Arrival Cost Research Articles

Optimizing dedicated lanes and tolling schemes for connected and autonomous vehicles to address bottleneck congestion considering morning commuter departure choices

The introduction of connected and autonomous vehicles (CAVs) provides a significant opportunity to address the persistently increasing problem of urban traffic congestion. By virtue of their connectivity and automation features, CAVs can reduce vehicle headways, thereby increasing road capacity and enhancing throughput. It has been hypothesized that CAV-infrastructure design policies can influence traveler behavior in ways that could reduce congestion. This research focuses on the potential of using CAV-dedicated lanes (CAVL) to alleviate traffic congestion in a bottleneck corridor that serves both human-driven vehicles (HDVs) and CAVs. We delve into investigating the impacts of CAVLs on the departure time and lane choices of morning commuters. The study first expresses traffic equilibrium conditions as a linear program with complementarity constraints. Then, a system-optimal commute congestion management design is formulated to minimize the overall system cost, which consists of queuing delays and early and late arrival costs. The results of the computational experiments suggest that: (i) the CAV technological advancements can significantly reduce traffic congestion under CAVL deployment with an almost similar effect as a tolling policy; and (ii) the lower value of time for CAV commuters leads them to depart closer to their desired arrival time without a tolling policy, which could significantly increase the bottleneck traffic congestion that commuters experience, particularly HDVs.

Approximating arrival costs in distributed moving horizon estimation: A recursive method

In this paper, we present a new approach to distributed moving horizon estimation for constrained nonlinear processes. The method involves approximating the arrival costs of local estimators through a recursive framework. First, distributed full-information estimation for linear unconstrained systems is presented, which serves as the foundation for deriving the analytical expression of the arrival costs for the local estimators. Subsequently, we develop a recursive arrival cost design for linear distributed moving horizon estimation. Sufficient conditions are derived to ensure the stability of the estimation error for constrained linear systems. Next, we extend the arrival cost design derived for linear systems to account for nonlinear systems, and a partition-based constrained distributed moving horizon estimation algorithm for nonlinear systems is formulated. A benchmark chemical process is used to illustrate the effectiveness and superiority of the proposed method.

A Recursive Approach to Approximate Arrival Costs in Distributed Moving Horizon Estimation

In this paper, we present a novel approach to distributed moving horizon estimation for nonlinear processes. The method involves approximating the arrival costs of local estimators through a recursive framework. First, we formulate distributed full-information estimation for linear unconstrained systems, which serves as the foundation for deriving the analytical expression of the arrival cost. Subsequently, a recursive arrival cost design for linear distributed moving horizon estimation is developed. Then, we extend the arrival cost design obtained for linear systems to account for the nonlinear context, and a partition-based constrained distributed moving horizon estimation algorithm for nonlinear systems is formulated. A chemical process is introduced to illustrate the effectiveness of the proposed method.

Maximum-likelihood arrival cost for moving-horizon estimation – Application to mammalian cell culture

Moving-horizon estimation performance depends on the arrival-cost approximation. Different methods exist to approximate the arrival cost with different trade-offs, such as limited performance, complex implementation, or abusive computational cost. In particular, we can distinguish two different methods based on using an external filter or the optimality conditions to calculate the covariance of the estimations. This paper presents a simpler alternative for the arrival-cost approximation based on maximum-likelihood estimation. The performance of this approximation is assessed using a mammalian cell culture case study where biomass and glutamine concentrations are estimated.

Consensus-based distributed moving horizon estimation with constraints

This paper concerns distributed state estimation for linear systems over a sensor network. Two novel algorithms utilizing the framework of moving horizon estimation (MHE) are proposed, which are fully distributed, scalable and allow for taking into account constraints on the noises and the system states. The proposed methods estimate the state by minimizing a local quadratic objective function, which can be efficiently solved by quadratic programming (QP). Consensus technique is employed to fuse information to construct the local quadratic objective function for each node. The first algorithm, which minimizes a quadratic function involving consensus on measurement costs (CM), approaches the centralized MHE with a sufficiently large number of consensus steps. The second one involving consensus both on arrival costs (CA) and measurement costs, enjoys the benefits of both the CA and CM. To avoid directly running consensus on some functions, a novel consensus strategy for the CM is developed. The estimation errors of the proposed methods are proven to be stochastically ultimately bounded under certain conditions. Finally, numerical results are presented to verify the effectiveness of the developed algorithms.

