to approximate frequency response data with SPR transfer functions using Generalized Orthonormal Basis Functions (GOBFs) is presented. Prior knowledge of the system helps us to get approximate pole locations, which can then be used to construct GOBFs. Next, a convex optimization problem will be formulated to obtain an estimate of the SPR transfer function., Comment: arXiv admin note: substantial text overlap with arXiv:2109.12460

In December 2017, Seagate unveiled the Multi Actuator Technology to double the data performance of the future generation hard disk drives (HDD). This technology will equip drives with two dual stage actuators (DSA) each comprising of a voice coil motor (VCM) actuator and a piezoelectric micro actuator (MA) operating on the same pivot point. Each DSA is responsible for controlling half of the drive's arms. As both the DSAs operate independently on the same pivot timber, the control forces and torques generated by one can affect the operation of the other and thereby worsening the performance drastically. In this paper, a robust adaptive feedforward controller is designed as an add-on controller to an existing stabilizing feedback controller to reject the disturbances transferred through the common pivot timber by shaping the references to the VCM actuator and the total output of the dual stage system.

Multi Actuator Technology in Hard Disk drives (HDDs) equips drives with two dual stage actuators (DSA) each comprising of a voice coil motor (VCM) actuator and a piezoelectric micro actuator (MA) operating on the same pivot point. Each DSA is responsible for controlling half of the drive's arms. As both the DSAs operate independently on the same pivot timber, the control forces and torques generated by one affect the operation of the other. The feedback controllers might not completely reject these transferred disturbances and a need to design feedforward controllers arises, which require a good model of the disturbance process. The usual system identification techniques produce a biased estimate because of the presence of the runout which is a colored noise. In this paper, we use the OKID framework to estimate this disturbance cross transfer function from the VCM control input of one DSA to the output of the other DSA from the collected time series data corrupted by colored noise., Comment: 4 pages, 3 figures

Highway on-ramps are regarded as typical bottlenecks in transportation networks. In previous work, mainline vehicles' selfish lane choice behavior at on-ramps is studied and regarded as one cause leading to on-ramp inefficiency. When on-ramp vehicles plan to merge into the mainline of the highway, mainline vehicles choose to either stay steadfast on the current lane or bypass the merging area by switching to a neighboring lane farther from the on-ramp. Selfish vehicles make the decisions to minimize their own travel delay, which compromises the efficiency of the whole on-ramp. Results in previous work have shown that, if we can encourage a proper portion of mainline vehicles to bypass rather than to stay steadfast, the social traffic conditions can be improved. In this work, we consider employing a proportion of altruistic vehicles among the selfish mainline vehicles to improve the efficiency of the on-ramps. The altruistic vehicles are individual optimizers, making decisions whether to stay steadfast or bypass to minimize their own altruistic cost, which is a weighted sum of the travel delay and their negative impact on other vehicles. We first consider the ideal case that altruistic costs can be perfectly measured by altruistic vehicles. We give the conditions for the proportion of altruistic vehicles and the weight configuration of the altruistic costs, under which the social delay can be decreased or reach the optimal. Subsequently, we consider the impact of uncertainty in the measurement of altruistic costs and we give the optimal weight configuration for altruistic vehicles which minimizes the worst-case social delay under such uncertainty.

We consider the scenario where human-driven/autonomous vehicles with low/high occupancy are sharing a segment of highway and autonomous vehicles are capable of increasing the traffic throughput by preserving a shorter headway than human-driven vehicles. We propose a toll lane framework where a lane on the highway is reserved freely for autonomous vehicles with high occupancy, which have the greatest capability to increase social mobility, and the other three classes of vehicles can choose to use the toll lane with a toll or use the other regular lanes freely. All vehicles are assumed to be only interested in minimizing their own travel costs. We explore the resulting lane choice equilibria under the framework and establish desirable properties of the equilibria, which implicitly compare high-occupancy vehicles with autonomous vehicles in terms of their capabilities to increase social mobility. We further use numerical examples in the optimal toll design, the occupancy threshold design, and the policy design problems to clarify the various potential applications of this toll lane framework that unites high-occupancy vehicles and autonomous vehicles. To our best knowledge, this is the first work that systematically studies a toll lane framework that unites autonomous vehicles and high-occupancy vehicles on the roads.

