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The advent of autonomous racing events, such as Formula Student Driverless Cup, requires online motion planning algorithms that push the vehicle to its limits while ensuring vehicle stability and preventing road departure. A popular method to find the optimal control input to drive at the limits of the car is Nonlinear Model Predictive Control (NMPC). However, when NMPC is used, often a trade-off has to be made between performance, accuracy, and computational complexity. In this manuscript, the principle of cascading different vehicle models is used to construct the prediction horizon. Initially, a two-track model optimizes steering and motor input, utilizing torque vectoring benefits. The horizon is then extended with a single-track model, and a lower fidelity point mass model, effectively reducing computational complexity. Furthermore, by adopting a curvilinear reference frame, a transformation towards the spatial domain is obtained, which allows us to use time as an optimization variable. A simulation study is performed for varying prediction horizon lengths which show the advantages of the cascaded vehicle model, achieving an 86% reduction in computation time with comparable lap times.

Cooperative Adaptive Cruise Control (CACC) has the potential to increase road throughput and safety. By utilizing vehicle-to-vehicle (V2V) communication, string stability can be achieved at short inter-vehicle distances. This paper presents a decentralized control approach suitable for heterogeneous platoons with drivetrain delays. By approximating the plant with delay during the controller design, a controller is obtained that ensures string stable behavior and has a nominal performance similar to an approach where the delay is compensated by a Smith predictor. The controller presented in this paper has the added benefit that the feedback action can be determined directly by measured signals and the error converges to zero in steady state situations. By combining the controller with an acceleration observer and error observer, undesired effects of measurement noise are mitigated.

Road throughput can be increased by cooperative adaptive cruise control (CACC), which allows vehicles to drive at short inter-vehicle distances without compromising string stability by using wireless inter-vehicle communications. Practical application, however, may involve vehicles with different driveline dynamics, thus forming a heterogeneous platoon. This property potentially requires knowledge of other vehicle's driveline dynamics for implementation of CACC, which may not be available. As opposed to robust or adaptive approaches, the heterogeneity problem is solved here by revisiting an existing, widely adopted controller for homogeneous strings using an input-output linearization approach. As a result, a class of controllers is obtained which allows for vehicle strings that are heterogeneous with respect to driveline dynamics, without requiring knowledge of these dynamics. Furthermore, it is shown that the new controller represents a class of controllers that encompasses the original homogeneous controller. To illustrate the performance of the new controller, simulations of a heterogeneous platoon are presented and the string stability properties are assessed. From this analysis, it appears that the new controller performs at least as good as the original one, in terms of minimum string-stable time gap, settling time, and maximum jerk.

This paper presents an intersection access management methodology that optimizes the crossing sequence of an automated intersection, where the low-level vehicle control is performed by a cooperative intersection control (CIC) strategy. While the CIC regulates the safe and efficient relative motion of vehicles in the intersection, a high-level hybrid queuing model is proposed to describe the dynamics of the vehicle queues associated to each intersection lane. This model, including constraints, is used to design an optimal access management approach based on the model predictive control that minimizes the time that the vehicles spend within the intersection, thereby optimizing the traffic throughput of the intersection. The performance of this methodology is studied by means of two representative examples. The impact of the design parameters of the optimal access management approach is shown for a T-intersection case study. Moreover, using a real-life five lane intersection case study, the proposed approach is compared to a vehicle-actuated traffic light approach, and a first come first served approach. The comparison shows the benefits of the automated optimal serving of vehicles from different lanes.

Road throughput can be increased by cooperative adaptive cruise control (CACC), which allows vehicles to drive at short inter-vehicle distances without compromising string stability by using wireless inter-vehicle communications. Practical application, however, may involve vehicles with different driveline dynamics, thus forming a heterogeneous platoon. This property potentially requires knowledge of other vehicle's driveline dynamics for implementation of CACC, which may not be available. As opposed to robust or adaptive approaches, the heterogeneity problem is solved here by revisiting an existing, widely adopted controller for homogeneous strings using an input-output linearization approach. As a result, a class of controllers is obtained which allows for vehicle strings that are heterogeneous with respect to driveline dynamics, without requiring knowledge of these dynamics. Furthermore, it is shown that the new controller represents a class of controllers that encompasses the original homogeneous controller. To illustrate the performance of the new controller, simulations of a heterogeneous platoon are presented and the string stability properties are assessed. From this analysis, it appears that the new controller performs at least as good as the original one, in terms of minimum string-stable time gap, settling time, and maximum jerk.