Moving horizon estimation of vehicle state and parameters

For the active safety control of the vehicle, it is extremely important to estimate the vehicle state in real-time and accurately during the driving process. A joint state and parameter estimation method based on QR decomposition and receding horizon estimation (RHE) is proposed. Firstly, by introducing the receding horizon strategy, the authors optimized the state and parameter estimation with a fixed number of variables, which can better deal with the estimation problem of time-varying parameters. Then, based on the principle of forward dynamic programming, the calculation of arrival cost is transformed into a least square equation, which is solved by QR decomposition. At the same time, an update method of arrival cost based on QR decomposition is given. In this way, the whole receding horizon estimation method is based on the optimization, and the feedback mechanism is introduced to improve the estimation accuracy and speed. The simulation results show that the accuracy of receding horizon estimation is obviously better than that of unscented Kalman filter (UKF), and the arrival cost update method based on QR decomposition is more convenient than the traditional arrival cost update method based on error covariance estimation.

Joint State and Parameter Estimation for Hypersonic Glide Vehicles Based on Moving Horizon Estimation via Carleman Linearization

Aimed at joint state and parameter estimation problems in hypersonic glide vehicle defense, a novel moving horizon estimation algorithm via Carleman linearization is developed in this paper. First, the maneuver characteristic parameters that reflect the target maneuver law are extended into the state vector, and a dynamic tracking model applicable to various hypersonic glide vehicles is constructed. To improve the estimation accuracy, constraints such as path and parameter change amplitude constraints in flight are taken into account, and the estimation problem is transformed into a nonlinear constrained optimal estimation problem. Then, to solve the problem of high time cost for solving a nonlinear constrained optimal estimation problem, in the framework of moving horizon estimation, nonlinear constrained optimization problems are transformed into bilinear constrained optimization problems by linearizing the nonlinear system via Carleman linearization. For ensuring the consistency of the linearized system with the original nonlinear system, the linearized model is continuously updated as the window slides forward. Moreover, a CKF-based arrival cost update algorithm is also provided to improve the estimation accuracy. Simulation results demonstrate that the proposed joint state and parameter estimation algorithm greatly improves the estimation accuracy while reducing the time cost significantly.

An Extended Moving Horizon Estimation embedded with an Abridged Gaussian Sum Extended Kalman Filer to handle non-Gaussian noises

Most industrial processes involve changes in the operating conditions that may lead to non-Gaussian process uncertainties and measurement noises. Recently, an Abridged Gaussian Sum Extended Kalman Filter (AGS-EKF) and Extended Moving Horizon Estimation (EMHE) frameworks were proposed to capture non-Gaussian random uncertainties and noises often present in the chemical systems. Gaussian mixture models (GMM) are used in both estimation schemes to efficiently approximate the non-Gaussian distributions. Previous studies on EMHE considered a sufficiently long estimation horizon to minimize the arrival cost effect. The present work aims to further improve the performance of EMHE by introducing a suitable arrival cost estimator to shorten the estimation horizon. As the focus of this study is on systems involving non-Gaussian noises, AGS-EKF as a non-Gaussian state estimator is selected to estimate the arrival cost. The performance of the proposed estimation framework was tested using the open-loop unstable Williams-Otto reactor considering non-Gaussian uncertainties and noises. The results revealed that the proposed estimation framework improves the estimation in the presence of non-Gaussian noises when compared to the standard framework (MHE combined with EKF) thus making it a suitable estimation method for systems involving non-Gaussian noises.

