arXiv subjects

Eric Feron

Publications and source records attributed to Eric Feron.

72 records · Page 4Linked to original sources

arXiv2012

Gain Scheduling Control of Gas Turbine Engines: Absolute Stability by Finding a Common Lyapunov Matrix

This manuscript aims to develop and describe gain scheduling control concept for a gas turbine engine which drives a variable pitch propeller. An architecture for gain-scheduling control is developed that controls the turboshaft engine for large thrust commands in stable fashion with good performance. Fuel ow and propeller pitch angle are the two control inputs of the system. New stability proof has been developed for gain scheduling control of gas turbine engines using global linearization and LMI techniques. This approach guarantees absolute stability of the closed loop gas turbine engine systems with gain-scheduling controllers.

math.OC↗

arXiv2011

Optimization of Lyapunov Invariants in Verification of Software Systems (Extended Version)

The paper proposes a control-theoretic framework for verification of numerical software systems, and puts forward software verification as an important application of control and systems theory. The idea is to transfer Lyapunov functions and the associated computational techniques from control systems analysis and convex optimization to verification of various software safety and performance specifications. These include but are not limited to absence of overflow, absence of division-by-zero, termination in finite time, presence of dead-code, and certain user-specified assertions. Central to this framework are Lyapunov invariants. These are properly constructed functions of the program variables, and satisfy certain properties-resembling those of Lyapunov functions-along the execution trace. The search for the invariants can be formulated as a convex optimization problem. If the associated optimization problem is feasible, the result is a certificate for the specification.

eess.SY↗

arXiv2011

Optimization of Lyapunov Invariants in Verification of Software Systems

eess.SY↗

arXiv2011

Environmental benefits of enhanced surveillance technology on airport departure operations

Airport departure operations constitute an important source of airline delays and passenger frustration. Excessive surface traffic is the cause of increased controller and pilot workload; It is also the source of increased emissions; It worsens traffic safety and often does not yield improved runway throughput. Acknowledging this fact, this paper explores some of the feedback mechanisms by which airport traffic can be optimized in real time according to its current degree of congestion. In particular, it examines the environmnetal benefits that improved surveillance technologies can bring in the context of gate- or spot-release aircraft strategies. It is shown that improvements can lead yield 4% to 6% emission reductions for busy airports like New-York La Guardia or Seattle Tacoma. These benefits come on top of the benefits already obtained by adopting threshold strategies currently under evaluation.

eess.SY↗

arXiv2011

ATC Taskload Inherent to the Geometry of Stochastic 4-D Trajectory Flows with Flight Technical Errors

A method to quantify the probabilistic controller taskload inherent to maintaining aircraft adherence to 4-D trajectories within flow corridors is presented. An Ornstein-Uhlenbeck model of the aircraft motion and a Poisson model of the flow scheduling are introduced along with reasonable numerical values of the model parameters. Analytic expressions are derived for the taskload probability density functions for basic functional elements of the flow structure. Monte Carlo simulations are performed for these basic functional elements and the controller taskload probabilities are exhibited.

eess.SY↗

arXiv2011

Aircraft Proximity Maps Based on Data-Driven Flow Modeling

With the forecast increase in air traffic demand over the next decades, it is imperative to develop tools to provide traffic flow managers with the information required to support decision making. In particular, decision-support tools for traffic flow management should aid in limiting controller workload and complexity, while supporting increases in air traffic throughput. While many decision-support tools exist for short-term traffic planning, few have addressed the strategic needs for medium- and long-term planning for time horizons greater than 30 minutes. This paper seeks to address this gap through the introduction of 3D aircraft proximity maps that evaluate the future probability of presence of at least one or two aircraft at any given point of the airspace. Three types of proximity maps are presented: presence maps that indicate the local density of traffic; conflict maps that determine locations and probabilities of potential conflicts; and outliers maps that evaluate the probability of conflict due to aircraft not belonging to dominant traffic patterns. These maps provide traffic flow managers with information relating to the complexity and difficulty of managing an airspace. The intended purpose of the maps is to anticipate how aircraft flows will interact, and how outliers impact the dominant traffic flow for a given time period. This formulation is able to predict which "critical" regions may be subject to conflicts between aircraft, thereby requiring careful monitoring. These probabilities are computed using a generative aircraft flow model. Time-varying flow characteristics, such as geometrical configuration, speed, and probability density function of aircraft spatial distribution within the flow, are determined from archived Enhanced Traffic Management System data, using a tailored clustering algorithm. Aircraft not belonging to flows are identified as outliers.

eess.SY↗

arXiv2010

Stability of Spatially Distributed, Intersecting Aircraft Flows Under Sequential Conflict Resolution Schemes