This paper presents an intersection access management methodology that optimizes the crossing sequence of an automated intersection, where the low-level vehicle control is performed by a cooperative intersection control (CIC) strategy. While the CIC regulates the safe and efficient relative motion of vehicles in the intersection, a high-level hybrid queuing model is proposed to describe the dynamics of the vehicle queues associated to each intersection lane. This model, including constraints, is used to design an optimal access management approach based on the model predictive control that minimizes the time that the vehicles spend within the intersection, thereby optimizing the traffic throughput of the intersection. The performance of this methodology is studied by means of two representative examples. The impact of the design parameters of the optimal access management approach is shown for a T-intersection case study. Moreover, using a real-life five lane intersection case study, the proposed approach is compared to a vehicle-actuated traffic light approach, and a first come first served approach. The comparison shows the benefits of the automated optimal serving of vehicles from different lanes.

A gzipped-tar file containing the files we used for generating the result in our 2013 paper: M.P.M. Hendriks, E. Lefeber, J.T. Udding, Simultaneous berth allocation and yard planning at tactical level, OR Spectrum 35(2), 441-456, 2013.

A gzipped-tar file containing the files we used for generating the result in our 2013 paper: M.P.M. Hendriks, E. Lefeber, J.T. Udding, Simultaneous berth allocation and yard planning at tactical level, OR Spectrum 35(2), 441-456, 2013.

In this paper we consider the optimization of integral fixed-time (traffic light) schedules for isolated intersections. Such integral schedule has an integral period duration and, moreover, for this schedule all switches to green, yellow and red are scheduled at an integral second. These schedules are desired in practice because they are clear, presentable and easy to work with. Much research has been devoted to the optimization of fixed-time (traffic light) schedules for isolated intersection. However, these methods optimize over all fixed-time schedules and do not necessarily return an integral one. One can simply obtain an integral schedule from any fixed-time schedule by rounding the period duration and the switching times to the nearest integer. However, such an approach might result in an integral schedule that is infeasible. In this paper we give a more rigourous approach to find the optimal integral fixed-time schedule that minimizes the average delay that road users experience at the intersection.

This document contains the data of ten real-life intersections. This data can be used for the optimization of the geometric layout of the intersection, e.g., optimizing the arrival lanes, departure lanes and lane markings at the intersection.

This document contains the data of thirteen real-life intersections. This data can be used for the optimization of fixed-time traffic light control. A fixed-time controller visualizes when each traffic light is green, yellow and red during a repeating period.

In this paper we consider the optimization of integral fixed-time (traffic light) schedules for isolated intersections. Such integral schedule has an integral period duration and, moreover, for this schedule all switches to green, yellow and red are scheduled at an integral second. These schedules are desired in practice because they are clear, presentable and easy to work with. Much research has been devoted to the optimization of fixed-time (traffic light) schedules for isolated intersection. However, these methods optimize over all fixed-time schedules and do not necessarily return an integral one. One can simply obtain an integral schedule from any fixed-time schedule by rounding the period duration and the switching times to the nearest integer. However, such an approach might result in an integral schedule that is infeasible. In this paper we give a more rigourous approach to find the optimal integral fixed-time schedule that minimizes the average delay that road users experience at the intersection.

This document contains the data of ten real-life intersections. This data can be used for the optimization of the geometric layout of the intersection, e.g., optimizing the arrival lanes, departure lanes and lane markings at the intersection.

This document contains the data of thirteen real-life intersections. This data can be used for the optimization of fixed-time traffic light control. A fixed-time controller visualizes when each traffic light is green, yellow and red during a repeating period.

We generalize the standard multi-class queueing network model by allowing both standard queues and infinite virtual queues which have an infinite supply of work. We pose the general problem of finding policies which allow some of the nodes of the network to work with full utilization, and yet keep all the standard queues in the system stable. Toward this end we show that re-entrant lines, systems of two re-entrant lines through two service stations, and rings of service stations can be stabilized with priority policies under certain parameter restrictions. The analysis throughout the paper depends on model and policy and illustrates the difficulty in solving the general problem.