Enhancement of the Moving Horizon Estimation Performance Based on an Adaptive Estimation Algorithm

Although moving horizon estimation (MHE) is a very efficient technique for estimating parameters and states of constrained dynamical systems, however, the approximation of the arrival cost remains a major challenge and therefore a popular research topic. The importance of the arrival cost is such that it allows information from past measurements to be introduced into current estimates. In this paper, using an adaptive estimation algorithm, we approximate and update the parameters of the arrival cost of the moving horizon estimator. The proposed method is based on the least-squares algorithm but includes a variable forgetting factor which is based on the constant information principle and a dead zone which ensures robustness. We show by this method that a fairly good approximation of the arrival cost guarantees the convergence and stability of estimates. Some simulations are made to show and demonstrate the effectiveness of the proposed method and to compare it with the classical MHE.

Target-Oriented User Equilibrium Considering Travel Time, Late Arrival Penalty, and Travel Cost on the Stochastic Tolled Traffic Network

In this paper, we employ a target-oriented approach to analyze the multi-attribute route choice decision of travelers in the stochastic tolled traffic network, considering the influence of three attributes, which are (stochastic) travel time, (stochastic) late arrival penalty, and (deterministic) travel cost. We introduce a target-oriented multi-attribute travel utility model for this analysis, where each attribute is assigned a target by travelers, and travelers’ objective is to maximize their travel utility that is determined by the achieved targets. Moreover, the interaction between targets is interpreted as complementarity relationship between them, which can further affect their travel utility. In addition, based on this travel utility model, a target-oriented multi-attribute user equilibrium model is proposed, which is formulated as a variational inequality problem and solved with the method of successive average. Target for travel time is determined via travelers’ on-time arrival probability, while targets for late arrival penalty and travel cost are given exogenously. Lastly, we apply the proposed model on the Braess and Nguyen–Dupuis traffic networks, and conduct sensitivity analysis of the parameters, including these three targets and the target interaction between them. The study in this paper can provide a new perspective for travelers’ multi-attribute route choice decision, which can further show some implications for the policy design.

Zero-order moving horizon estimation for large-scale nonlinear processes

Moving Horizon Estimation (MHE) is an optimization-based approach to nonlinear state estimation where the state estimate is obtained as the solution of a nonlinear optimization problem. Especially for large-scale nonlinear systems, the computational burden associated with the numerical solution of nonlinear optimization problems poses a major challenge when applying MHE in practice. To alleviate the computational effort, we propose an inexact, but computationally less expensive variant of the Gauss–Newton algorithm tailored to the nonlinear least-squares problem arising from the MHE formulation. The proposed algorithm combines two ideas: On the one hand, it uses the fact that the arrival cost matrix appears naturally within the Gauss–Newton Hessian approximation in order to avoid any explicit arrival cost update. On the other hand, the method follows a zero-order optimization approach, where fixed sensitivity approximations are used in order to reduce the number of sensitivity evaluations, while accepting some loss of optimality. The combination of these two ideas allows one to reuse the factorizations of the Hessian blocks associated with each stage, when moving from one MHE problem to the next, therefore significantly reducing the computational complexity. Additionally, a tailored integration method for large-scale stiff systems is proposed that can efficiently propagate approximate forward sensitivities, which are used within the inexact MHE algorithm. Both estimation accuracy and computational efficiency of the proposed method are evaluated by applying it to two case studies: a small-scale batch reactor model and the large-scale dynamic process of acrylic acid production.