In this paper, a frequency separation based adaptive feedforward control algorithm is developed with the ability to identify the plant and do compensation region by region. In this algorithm, the accelerometer signal is filtered by a series of uniformly distributed bandpass filters to generate a bunch of subband signals which are mutually exclusive in spectrum. In each subband, the corresponding subband signal acts as the feedforward signal and only the frequency response of system in that region needs to be identified, thus a pretty low order model can be expected to have efficient compensation. Starting from the first region, the feedforward control parameters are learned simultaneously with the low order plant model in the same region and then moves to the next region until all the regions are performed., Comment: 6 Pages, 9 figures, conference paper

In this paper we present a model-predictive control (MPC) based approach for vehicle platooning in an urban traffic setting. Our primary goal is to demonstrate that vehicle platooning has the potential to significantly increase throughput at intersections, which can create bottlenecks in the traffic flow. To do so, our approach relies on vehicle connectivity: vehicle-to-vehicle (V2V) and vehicle-to-infrastructure (V2I) communication. In particular, we introduce a customized V2V message set which features a velocity forecast, i.e. a prediction on the future velocity trajectory, which enables platooning vehicles to accurately maintain short following distances, thereby increasing throughput. Furthermore, V2I communication allows platoons to react immediately to changes in the state of nearby traffic lights, e.g. when the traffic phase becomes green, enabling additional gains in traffic efficiency. We present our design of the vehicle platooning system, and then evaluate performance by estimating the potential gains in terms of throughput using our results from simulation, as well as experiments conducted with real test vehicles on a closed track. Lastly, we briefly overview our demonstration of vehicle platooning on public roadways in Arcadia, CA., Comment: 14 pages, 11 figures, 4 tables

In Part I of this paper series, several macroscopic traffic model elements for mathematically describing freeway networks equipped with managed lane facilities were proposed. These modeling techniques seek to capture at the macroscopic the complex phenomena that occur on managed lane-freeway networks, where two parallel traffic flows interact with each other both in the physical sense (how and where cars flow between the two lane groups) and the physiological sense (how driving behaviors are changed by being adjacent to a quantitatively and qualitatively different traffic flow). The local descriptions we developed in Part I are not the only modeling complexity introduced in managed lane-freeway networks. The complex topologies mean that network-scale modeling of a freeway corridor is increased in complexity as well. The already-difficult model calibration problem for a dynamic model of a freeway becomes more complex when the freeway becomes, in effect, two interrelating flow streams. In the present paper, we present an iterative-learning-based approach to calibrating our model's physical and driver-behavioral parameters. We consider the common situation where a complex traffic model needs to be calibrated to recreate real-world baseline traffic behavior, such that counterfactuals can be generated by training purposes. Our method is used to identify traditional freeway parameters as well as the proposed parameters that describe managed lane-freeway-network-specific behaviors. We validate our model and calibration methodology with case studies of simulations of two managed lane-equipped California freeways., Comment: Part I is here: arXiv:1609.09470

Many potential applications of reinforcement learning in the real world involve interacting with other agents whose numbers vary over time. We propose new neural policy architectures for these multi-agent problems. In contrast to other methods of training an individual, discrete policy for each agent and then enforcing cooperation through some additional inter-policy mechanism, we follow the spirit of recent work on the power of relational inductive biases in deep networks by learning multi-agent relationships at the policy level via an attentional architecture. In our method, all agents share the same policy, but independently apply it in their own context to aggregate the other agents' state information when selecting their next action. The structure of our architectures allow them to be applied on environments with varying numbers of agents. We demonstrate our architecture on a benchmark multi-agent autonomous vehicle coordination problem, obtaining superior results to a full-knowledge, fully-centralized reference solution, and significantly outperforming it when scaling to large numbers of agents.

