René Boel

Brief paper: Freeway traffic estimation within particle filtering framework

This paper formulates the problem of real-time estimation of traffic state in freeway networks by means of the particle filtering framework. A particle filter (PF) is developed based on a recently proposed speed-extended cell-transmission model of freeway traffic. The freeway is considered as a network of components representing different freeway stretches called segments. The evolution of the traffic in a segment is modelled as a dynamic stochastic system, influenced by states of neighbour segments. Measurements are received only at boundaries between some segments and averaged within possibly irregular time intervals. This limits the measurement update in the PF to only these time instants when a new measurement arrives, while in between measurement updates any simulation model can be used to describe the evolution of the particles. The PF performance is validated and evaluated using synthetic and real traffic data from a Belgian freeway. An unscented Kalman filter is also presented. A comparison of the PF with the unscented Kalman filter is performed with respect to accuracy and complexity.

Optimal Control of Jump Processes

The paper proposes an abstract model for the problem of optimal control of systems subject to random perturbations, for which the principle of optimality takes on an appealing form. This model is specialized to the case where the state of the controlled system is realized as a jump process. The additional structure permits operationally useful optimality conditions. Some illustrative examples are solved.

Decentralized failure diagnosis for discrete-event systems with costly communication between diagnosers

Reliable supervisory control of engineering systems requires failure diagnosis algorithms for discrete-event systems. For large, modularly designed plants, such as communication networks, robustness considerations and limitations on the communication between local sensors lead to decentralized implementations of failure diagnosis algorithms. A trade-off has to be made between the speed of diagnosis and the cost of communication and computation. An algorithm is proposed for decentralized failure diagnosis with asymmetric communication in which Diagnoser 2 also estimates the observer state of Diagnoser 1 and sends only that subset of failure states which is relevant for the other diagnoser when this is useful for Diagnoser 1s control task of failure detection and diagnosis. This algorithm can help in suggesting practically implementable heuristic algorithms.

A Continuous Petri Net Approach for Model Predictive Control of Traffic Systems

Traffic systems are often highly populated discrete event systems that exhibit several modes of behavior such as free flow traffic, traffic jams, stop-and-go waves, etc. An appropriate closed loop control of the congested system is crucial in order to avoid undesirable behavior. This paper proposes a macroscopic model based on continuous Petri nets as a tool for designing control laws that improve the behavior of traffic systems. The main reason to use a continuous model is to avoid the state explosion problem inherent to large discrete event systems. The obtained model captures the different operation modes of a traffic system and is highly compositional. In order to handle the variability of the traffic conditions, a model predictive control strategy is proposed and validated.

A particle filter for freeway traffic estimation

This paper considers the traffic flow estimation problem for the purposes of on-line traffic prediction, mode detection and ramp-metering control. The solution to the estimation problem is given within the Bayesian recursive framework. A particle filter (PF) is developed based on a freeway traffic model with aggregated states and an observation model with aggregated variables. The freeway is considered as a network of components, each component representing a different section of the traffic network. The freeway traffic is modeled as a stochastic hybrid system, i.e. each traffic section possesses continuous and discrete states, interacting with states of neighbor sections. The state update step in the recursive Bayesian estimator is performed through sending and receiving functions describing propagation of perturbations from upstream to downstream, and from downstream to upstream sections. Measurements are received only on boundaries between some sections and averaged within regular or irregular time intervals. A particle filter is developed with measurement updates each time when a new measurement becomes available, and with possibly many state updates in between consecutive measurement updates. It provides an approximate but scalable solution to the difficult state estimation and prediction problem with limited, noisy observations. The filter performance is validated and evaluated by Monte Carlo simulation.