Assessing the Impact of EKF as the Arrival Cost in the Moving Horizon Estimation under Nonlinear Model Predictive Control

In this work, we investigate the performance of nonlinear model predictive control (NMPC) and moving horizon estimation (MHE) in a feedback control system subject to different arrival cost (AC) approximation methods, process uncertainties with non-Gaussian distributions, and plant designs. In particular, we investigate the performance of an extended Kalman filter (EKF) as an AC estimator for large and complex applications. Considering the significant impact of state estimations as the initial condition of the NMPC problem, together with the importance of the AC approximation in the success of the MHE framework, it is expected that a poor approximation of the AC may lead to poor closed-loop performance. Different arrival cost estimation methods including the traditional EKF and constrained particle filtering were evaluated in this work. The closed-loop framework was tested on two industrial applications: a wastewater treatment plant and a high-impact polystyrene process. Error analysis on the convergence of the EKF-based AC estimator is presented in this work to provide insights into the performance of EKF as an AC estimator under different scenarios. The results show that an appropriate arrival cost estimation method such as EKF is adequate to maintain the operation of large and challenging systems in a closed-loop using an MHE–NMPC framework.

Robust stability of moving horizon estimation for non‐linear systems with bounded disturbances using adaptive arrival cost

Fil: Deniz, Nestor Nahuel. Consejo Nacional de Investigaciones Cientificas y Tecnicas. Centro Cientifico Tecnologico Conicet - Santa Fe. Instituto de Investigacion en Senales, Sistemas e Inteligencia Computacional. Universidad Nacional del Litoral. Facultad de Ingenieria y Ciencias Hidricas. Instituto de Investigacion en Senales, Sistemas e Inteligencia Computacional; Argentina. Universidad Nacional del Litoral. Facultad de Ingenieria y Ciencias Hidricas; Argentina

Moving Horizon Estimation for Uncertain Networked Control Systems with Packet Loss

This paper studies a moving horizon estimation approach to solve the constrained state estimation problem for uncertain networked systems with random packet loss. The system model error range is known, and the packet loss phenomena are modeled by a binary switching random sequence. Taking the model error, the packet loss, the system constraints, and the network transmission noise into account, a time-varying weight matrix is obtained by solving a least-square problem. Then, a robust moving horizon estimator is designed to estimate the system state by minimizing an optimization problem with an arrival cost function. The proposed estimator ensures that the optimal estimated state can be obtained in the worst case. Furthermore, the asymptotic convergence of the estimator is analyzed and some sufficient conditions for convergence are given. Finally, the validity of the proposed approach can be demonstrated by numerical simulations.

Holistic tactical-level planning in liner shipping: an exact optimization approach

Effective liner shipping is important for the global seaborne trade. The volume of cargoes transported by liner shipping has been increasing over the past decades. Liner shipping companies face three levels of decision problems, including strategic, tactical, and operational problems. The tactical-level decisions are commonly made every three to 6 months. These decisions include: (1) port service frequency determination; (2) fleet deployment; (3) sailing speed optimization; and (4) vessel schedule design. Most of the concurrent liner shipping studies have addressed the tactical-level decision problems separately. Even though a few studies have proposed joint planning models that capture multiple decision problems at the same time, none of the conducted studies has integrated all the four tactical-level decision problems. To address this gap in the state-of-the-art, this study presents a holistic optimization model that addresses all the tactical-level liner shipping decision problems, aiming to maximize the total profit obtained from liner shipping services. The key route service cost components, found in the liner shipping literature, are considered in this study, which include: (1) vessel operational cost; (2) vessel chartering cost; (3) port handling cost; (4) port late arrival cost; (5) fuel consumption cost; (6) container inventory costs in sea and at ports of call; and (7) emission costs in sea and at ports of call. An exact optimization approach is adopted for the developed mathematical model. The computational experiments, conducted for a set of Asia-North America liner shipping routes, showcase the efficiency of the proposed approach and offer some important managerial insights.

Distributed Moving-Horizon Estimation With Arrival-Cost Consensus

The paper deals with the problem of estimating the state of a linear system over a peer-to-peer network of linear sensors. The proposed approach is fully distributed, scalable, and allows for taking into account constraints on noise and state variables by resorting to the moving-horizon estimation paradigm. Each network node computes its local state estimate by minimizing a cost function defined over a sliding window of fixed size. The cost function includes a fused arrival cost, which is computed in a distributed way by performing a consensus on the local arrival costs. The proposed estimator guarantees stability of the estimation error dynamics in all network nodes, under the minimal requirements of network connectivity and collective observability, and for any number of consensus steps. Numerical simulations are provided to demonstrate the practical effectiveness of the approach.