Deep neural networks can be powerful tools, but require careful application-specific design to ensure that the most informative relationships in the data are learnable. In this paper, we apply deep neural networks to the nonlinear spatiotemporal physics problem of vehicle traffic dynamics. We consider problems of estimating macroscopic quantities (e.g., the queue at an intersection) at a lane level. First-principles modeling at the lane scale has been a challenge due to complexities in modeling social behaviors like lane changes, and those behaviors' resultant macro-scale effects. Following domain knowledge that upstream/downstream lanes and neighboring lanes affect each others' traffic flows in distinct ways, we apply a form of neural attention that allows the neural network layers to aggregate information from different lanes in different manners. Using a microscopic traffic simulator as a testbed, we obtain results showing that an attentional neural network model can use information from nearby lanes to improve predictions, and, that explicitly encoding the lane-to-lane relationship types significantly improves performance. We also demonstrate the transfer of our learned neural network to a more complex road network, discuss how its performance degradation may be attributable to new traffic behaviors induced by increased topological complexity, and motivate learning dynamics models from many road network topologies., Comment: To appear at 2019 IEEE Conference on Intelligent Transportation Systems

Road network junctions, such as merges and diverges, often act as bottlenecks that initiate and exacerbate congestion. More complex junction configurations lead to more complex driver behaviors, resulting in aggregate congestion patterns that are more difficult to predict and mitigate. In this paper, we discuss diverge configurations where vehicles on some lanes can enter only one of the downstream roads, but vehicles on other lanes can enter one of several downstream roads. Counterintuitively, these bifurcating lanes, rather than relieving congestion (by acting as a versatile resource that can serve either downstream road as the demand changes), often cause enormous congestion due to lane changing. We develop an aggregate lane--changing model for this situation that is expressive enough to model drivers' choices and the resultant congestion, but simple enough to easily analyze. We use a game-theoretic framework to model the aggregate lane choice behavior of selfish vehicles as a Wardrop equilibrium (an aggregate type of Nash equilibrium). We then establish the existence and uniqueness of this equilibrium. We explain how our model can be easily calibrated using simulation data or real data, and we present results showing that our model successfully predicts the aggregate behavior that emerges from widely-used behavioral lane-changing models. Our model's expressiveness, ease of calibration, and accuracy may make it a useful tool for mitigating congestion at these complex diverges., Comment: 15 pages, 5 figures

In a traffic network, vehicles normally select their routes selfishly. Consequently, traffic networks normally operate at an equilibrium characterized by Wardrop conditions. However, it is well known that equilibria are inefficient in general. In addition to the intrinsic inefficiency of equilibria, the authors recently showed that, in mixed-autonomy networks in which autonomous vehicles maintain a shorter headway than human-driven cars, increasing the fraction of autonomous vehicles in the network may increase the inefficiency of equilibria. In this work, we study the possibility of obviating the inefficiency of equilibria in mixed-autonomy traffic networks via pricing mechanisms. In particular, we study assigning prices to network links such that the overall or social delay of the resulting equilibria is minimum. First, we study the possibility of inducing such optimal equilibria by imposing a set of undifferentiated prices, i.e. a set of prices that treat both human-driven and autonomous vehicles similarly at each link. We provide an example which demonstrates that undifferentiated pricing is not sufficient for achieving minimum social delay. Then, we study differentiated pricing where the price of traversing each link may depend on whether vehicles are human-driven or autonomous. Under differentiated pricing, we prove that link prices obtained from the marginal cost taxation of links will induce equilibria with minimum social delay if the degree of road capacity asymmetry (i.e. the ratio between the road capacity when all vehicles are human-driven and the road capacity when all vehicles are autonomous) is homogeneous among network links.