We generalize the standard multi-class queueing network model by allowing both standard queues and infinite virtual queues which have an infinite supply of work. We pose the general problem of finding policies which allow some of the nodes of the network to work with full utilization, and yet keep all the standard queues in the system stable. Toward this end we show that re-entrant lines, systems of two re-entrant lines through two service stations, and rings of service stations can be stabilized with priority policies under certain parameter restrictions. The analysis throughout the paper depends on model and policy and illustrates the difficulty in solving the general problem.

We generalize the standard multi-class queueing network model by allowing both standard queues and in??nite virtual queues which have infinite supply of work. We pose the general problem of finding policies which allow some of the nodes of the network to work with full utilization, and yet keep all the standard queues in the system stable. Towards this end we show that re-entrant lines, systems of two re-entrant lines through two service stations, and rings of service stations can be stabilized with priority policies under certain parameter restrictions. We further establish simple diffusion limits for the departure and work allocation processes. The analysis throughout the paper depends on model and policy and illustrates the difficulty in solving the general problem.

We generalize the standard multi-class queueing network model by allowing both standard queues and in??nite virtual queues which have infinite supply of work. We pose the general problem of finding policies which allow some of the nodes of the network to work with full utilization, and yet keep all the standard queues in the system stable. Towards this end we show that re-entrant lines, systems of two re-entrant lines through two service stations, and rings of service stations can be stabilized with priority policies under certain parameter restrictions. We further establish simple diffusion limits for the departure and work allocation processes. The analysis throughout the paper depends on model and policy and illustrates the difficulty in solving the general problem.

In this paper we consider output feedback tracking of ships withposition and orientation measurements only. Ship dynamics are highlynonlinear, and for tracking control, as opposed to dynamic positioning,these nonlinearities have to be taken into account in the controldesign. We propose an observer-controller scheme which takes intoaccount the complete ship dynamics, including Coriolis and centripetalforces and nonlinear damping, and results in a semi-globallyuniformly stable closed-loop system.Furthermore, a gain tuning procedure forthe observer-controller scheme is developed.Experimental results are presented where the observer-controller schemeis implemented onboard a Froude scaled 1:70 model supply ship. Theexperimentally obtained results are compared with simulation resultsunder ideal conditions and both support the theoretical results onsemi-global exponential stability of the closed-loop system.

Model Predictive Control (MPC) is a well established method in control theory and engineering practice. It is often the method of choice for systems that need to be controlled in view of constraints. The main idea of MPC is to solve an optimization problem over a given time horizon at each control epoch, and to use the obtained solution for controlling the system until the next control epoch. In many cases this optimization problem can be formulated as a tractable quadratic programming problem. In this paper we apply MPC to discrete-time queueing networks that incorporate multiple product routes, delays, self-generated arrivals and multi-job processing. We compare our MPC-based controller to simple threshold policies and show improved performance. We also mention some open theoretical problems related to this control method.

We consider a container terminal operator who faces the problem ofconstructing a cyclic berth plan. Such a plan defines the arrival anddeparture times of each cyclically calling vessel on a terminal, takinginto account the expected number of containers to be handled and thenecessary quay and crane capacity to do so. Conventional berth planningmethods ignore the fact that, in practice, container terminal operatorand shipping line agree upon an arrival window rather than an arrivaltime: if a vessel arrives within that window then a certain vesselproductivity and hence departure time is guaranteed.The contributions of this paper are twofold. We not only minimize thepeak loading of quay cranes in a port, but also explicitly take intoaccount the arrival window agreements between the terminal operator andshipping lines. We present a robust optimization model for cyclicberth planning. Computational results on a real-world scenario for acontainer terminal in Antwerp show that the robust planning model canreach a substantial reduction in the crane capacity that is necessary tomeet the window arrival agreements, as compared to a deterministicplanning approach.

Model Predictive Control (MPC) is a well established method in control theory and engineering practice. It is often the method of choice for systems that need to be controlled in view of constraints. The main idea of MPC is to solve an optimization problem over a given time horizon at each control epoch, and to use the obtained solution for controlling the system until the next control epoch. In many cases this optimization problem can be formulated as a tractable quadratic programming problem. In this paper we apply MPC to discrete-time queueing networks that incorporate multiple product routes, delays, self-generated arrivals and multi-job processing. We compare our MPC-based controller to simple threshold policies and show improved performance. We also mention some open theoretical problems related to this control method.

