Modelling and controlling traffic behaviour with continuous Petri nets

Traffic systems are discrete systems that can be heavily populated. One way of overcoming the state explosion problem inherent to heavily populated discrete systems is to relax the discrete model. Continuous Petri nets (PN) represent a relaxation of the original discrete Petri nets that leads to a compositional formalism to model traffic behaviour. This paper introduces some new features of continuous Petri nets that are useful to obtain realistic but compact models for traffic systems. Combining these continuous PN models with discrete PN models of traffic lights leads to a hybrid Petri net model that is appropriate for predicting traffic behaviour, and for designing trac light controllers that minimize the total delay of the vehicles in the system

On Fault Diagnosis of random Free-choice Petri Nets

This paper presents an on-line diagnosis algorithm for Petri nets where a priori probabilistic knowledge about the plant operation is available. We follow the method developed by Benveniste, Fabre, and Haar to assign probabilities to configurations in a net unfolding thus avoiding the need for randomizing all concurrent interleavings of transitions. We consider different settings of the diagnosis problem, including estimating the likelihood that a fault may have happened prior to the most recent observed event, the likelihood that a fault will have happened prior to the next observed event. A novel problem formulation treated in this paper considers deterministic diagnosis of faults that occurred prior to the most recent observed event, and simultaneous calculation of the likelihood that a fault will occur prior to the next observed event

Distributed voltage control in electrical power systems

Voltage instability stems from the attempt of load dynamics to restore power consumption beyond the capability of the combined transmission and generation system. Discrete event controllers such as load tap changing transformers (LTCs), electronically controlled HVDC lines and switched capacitor banks can locally maintain the voltage but following a major disturbance that causes a strong decrease in the voltages, there are some interaction between LTCs action and up to now there has been relatively little attention paid to coordination between important components in voltage stability using message exchange between them and applying distributed control and taking discrete events into account. So, this study aims at voltage stability enhancement by using coordinated control of the discrete event controllers by using message exchange between the different local control agents. Various approaches for coordinating local controllers (e.g. distributed model predictive controllers) will be investigated. The influence of the discrete event driven local voltage controllers on remote locations of the network has to be investigated in a hybrid systems model framework

Distributed control of urban traffic networks using hybrid models

Urban traffic control poses a challenging problem in terms of coordinating the different traffic lights that can be used in order to influence the traffic flow. Model based control requires hybrid systems models consisting of interacting fluid flow Petri net models for controlled and uncontrolled intersections, and cell transmission models for links connecting the intersections. This paper proposes a simulation based distributed model predictive control algorithm for solving this problem

A platoon based model for urban traffic networks: identification, modeling and distributed control

Urban traffic control poses a challenging problem in terms of coordinating the different traffic lights that can be used in order to influence the traffic flow. The goal of this approach is to identify and to develop hybrid system models of controlled and uncontrolled intersections and links in urban traffic networks based on formation of platoons. The other purpose is to develop a feedback control algorithm that optimizes the signal timing plan based on the strategy of platoons formation estimated via the vehicle re-identification technology

Particle filter state estimator for large urban networks

This paper applies a particle filter (PF) state estimator to urban traffic networks. The traffic network consists of signalized intersections, the roads that link these intersections, and sensors that detect the passage time of vehicles. The traffic state X(t) specifies at each time time t the state of the traffic lights, the queue sizes at the intersections, and the location and size of all the platoons of vehicles inside the system. The basic entity of our model is a platoon of vehicles that travel close together at approximately the same speed. This leads to a discrete event simulation model that is much faster than microscopic models representing individual vehicles. Hence it is possible to execute many random simulation runs in parallel. A particle filter (PF) assigns weights to each of these simulation runs, according to how well they explain the observed sensor signals. The PF thus generates estimates at each time t of the location of the platoons, and more importantly the queue size at each intersection. These estimates can be used for controlling the optimal switching times of the traffic light

On extended Kalman filters with augmented state vectors for the stator flux estimation in SPMSMs

The demand for highly dynamic electrical drives, characterized by high quality torque control, in a wide variety of applications has grown tremendously during the past decades. Direct torque control (DTC) for permanent magnet synchronous motors (PMSM) can provide this accurate and fast torque control. When applying DTC the change of the stator flux linkage vector is controlled, based on torque and flux errors. As such the estimation of the stator flux linkage is essential. In the literature several possible solutions for the estimation of the stator flux linkage are proposed. In order to overcome problems associated with the integration of the back-emf, the use of state observers has been advocated in the literature. Several types of state observers have been conceived and implemented for PMSMs, especially the Extended Kalman Filter (EKF) has received much attention. In most reported applications however the EKF is only used to estimate the speed and rotor position of the PMSM in order to realize field oriented current control in a rotor reference frame. Far fewer publications mention the use of an EKF to estimate the stator flux linkage vector in order to apply DTC. Still the performance of the EKF in the estimation of the stator flux linkage vector has not yet been thoroughly investigated. In this paper the performance of the EKF for stator flux linkage is studied and simulated. The possibilities to improve the estimation by augmenting the state vector and the consequences of these alterations are explored. Important practical aspects for FPGA implementation are discussed

Parameter estimation for stochastic hybrid model applied to urban traffic flow estimation

This study proposes a novel data-based approach for estimating the parameters of a stochastic hybrid model describing the traffic flow in an urban traffic network with signalized intersections. The model represents the evolution of the traffic flow rate, measuring the number of vehicles passing a given location per time unit. This traffic flow rate is described using a mode-dependent first-order autoregressive (AR) stochastic process. The parameters of the AR process take different values depending on the mode of traffic operation – free flowing, congested or faulty – making this a hybrid stochastic process. Mode switching occurs according to a first-order Markov chain. This study proposes an expectation-maximization (EM) technique for estimating the transition matrix of this Markovian mode process and the parameters of the AR models for each mode. The technique is applied to actual traffic flow data from the city of Jakarta, Indonesia. The model thus obtained is validated by using the smoothed inference algorithms and an online particle filter. The authors also develop an EM parameter estimation that, in combination with a time-window shift technique, can be useful and practical for periodically updating the parameters of hybrid model leading to an adaptive traffic flow state estimator

Optimal control and optimal sensor activation for Markov decision problems with costly observations

This paper considers partial observation Markov decision processes. Besides the classical control decisions influencing the transition probabilities of the Markov process, we also consider control actions that can activate the sensors to provide more or less accurate information about the system state, explicitly including the cost of activating sensors. We synthesize control laws that minimize a discounted operating cost of the system over an infinite interval of time, where the instantaneous cost function depends on the current state, the control influencing the transition probabilities, and the control actions activating the sensors. A general computationally efficient optimal solution for this problem is not known. Hence we design supoptimal controllers that only use knowledge of the value function for the full state information Markov decision problem. Our solution guarantees that the discounted cost of operating the plant increases only by a bounded amount with respect to the minimal cost for the full state information problem. A new concept of pinned conditional distributions of the state given the observed history of the plant is required in order to implement these control laws online