It is known that connected and autonomous vehicles are capable of maintaining shorter headways and distances when they form platoons of vehicles. Thus, such technologies can result in increases in the capacities of traffic networks. Consequently, it is envisioned that their deployment will boost the network mobility. In this paper, we verify the validity of this impact under selfish routing behavior of drivers in traffic networks with mixed autonomy, i.e. traffic networks with both regular and autonomous vehicles. We consider a nonatomic routing game on a network with inelastic (fixed) demands for the set of network O/D pairs, and study how replacing a fraction of regular vehicles by autonomous vehicles will affect the mobility of the network. Using the well known US bureau of public roads (BPR) traffic delay models, we show that the resulting Wardrop equilibrium is not necessarily unique even in its weak sense for networks with mixed autonomy. We state the conditions under which the total network delay is guaranteed not to increase as a result of autonomy increase. However, we show that when these conditions do not hold, counter intuitive behaviors may occur: the total delay can grow by increasing the network autonomy. In particular, we prove that for networks with a single O/D pair, if the road degrees of asymmetry are homogeneous, the total delay is 1) unique, and 2) a nonincreasing continuous function of network autonomy fraction. We show that for heterogeneous degrees of asymmetry, the total delay is not unique, and it can further grow with autonomy increase. We demonstrate that similar behaviors may be observed in networks with multiple O/D pairs. We further bound such performance degradations due to the introduction of autonomy in homogeneous networks.

We propose a map-aided vehicle localization method for GPS-denied environments. This approach exploits prior knowledge of the road grade map and vehicle on-board sensor measurements to accurately estimate the longitudinal position of the vehicle. Real-time localization is crucial to systems that utilize position-dependent information for planning and control. We validate the effectiveness of the localization method on a hierarchical control system. The higher level planner optimizes the vehicle velocity to minimize the energy consumption for a given route by employing traffic condition and road grade data. The lower level is a cruise control system that tracks the position-dependent optimal reference velocity. Performance of the proposed localization algorithm is evaluated using both simulations and experiments.

Vehicle bypassing is known to negatively affect delays at traffic diverges. However, due to the complexities of this phenomenon, accurate and yet simple models of such lane change maneuvers are hard to develop. In this work, we present a macroscopic model for predicting the number of vehicles that bypass at a traffic diverge. We take into account the selfishness of vehicles in selecting their lanes; every vehicle selects lanes such that its own cost is minimized. We discuss how we model the costs experienced by the vehicles. Then, taking into account the selfish behavior of the vehicles, we model the lane choice of vehicles at a traffic diverge as a Wardrop equilibrium. We state and prove the properties of Wardrop equilibrium in our model. We show that there always exists an equilibrium for our model. Moreover, unlike most nonlinear asymmetrical routing games, we prove that the equilibrium is unique under mild assumptions. We discuss how our model can be easily calibrated by running a simple optimization problem. Using our calibrated model, we validate it through simulation studies and demonstrate that our model successfully predicts the aggregate lane change maneuvers that are performed by vehicles for bypassing at a traffic diverge. We further discuss how our model can be employed to obtain the optimal lane choice behavior of the vehicles, where the social or total cost of vehicles is minimized. Finally, we demonstrate how our model can be utilized in scenarios where a central authority can dictate the lane choice and trajectory of certain vehicles so as to increase the overall vehicle mobility at a traffic diverge. Examples of such scenarios include the case when both human driven and autonomous vehicles coexist in the network. We show how certain decisions of the central authority can affect the total delays in such scenarios via an example.

This paper presents a model-based method for fusing data from multiple sensors with a hypothesis-test-based component for rejecting potentially faulty or otherwise malign data. Our framework is based on an extension of the classic particle filter algorithm for real-time state estimation of uncertain systems with nonlinear dynamics with partial and noisy observations. This extension, based on classical statistical theories, utilizes statistical tests against the system's observation model. We discuss the application of the two major statistical testing frameworks, Fisherian significance testing and Neyman-Pearsonian hypothesis testing, to the Monte Carlo and sensor fusion settings. The Monte Carlo Neyman-Pearson test we develop is useful when one has a reliable model of faulty data, while the Fisher one is applicable when one may not have a model of faults, which may occur when dealing with third-party data, like GNSS data of transportation system users. These statistical tests can be combined with a particle filter to obtain a Monte Carlo state estimation scheme that is robust to faulty or outlier data. We present a synthetic freeway traffic state estimation problem where the filters are able to reject simulated faulty GNSS measurements. The fault-model-free Fisher filter, while underperforming the Neyman-Pearson one when the latter has an accurate fault model, outperforms it when the assumed fault model is incorrect., Comment: IEEE Intelligent Transportation Systems Magazine, special issue on GNSS-based positioning