We consider a container terminal operator who faces the problem ofconstructing a cyclic berth plan. Such a plan defines the arrival anddeparture times of each cyclically calling vessel on a terminal, takinginto account the expected number of containers to be handled and thenecessary quay and crane capacity to do so. Conventional berth planningmethods ignore the fact that, in practice, container terminal operatorand shipping line agree upon an arrival window rather than an arrivaltime: if a vessel arrives within that window then a certain vesselproductivity and hence departure time is guaranteed.The contributions of this paper are twofold. We not only minimize thepeak loading of quay cranes in a port, but also explicitly take intoaccount the arrival window agreements between the terminal operator andshipping lines. We present a robust optimization model for cyclicberth planning. Computational results on a real-world scenario for acontainer terminal in Antwerp show that the robust planning model canreach a substantial reduction in the crane capacity that is necessary tomeet the window arrival agreements, as compared to a deterministicplanning approach.

Predicting the cycle time distribution as a function of throughput is helpful in making a trade-off between workstation productivity and meeting due dates. To predict cycle time distributions, detailed models are almost exclusively used, which require considerable development and maintenance effort. Instead, we propose a so-called aggregate model to predict cycle time distributions, which is a lumped-parameter representation of the queueing system. The lumped parameters of the model are determined directly from arrival and departure events measured at the workstation. The paper demonstrates that the aggregate model can accurately predict the cycle time distribution of workstations in semiconductor manufacturing, in particular the tail of the distribution

Predicting the cycle time distribution as a function of throughput is helpful in making a trade-off between workstation productivity and meeting due dates. To predict cycle time distributions, detailed models are almost exclusively used, which require considerable development and maintenance effort. Instead, we propose a so-called aggregate model to predict cycle time distributions, which is a lumped-parameter representation of the queueing system. The lumped parameters of the model are determined directly from arrival and departure events measured at the workstation. The paper demonstrates that the aggregate model can accurately predict the cycle time distribution of workstations in semiconductor manufacturing, in particular the tail of the distribution

In this report we consider the optimal control problem of emptying a deterministic single server multiclass queuing system without arrivals. We assume that the server is able to serve several queues simultaneously, each at its own rate, independent of the number of queues being served. We showed that the optimal sequence of modes is ordered by rate of cost decrease. However, queues are not necessarily emptied. We propose a dynamic programming approach for solving the problem, which reduces the multiparametric QP (mpQP) to a series of problems that can be solved readily.

We present an MILP formulation to construct a strategic, cyclic terminal allocation and time scheduling for a set of container vessels, which are processed by a multi-terminal port operator. Our case study is about balancing the workload over time, minimizing inter-terminal transport and minimizing deviations from the existing time schedule.

We consider a container operator, who serves a number of shipping lines by discharging and loading their periodically arriving container vessels. Disruptions on vessels’ travel times lead to stochastic arrivals in the port. To cope with these disturbances, the operator and each vessel line agree on two types of arrivals: arrivals i) within, and ii) out of a so-called arrival window. If a vessel arrives within its window, the operator guarantees a maximal process time. If not, the operator is not bound to any guaranteed process time. The problem is to construct a periodic window-based i) arrival, ii) departure and iii) time-variant crane capacity plan to minimize the maximal crane capacity reservation. In this paper, we propose a mixed integer linear program (MILP) that minimizes the maximal crane capacity reservation while window agreements are satisfied for all scenarios in which vessels arrive within their windows. Results of a case study suggest that with slight modifications to an existing plan, significant reductions in the maximal crane capacity reservation can be achieved. As a particular case, the MILP determines the conventional optimal window-ignoring plan. Results suggest that although the windowignoring plan on itself requires less crane capacity than the window-based plan, it is much more sensitive to the arrival window agreements.