This paper discusses the effect of sequential conflict resolution maneuvers of an infinite aircraft flow through a finite control volume. Aircraft flow models are utilized to simulate traffic flows and determine stability. Pseudo-random flow geometry is considered to determine airspace stability in a more random airspace, where aircraft flows are spread over a given positive width. The use of this aircraft flow model generates a more realistic flow geometry. A set of upper bounds on the maximal aircraft deviation during conflict resolution is derived. Also with this flow geometry it is proven that these bounds are not symmetric, unlike the symmetric bounds derived in previous papers for simpler flow configurations. Stability is preserved under sequential conflict resolution algorithms for all flow geometries discussed in this paper.

math.OC↗

arXiv2010

Trajectory Clustering and an Application to Airspace Monitoring

This paper presents a framework aimed at monitoring the behavior of aircraft in a given airspace. Nominal trajectories are determined and learned using data driven methods. Standard procedures are used by air traffic controllers (ATC) to guide aircraft, ensure the safety of the airspace, and to maximize the runway occupancy. Even though standard procedures are used by ATC, the control of the aircraft remains with the pilots, leading to a large variability in the flight patterns observed. Two methods to identify typical operations and their variability from recorded radar tracks are presented. This knowledge base is then used to monitor the conformance of current operations against operations previously identified as standard. A tool called AirTrajectoryMiner is presented, aiming at monitoring the instantaneous health of the airspace, in real time. The airspace is "healthy" when all aircraft are flying according to the nominal procedures. A measure of complexity is introduced, measuring the conformance of current flight to nominal flight patterns. When an aircraft does not conform, the complexity increases as more attention from ATC is required to ensure a safe separation between aircraft.

cs.LG↗

arXiv2009

Using Ellipsoidal Domains to Analyze Control Systems Software

We propose a methodology for the automatic verification of safety properties of controllers based on dynamical systems, such as those typically used in avionics. In particular, our focus is on proving stability properties of software implementing linear and some non-linear controllers. We develop an abstract interpretation framework that follows closely the Lyapunov methods used in proofs at the model level and describe the corresponding abstract domains, which for linear systems consist of ellipsoidal constraints. These ellipsoidal domains provide abstractions for the values of state variables and must be combined with other domains that model the remaining variables in a program. Thus, the problem of automatically assigning the right type of abstract domain to each variable arises. We provide an algorithm that solves this classification problem in many practical cases and suggest how it could be generalized to more complicated cases. We then find a fixpoint by solving a matrix equation, which in the linear case is just the discrete Lyapunov equation. Contrary to most cases in software analysis, this fixpoint cannot be reached by the usual iterative method of propagating constraints until saturation and so numerical methods become essential. Finally, we illustrate our methodology with several examples.

cs.PL↗

arXiv2008

Control software analysis, part II: Closed-loop analysis

The analysis and proper documentation of the properties of closed-loop control software presents many distinct aspects from the analysis of the same software running open-loop. Issues of physical system representations arise, and it is desired that such representations remain independent from the representations of the control program. For that purpose, a concurrent program representation of the plant and the control processes is proposed, although the closed-loop system is sufficiently serialized to enable a sequential analysis. While dealing with closed-loop system properties, it is also shown by means of examples how special treatment of nonlinearities extends from the analysis of control specifications to code analysis.

cs.SE↗

arXiv2008

Scheduling Kalman Filters in Continuous Time

A set of N independent Gaussian linear time invariant systems is observed by M sensors whose task is to provide the best possible steady-state causal minimum mean square estimate of the state of the systems, in addition to minimizing a steady-state measurement cost. The sensors can switch between systems instantaneously, and there are additional resource constraints, for example on the number of sensors which can observe a given system simultaneously. We first derive a tractable relaxation of the problem, which provides a bound on the achievable performance. This bound can be computed by solving a convex program involving linear matrix inequalities. Exploiting the additional structure of the sites evolving independently, we can decompose this program into coupled smaller dimensional problems. In the scalar case with identical sensors, we give an analytical expression of an index policy proposed in a more general context by Whittle. In the general case, we develop open-loop periodic switching policies whose performance matches the bound arbitrarily closely.

math.OC↗

arXiv2008

Control software analysis, Part I Open-loop properties

As the digital world enters further into everyday life, questions are raised about the increasing challenges brought by the interaction of real-time software with physical devices. Many accidents and incidents encountered in areas as diverse as medical systems, transportation systems or weapon systems are ultimately attributed to "software failures". Since real-time software that interacts with physical systems might as well be called control software, the long litany of accidents due to real-time software failures might be taken as an equally long list of opportunities for control systems engineering. In this paper, we are interested only in run-time errors in those pieces of software that are a direct implementation of control system specifications: For well-defined and well-understood control architectures such as those present in standard textbooks on digital control systems, the current state of theoretical computer science is well-equipped enough to address and analyze control algorithms. It appears that a central element to these analyses is Lyapunov stability theory, which translate into invariant theory in computer implementations.