To help mitigate road congestion caused by the unrelenting growth of traffic demand, many transportation authorities have implemented managed lane policies, which restrict certain freeway lanes to certain types of vehicles. It was originally thought that managed lanes would improve the use of existing infrastructure through demand-management behaviors like carpooling, but implementations have often been characterized by unpredicted phenomena that are sometimes detrimental to system performance. The development of traffic models that can capture these sorts of behaviors is a key step for helping managed lanes deliver on their promised gains. Towards this goal, this paper presents an approach for solving for driver behavior of entering and exiting managed lanes at the macroscopic (i.e., fluid approximation of traffic) scale. Our method is inspired by recent work in extending a dynamic-system-based modeling framework from traffic behaviors on individual roads, to models at junctions, and can be considered a further extension of this dynamic-system paradigm to the route/lane choice problem. Unlike traditional route choice models that are often based on discrete-choice methods and often rely on computing and comparing drivers' estimated travel times from taking different routes, our method is agnostic to the particular choice of physical traffic model and is suited specifically towards making decisions at these interfaces using only local information. These features make it a natural drop-in component to extend existing dynamic traffic modeling methods., Comment: 2018 ASME Dynamic Systems and Control Conference (DSCC 2018)

A frequency based data-driven control design considering mixed H2/H-infinity control objectives is developed for multiple input-single output systems. The main advantage of the data-driven control over the model-based control is its ability to use the frequency response measurements of the controlled plant directly without the need to identify a model for the plant. In the proposed methodology, multiple sets of measurements can be considered in the design process to accommodate variations in the system dynamics. The controller is obtained by translating the mixed H2/H-infinity control objectives into a convex optimization problem. The H-infinity norm is used to shape closed loop transfer functions and guarantee closed loop stability, while the H2 norm is used to constrain and/or minimize the variance of signals in the time domain. The proposed data-driven design methodology is used to design a track following controller for a dual-stage HDD. The sensitivity decoupling structure[16] is considered as the controller structure. The compensators inside this controller structure are designed and compared by decoupling the system into two single input-single-output systems as well as solving for a single input-double output controller.

This paper addresses an open problem in traffic modeling: the second-order macroscopic node problem. A second-order macroscopic traffic model, in contrast to a first-order model, allows for variation of driving behavior across subpopulations of vehicles in the flow. The second-order models are thus more descriptive (e.g., they have been used to model variable mixtures of behaviorally-different traffic, like car/truck traffic, autonomous/human-driven traffic, etc.), but are much more complex. The second-order node problem is a particularly complex problem, as it requires the resolution of discontinuities in traffic density and mixture characteristics, and solving of throughflows for arbitrary numbers of input and output roads to a node (in other words, this is an arbitrary-dimensional Riemann problem with two conserved quantities). In this paper, we extend the well-known "Generic Class of Node Model" constraints to the second order and present a simple solution algorithm to the second-order node problem. Our solution makes use of a recently-introduced dynamic system characterization of the first-order node model problem, which gives insight and intuition as to the continuous-time dynamics implicit in node models. We further argue that the common "supply and demand" construction of node models that decouples them from link models is not suitable to the second-order node problem. Our second-order node model and solution method have immediate applications in allowing modeling of behaviorally-complex traffic flows of contemporary interest (like partially-autonomous-vehicle flows) in arbitrary road networks.