Dynamic Multi-Tenant Coordination for Sustainable Colocation Data Centers

Colocation data centers are an important type of data centers that have some unique challenges in managing their energy consumption. Tenants in a colocation data center usually manage their servers independently without coordination, leading to inefficiency. To address this issue, we propose a formulation of coordinated energy management for colocation data centers. Considering the randomness of workload arrival and electricity cost function, we formulate it as a stochastic optimization problem, and then develop an online algorithm to solve it efficiently. Our algorithm is based on Lyapunov optimization, which only needs to track the instantaneous values of the underlying random factors without requiring any knowledge of the statistics or future information. Moreover, alternating direction method of multipliers (ADMM) is utilized to implement our algorithm in a decentralized way, making it easy to be implemented in practice. We analyze the performance of our online algorithm, proving that it is asymptotically optimal and robust to the statistics of the involved random factors. Moreover, extensive trace-based simulations are conducted to illustrate the effectiveness of our approach.

Sensor placement and moving horizon state/parameter estimation for flexible hypersonic vehicles

Considering the nonlinearity, uncertainty, and rigid/elastic coupling, a state/parameter joint estimation method is essential for control system design or fault diagnosis of flexible hypersonic vehicles. With the goal of improving state/parameter estimation accuracy, this paper proposes a sensor placement strategy and a moving horizon estimation algorithm with a QR-decomposition-based arrival cost update strategy (MHE-QR). To enhance observability, a novel double sensor placement strategy, in which the sensor positions are obtained via solving a constrained nonlinear optimization problem, is developed. The MHE-QR algorithm transforms the arrival cost update problem into a least square problem and solves it utilizing QR decomposition. With this QR-decomposition-based arrival update strategy, the state/parameter estimation problem is solved as a nonlinear programming problem in the framework of moving horizon estimation. Finally, the performance of sensor placement strategy and MHE-QR is evaluated by Monte Carlo simulations in 10 different scenarios. Simulation results demonstrate that the sensor placement strategy and MHE-QR algorithm can effectively improve the estimation accuracy, convergence speed and computation rate. Additionally, the CPU time of MHE-QR validates its real-time applicability.

Logistics scheduling to minimize the sum of total weighted inventory cost and transport cost

Abstract This paper studies the logistics scheduling problem in the context of a three-stage supply chain comprising a supplier, a manufacturer, and a customer. The supplier supplies raw materials (jobs) to the manufacturer, which processes them into finished products (processed jobs) and transports them to the customer. We analyze the problem using a batching and scheduling model involving both batch supply and batch delivery. The objective is to minimize the sum of the total weighted inventory cost and transport cost. The inventory cost is related to the job flow time, which is the time between the arrival of a job to the manufacturer and the time it is finished processing and leaves the manufacturer. The transport cost is related to the number of batches created. Four cases associated with batch supply and batch delivery, depending on the relative strengths of the arrival cost, inventory cost, and delivery cost are discussed in this paper. We show that all the cases are NP-hard when the number of batches has a constant upper bound, and give a fully polynomial-time approximation scheme for each case.

Enforcement of labor market regulations: heterogeneous compliance and adjustment across gender

This paper explores microdata from Argentine household surveys to analyze how changes in the enforcement of labor regulations affect the compliance level and other labor outcomes among men and women. Using information of the highly decentralized labor inspection system in Argentina, I construct an enforcement measure with variation at the province, sector, and time level (share of inspected firms) which I instrument using a measure of the arrival cost of labor inspectors to the firms. The main findings reveal that when enforcement increases, the compliance with mandated benefits and formal wages increase among men, while informal wages decline. Among women, the compliance level declines jointly with informal wages. These heterogenous impacts are explained by labor regulations that make formal and informal men more substitutable in the production process than formal and informal women.