cs.SE↗

arXiv2008

Collaborative Virtual Queue: Fair Management of Congested Departure Operations and Benefit Analysis

Due to the stochastic nature of departure operations, working at full capacity makes major US airports very sensitive to uncertainties. Consequently, airport ground operations face critically congested taxiways and long runway queues. In this report, we show how improved management of departure operations from the ready-to-push-back time to the wheels-off time can potentially yield significant benefits to airlines and air traffic services. We develop a Collaborative Virtual Queue to enable better optimization capabilities during congested situations while taking into account the laissez-faire competitive environment. Results are evaluated using a departure system model, validated using current statistics and previous studies. First, the Collaborative Virtual Queue enables keeping aircraft away from runway queues, which increases wheels-off time predictability. Second, holding aircraft enables last-minute intra-airline flight switching. This creates new optimization capabilities for airlines i.e. it gives airlines the flexibility to prioritize their flight sequence in real-time. These capabilities are illustrated by the trade-off between minimizing the average passenger waiting time and minimizing the level of unfairness between aircraft of the same airline. For instance, airlines could choose to decrease by up to 15% their average passenger waiting time by prioritizing heavy planes over small planes when the taxiway system is congested.

cs.OH↗

arXiv2008

A Linear Programming Relaxation and a Heuristic for the Restless Bandit Problem with General Switching Costs

We extend a relaxation technique due to Bertsimas and Nino-Mora for the restless bandit problem to the case where arbitrary costs penalize switching between the bandits. We also construct a one-step lookahead policy using the solution of the relaxation. Computational experiments and a bound for approximate dynamic programming provide some empirical support for the heuristic.

math.OC↗

arXiv2008

Graceful Degradation of Air Traffic Operations

The introduction of new technologies and concepts of operation in the air transportation system is not possible, unless they can be proven not to adversely affect the system operation under not only nominal, but also degraded conditions. In extreme scenarios, degraded operations due to partial or complete technological failures should never endanger system safety. Many past system evolutions, whether ground-based or airborne, have been based on trial-and-error, and system safety was addressed only after a specific event yielded dramatic or near- dramatic consequences. Future system evolutions, however, must leverage available computation, prior knowledge and abstract reasoning to anticipate all possible system degradations and prove that such degradations are graceful and safe. This paper is concerned with the graceful degradation of high-density, structured arrival traffic against partial or complete surveillance failures. It is shown that for equal performance requirements, some traffic configurations might be easier to handle than others, thereby offering a quantitative perspective on these traffic configurations. ability to "gracefully degrade". To support our work, we also introduce a new conflict resolution algorithm, aimed at solving conflicts involving many aircraft when aircraft position information is in the process of degrading.

cs.OH↗

arXiv2007

Performance Evaluation of a Multi-Agent Risk-Sensitive Tracking System

In this paper, we consider a simple linear exponential quadratic Gaussian (LEQG) tracking problem for a multi-agent system. We study the dynamical behaviors of the group as we vary the risk-sensitivity parameter, comparing in particular the risk averse case to the LQG case. Then we consider the evolution of the performance per agent as the number of agents in the system increases. We provide some analytical as well as simulation results. In general, more agents are beneficial only if noisy agent dynamics and/or imperfect measurements are considered. The critical value of the risk sensitivity parameter above which the cost becomes infinite increases with the number of agents. In other words, for a fixed positive value of this parameter, there is a minimum number of agents above which the cost remains finite.

math.OC↗

arXiv2007

A Dynamic I/O Model for TRACON Traffic Management

This work investigates the TRACON flow management around a major airport. Aircraft flows are analyzed through a study of TRACON trajectories records. Rerouting and queuing processes are highlighted and airport characteristics are shown as function of the number of planes in the TRACON. Then, a simple input-output TRACON queuing and landing model is proposed. This model is calibrated and validated using available TRACON data. It reproduces the same phenomenon as the real system. This model is used to show the impact of limiting the number of aircrafts in the TRACON. A limited number of aircraft does not increase delays but reduces the controller's workload and increases safety.

cs.OH↗

arXiv2007

Certifying controls and systems software

Software system certification presents itself with many challenges, including the necessity to certify the system at the level of functional requirements, code and binary levels, the need to chase down run-time errors, and the need for proving timing properties of the eventual, compiled system. This paper illustrates possible approaches for certifying code that arises from control systems requirements as far as stability properties are concerned. The relative simplicity of the certification process should encourage the development of systematic procedures for certifying control system codes for more complex environments.

cs.SE↗