To help mitigate road congestion caused by the unrelenting growth of traffic demand, many transit authorities have implemented managed lane policies. Managed lanes typically run parallel to a freeway's standard, general-purpose (GP) lanes, but are restricted to certain types of vehicles. It was originally thought that managed lanes would improve the use of existing infrastructure through incentivization of demand-management behaviors like carpooling, but implementations have often been characterized by unpredicted phenomena that is often to detrimental system performance. This paper presents several macroscopic traffic modeling tools we have used for study of freeways equipped with managed lanes, or "managed lane-freeway networks." The proposed framework is based on the widely-used first-order kinematic wave theory. In this model, the GP and the managed lanes are modeled as parallel links connected by nodes, where certain type of traffic may switch between GP and managed lane links. Two types of managed lane topologies are considered: full-access, where vehicles can switch between the GP and the managed lanes anywhere; and separated, where such switching is allowed only at certain locations called gates. We also describe methods to incorporate in three phenomena into our model that are particular to managed lane-freeway networks. The inertia effect reflects drivers' inclination to stay in their lane as long as possible and switch only if this would obviously improve their travel condition. The friction effect reflects the empirically-observed driver fear of moving fast in a managed lane while traffic in the adjacent GP lanes moves slowly due to congestion. The smoothing effect describes how managed lanes can increase throughput at bottlenecks by reducing lane changes. We present simple models for each of these phenomena that fit within the general macroscopic theory., Comment: The above abstract is slightly abbreviated, please see the document for the full abstract

We are experiencing an explosion in the amount of sensors measuring our activities and the world around us. These sensors are spread throughout the built environment and can help us perform state estimation and control of related systems, but they are often built and/or maintained by third parties or system users. As a result, by outsourcing system measurement to third parties, the controller must accept their measurements without being able to directly verify the sensors' correct operation. Instead, detection and rejection of measurements from faulty sensors must be done with the raw data only. Towards this goal, we present a method of detecting possibly faulty behavior of sensors. The method does not require that the control designer have any model of faulty sensor behavior. As we discuss, it turns out that the widely-used particle filter state estimation algorithm provides the ingredients necessary for a hypothesis test against all ranges of correct operating behavior, obviating the need for a fault model to compare measurements. We demonstrate the applicability of our method by demonstrating its ability to reject faulty measurements and improve state estimation accuracy in a nonlinear vehicle traffic model without information of generated faulty measurements' characteristics. In our test, we correctly identify nearly 90% of measurements as faulty or non-faulty without having any fault model. This leads to only a 3% increase in state estimation error over a theoretical 100%-accurate fault detector., Comment: To appear at the 56th IEEE Conference on Decision and Control (CDC 2017)

The propagation of traffic congestion along roads is a commonplace nonlinear phenomenon. When many roads are connected in a network, congestion can spill from one road to others as drivers queue to enter a congested road, creating further nonlinearities in the network dynamics. This paper considers the node model problem, which refers to methods for solving for cross-flows when roads meet at a junction. We present a simple hybrid dynamic system that, given a macroscopic snapshot of the roads entering and exiting a node, intuitively models the node's throughflows over time. This dynamic system produces solutions to the node model problem that are equal to those produced by many popular node models without intuitive physical meanings. We also show how the earlier node models can be rederived as executions of our dynamic system. The intuitive physical description supplied by our system provides a base for control of the road junction system dynamics, as well as the emergent network dynamics., Comment: Appeared at NOLCOS 2016, 10th IFAC Symposium on Nonlinear Control Systems

A direct adaptive feedforward control method for tracking repeatable runout (RRO) in bit patterned media recording (BPMR) hard disk drives (HDD) is proposed. The technique estimates the system parameters and the residual RRO simultaneously and constructs a feedforward signal based on a known regressor. An improved version of the proposed algorithm to avoid matrix inversion and reduce computation complexity is given. Results for both MATLAB simulation and digital signal processor (DSP) implementation are provided to verify the effectiveness of the proposed algorithm., Comment: 3 pages and 4 figures. Submitted to ASME 2016 Conference on Information Storage and Processing Systems