We consider a container operator, who serves a number of shipping lines by discharging and loading their periodically arriving container vessels. Disruptions on vessels’ travel times lead to stochastic arrivals in the port. To cope with these disturbances, the operator and each vessel line agree on two types of arrivals: arrivals i) within, and ii) out of a so-called arrival window. If a vessel arrives within its window, the operator guarantees a maximal process time. If not, the operator is not bound to any guaranteed process time. The problem is to construct a periodic window-based i) arrival, ii) departure and iii) time-variant crane capacity plan to minimize the maximal crane capacity reservation. In this paper, we propose a mixed integer linear program (MILP) that minimizes the maximal crane capacity reservation while window agreements are satisfied for all scenarios in which vessels arrive within their windows. Results of a case study suggest that with slight modifications to an existing plan, significant reductions in the maximal crane capacity reservation can be achieved. As a particular case, the MILP determines the conventional optimal window-ignoring plan. Results suggest that although the windowignoring plan on itself requires less crane capacity than the window-based plan, it is much more sensitive to the arrival window agreements.

In this report we consider the optimal control problem of emptying a deterministic single server multiclass queuing system without arrivals. We assume that the server is able to serve several queues simultaneously, each at its own rate, independent of the number of queues being served. We showed that the optimal sequence of modes is ordered by rate of cost decrease. However, queues are not necessarily emptied. We propose a dynamic programming approach for solving the problem, which reduces the multiparametric QP (mpQP) to a series of problems that can be solved readily.

We present an MILP formulation to construct a strategic, cyclic terminal allocation and time scheduling for a set of container vessels, which are processed by a multi-terminal port operator. Our case study is about balancing the workload over time, minimizing inter-terminal transport and minimizing deviations from the existing time schedule.

The objective of this report is to develop a method to control a manufacturing system using feedback control. The manufacturing system of interest is a three machine multi-product flow line with stochastic process times, producing eight different product types in large quantities. The performance of the feedback controlled flow line is compared to the performance of the flow line controlled by several common control methods: push, pull, conwip, and POLCA control. The main performance criteria for the flow line are assumed to be the throughput of the system and the inventory level.

We present a case study based on a multi-terminal container operation in Antwerp, Belgium, where a set of cyclically calling container vessels is processed. The operator faces the problem of strategically allocating a terminal, a berthing interval, and a variable number of quay cranes to the vessels in the set. Restricting properties are terminal quay lengths, number of quay cranes and storage capacities. Currently, the operator's objective is to satisfy the preferences of the vessel lines, with respect to a terminal and berthing time, as much as possible. We are interested in the benefit of modifying a given allocation, i.e. the potential crane and inter-terminal costs savings if specific changes to a given allocation are allowed. An MILP is implemented in a two-step optimization, which enables us to efficiently investigate the benefit of modification. Experimental results suggest that small changes in a given allocation may lead to significant cost savings.

We consider a port consisting of a cluster of inter-related terminals, where container vessels arrive cyclically. The problem is to strategically assign a terminal and a time interval of berthing to each of the vessels in the cycle. Restricting properties are terminal quay lengths and quay crane capacity. Conflicting objectives are i) minimizing the number of required quay cranes, ii) minimizing the amount of inter-terminal traffic and iii) minimizing the total weighted deviation from desired berthing intervals. We formulate both a straightforward and an alternative mixed integer linear program to model this system. Results show that the alternative model is much faster solvable and enables to optimize real-life problems within a couple of hours.

In this report we will present three approaches to model manufacturing systems in an aggregate way leading to fast and effective (i.e., scalable) simulations that allow the development of simulation tools for rapid exploration of different production scenarios in a factory as well as in a whole supply chain. We will present the main ideas and show some validation studies. Fundamental references are given for more detailed studies.

We consider the control of flowlines consisting of switching servers, through which different types of jobs flow. Switching from one job type to an other takes time. Examples of such flowlines can be found in manufacturing industry, food processing industry, communication networks, data flow and traffic flow. The optimal process cycle with respect to work in process levels for a single switching server with two job types is known from previous work. This optimal work in process value is an absolute lower bound on average work in process levels for flowlines with more than one workstation. In this study we derive conditions for workstations in a flowline that have to be met in order to achieve the local minimal work in process level globally. Based on these conditions, the class of flowlines is characterized that can behave as if it were a single switching server.A state feedback controller is proposed that steers a trajectory to the desired trajectories for all servers in the flowline, from any arbitrary start point. Convergence to the desired process cycles is proven mathematically. Although the analysis is performed with a hybrid fluid model, the controller has successfully been implemented in a discrete event case study.