Voltage Coordination in Multi-Area Power Systems via Distributed Model Predictive Control

This paper proposes a coordination paradigm for properly coordinating local control actions, taken by many communicating control agents (CAs), in order to maintain multi-area power system voltages within acceptable bounds. The proposed control scheme is inspired by distributed model predictive control (DMPC), and relies on the communication of planned local control actions among neighboring CAs, each possibly operated by an independent transmission system operator (TSO). Each CA, knowing a local model of its own area, as well as reduced-order QSS models of its immediate neighboring areas, and assuming a simpler equivalent PV models for its remote neighbors, performs a greedy local optimization over a finite window in time, communicating its planned control input sequence to its immediate neighbors only. The good performance of the proposed real-time model-based feedback coordinating controller, following major disturbances, is illustrated using time-domain simulation of the well-known realistic Nordic32 test system, assuming worst-case conditions.

Structuring Acyclic Petri Nets for Reachability Analysis and Control

The incidence matrices—from places to transitions and vice versa—of an acyclic Petri net can obtain a block-triangular structure by reordering their rows and columns. This allows the efficient solution of some reachability problems for acyclic Petri nets. This result is further used in supervisory control of Petri nets; supervisors for Petri nets with uncontrollable transitions are constructed by extending the method of Yamalidou et al. (1996) to Petri nets where transitions can be executed simultaneously. A large class of Petri nets with uncontrollable transitions is given for which the maximally permissive supervisor can be realized by a Petri net. The original specification is algorithmically transformed—by using the results for acyclic Petri nets—into a new specification to take the presence of uncontrollable transitions into account. The supervisor is obtained by simple matrix multiplications and no linear integer programs need to be solved. Furthermore, a class of Petri nets is given for which the supervisor can be realized by extending the enabling rule with OR-logic.

On-Line Monitoring of Large Petri Net Models Under Partial Observation

We consider a Petri Net model of the plant. The observation is given by a subset of transitions whose occurrence is always and immediately sensed by a monitoring agent. Other transitions not in this subset are silent (unobservable). Classical on-line monitoring techniques, which are based on the estimation of the current state of the plant and the detection of the occurrence of undesirable events (faults), are not suitable for models of large systems due to high spatial complexity (exponential in the size of the entire model). In this paper we propose a method based on the explanation of plant observation. A legal trace minimally explains the observation if it includes all unobservable transitions whose firing is needed to enable the observed transitions. To do so, starting from an observable transition, using backward search techniques, a set of minimal explanations is derived, which are sufficient for detecting whether a fault event must have occurred for sure in the plant or not. The technique also allows production of a set of basis markings for the estimation of the current state of the plant. The set of all possible current markings can then be characterized as the unobservable reach of these basis markings. The computational complexity of the algorithm depends on the size of the largest connected subnet which includes only unobservable transitions. This allows monitoring of plants of any size in which there is no large unobservable subnet. We also illustrate the applicability of the method for the monitoring of a class of infinite state systems, unbounded Petri Nets with unobservable trap circuits, and we show how this can be useful for distributed implementations.

Robustness and risk-sensitive filtering

This paper gives a precise meaning to the robustness of risk-sensitive filters for problems in which one is uncertain as to the exact value of the probability model.

Parallelized Particle and Gaussian Sum Particle Filters for Large-Scale Freeway Traffic Systems

Large-scale traffic systems require techniques that are able to 1) deal with high amounts of data and heterogenous data coming from different types of sensors, 2) provide robustness in the presence of sparse sensor data, 3) incorporate different models that can deal with various traffic regimes, and 4) cope with multimodal conditional probability density functions (pdfs) for the states. Often, centralized architectures face challenges due to high communication demands. This paper develops new estimation techniques that are able to cope with these problems of large traffic network systems. These are parallelized particle filters (PPFs) and a parallelized Gaussian sum particle filter (PGSPF) that are suitable for online traffic management. We show how complex pdfs of the high-dimensional traffic state can be decomposed into functions with simpler forms and how the whole estimation problem solved in an efficient way. The proposed approach is general, with limited interactions, which reduce the computational time and provide high estimation accuracy. The efficiency of the PPFs and PGSPFs is evaluated in terms of accuracy, complexity, and communication demands and compared with the case where all processing is centralized.