This paper proposes a novel direct adaptive control method for rejecting unknown deterministic disturbances and tracking unknown trajectories in systems with uncertain dynamics when the disturbances or trajectories are the summation of multiple sinusoids with known frequencies, such as periodic profiles or disturbances. The proposed algorithm does not require a model of the plant dynamics and does not use batches of measurements in the adaptation process. Moreover, it is applicable to both minimum and non-minimum phase plants. The algorithm is a "direct" adaptive method, in the sense that the identification of system parameters and the control design are performed simultaneously. In order to verify the effectiveness of the proposed method, an add-on controller is designed and implemented in the servo system of a hard disk drive to track unknown nano-scale periodic trajectories., Comment: 8 pages, 6 Figures, Submitted to 55th IEEE Conference on Decision and Control

Macroscopic traffic models are necessary for simulation and study of traffic's complex macro-scale dynamics, and are often used by practitioners for road network planning, integrated corridor management, and other applications. These models have two parts: a link model, which describes traffic flow behavior on individual roads, and a node model, which describes behavior at road junctions. As the road networks under study become larger and more complex --- nowadays often including arterial networks --- the node model becomes more important. This paper focuses on the first order node model and has two main contributions. First, we formalize the multi-commodity flow distribution at a junction as an optimization problem with all the necessary constraints. Most interesting here is the formalization of input flow priorities. Then, we discuss a very common "conservation of turning fractions" or "first-in-first-out" (FIFO) constraint, and how it often produces unrealistic spillback. This spillback occurs when, at a diverge, a queue develops for a movement that only a few lanes service, but FIFO requires that all lanes experience spillback from this queue. As we show, avoiding this unrealistic spillback while retaining FIFO in the node model requires complicated network topologies. Our second contribution is a "partial FIFO" mechanism that avoids this unrealistic spillback, and a node model and solution algorithm that incorporates this mechanism. The partial FIFO mechanism is parameterized through intervals that describe how individual movements influence each other, can be intuitively described from physical lane geometry and turning movement rules, and allows tuning to describe a link as having anything between full FIFO and no FIFO. Excepting the FIFO constraint, the present node model also fits within the well-established "general class of first-order node models" for multi-commodity flows., Comment: The abstract on this info page is slightly abbreviated, please see the paper for the full abstract

In an age of ever-increasing penetration of GPS-enabled mobile devices, the potential of real-time "probe" location information for estimating the state of transportation networks is receiving increasing attention. Much work has been done on using probe data to estimate the current speed of vehicle traffic (or equivalently, trip travel time). While travel times are useful to individual drivers, the state variable for a large class of traffic models and control algorithms is vehicle density. Our goal is to use probe data to supplement traditional, fixed-location loop detector data for density estimation. To this end, we derive a method based on Rao-Blackwellized particle filters, a sequential Monte Carlo scheme. We present a simulation where we obtain a 30\% reduction in density mean absolute percentage error from fusing loop and probe data, vs. using loop data alone. We also present results using real data from a 19-mile freeway section in Los Angeles, California, where we obtain a 31\% reduction. In addition, our method's estimate when using only the real-world probe data, and no loop data, outperformed the estimate produced when only loop data were used (an 18\% reduction). These results demonstrate that probe data can be used for traffic density estimation.

We propose a macroscopic modeling framework for a network of roads and multi-commodity traffic. The proposed framework is based on the Lighthill-Whitham-Richards kinematic wave theory; more precisely, on its discretization, the Cell Transmission Model (CTM), adapted for networks and multi-commodity traffic. The resulting model is called the Link-Node CTM (LNCTM). In the LNCTM, we use the fundamental diagram of an "inverse lambda" shape that allows modeling of the capacity drop and the hysteresis behavior of the traffic state in a link that goes from free flow to congestion and back. A model of the node with multiple input and multiple output links accepting multi-commodity traffic is a cornerstone of the LNCTM. We present the multi-input-multi-output (MIMO) node model for multi-commodity traffic that supersedes previously developed node models. The analysis and comparison with previous node models are provided. Sometimes, certain traffic commodities may choose between multiple output links in a node based on the current traffic state of the node's input and output links. For such situations, we propose a local traffic assignment algorithm that computes how incoming traffic of a certain commodity should be distributed between output links, if this information is not known a priori., Comment: 34 pages with appendix and examples. Figures in black and white. v3: Typos corrected