We present a case study based on a multi-terminal container operation in Antwerp, Belgium, where a set of cyclically calling container vessels is processed. The operator faces the problem of strategically allocating a terminal, a berthing interval, and a variable number of quay cranes to the vessels in the set. Restricting properties are terminal quay lengths, number of quay cranes and storage capacities. Currently, the operator's objective is to satisfy the preferences of the vessel lines, with respect to a terminal and berthing time, as much as possible. We are interested in the benefit of modifying a given allocation, i.e. the potential crane and inter-terminal costs savings if specific changes to a given allocation are allowed. An MILP is implemented in a two-step optimization, which enables us to efficiently investigate the benefit of modification. Experimental results suggest that small changes in a given allocation may lead to significant cost savings.

The objective of this report is to develop a method to control a manufacturing system using feedback control. The manufacturing system of interest is a three machine multi-product flow line with stochastic process times, producing eight different product types in large quantities. The performance of the feedback controlled flow line is compared to the performance of the flow line controlled by several common control methods: push, pull, conwip, and POLCA control. The main performance criteria for the flow line are assumed to be the throughput of the system and the inventory level.

We consider a port consisting of a cluster of inter-related terminals, where container vessels arrive cyclically. The problem is to strategically assign a terminal and a time interval of berthing to each of the vessels in the cycle. Restricting properties are terminal quay lengths and quay crane capacity. Conflicting objectives are i) minimizing the number of required quay cranes, ii) minimizing the amount of inter-terminal traffic and iii) minimizing the total weighted deviation from desired berthing intervals. We formulate both a straightforward and an alternative mixed integer linear program to model this system. Results show that the alternative model is much faster solvable and enables to optimize real-life problems within a couple of hours.

In this report we will present three approaches to model manufacturing systems in an aggregate way leading to fast and effective (i.e., scalable) simulations that allow the development of simulation tools for rapid exploration of different production scenarios in a factory as well as in a whole supply chain. We will present the main ideas and show some validation studies. Fundamental references are given for more detailed studies.

We consider the control of flowlines consisting of switching servers, through which different types of jobs flow. Switching from one job type to an other takes time. Examples of such flowlines can be found in manufacturing industry, food processing industry, communication networks, data flow and traffic flow. The optimal process cycle with respect to work in process levels for a single switching server with two job types is known from previous work. This optimal work in process value is an absolute lower bound on average work in process levels for flowlines with more than one workstation. In this study we derive conditions for workstations in a flowline that have to be met in order to achieve the local minimal work in process level globally. Based on these conditions, the class of flowlines is characterized that can behave as if it were a single switching server.A state feedback controller is proposed that steers a trajectory to the desired trajectories for all servers in the flowline, from any arbitrary start point. Convergence to the desired process cycles is proven mathematically. Although the analysis is performed with a hybrid fluid model, the controller has successfully been implemented in a discrete event case study.

In this paper we study the control of switching servers, which can for example be found in manufacturing industry. In general, these systems are discrete event systems. A server processes multiple job types. Switching between the job types takes time and during that time, no jobs can be processed, so capacity is lost. How should a server switch between the job types in an efficient way? In this paper we derive the optimal process cycle with respect to work in process levels for a server with two job types and finite buffer capacities. The analysis is performed using a hybrid fluid model approximation. After the optimal process cycle has been defined, a state feedback controller is proposed that steers the trajectory of the system to this optimal cycle. Workstations are often placed in series to form a flowline of servers. Our goal is to control flowlines of switching servers in a way that the work in process level is minimized. In a flowline, only the most downstream workstation influences the work in process level of the system, since upstream workstations simply move jobs from one server to the other. If it is possible to have the most downstream workstation process in its optimal cycle and the other workstations can make this happen, then optimal work in process levels are achieved. This paper investigates under which conditions the upstream workstations can make the most downstream workstation work optimally. Conditions on the upstream workstations are derived and the class of flowlines is characterized for which the optimal process cycle of an isolated downstream workstation can become the optimal process cycle for the flowline. For a flowline consisting of two workstations, a state feedback controller is proposed and convergence to the optimal process cycle is proved mathematically. An extensive case study demonstrates how the controller performs, for both the hybrid fluid model and in a discrete event implementation with stochastic inter-arrival and process t