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SummaryWe deploy an adaptive observer recently developed for general hyperbolic partial differential equation (PDE) systems to detect and diagnose various drilling incidents. The well is modeled by a distributed PDE which, contrary to lumped models, preserves fundamental properties of well-flow dynamics enabling faster and more accurate incident detection and estimation. Wired drillpipe technology with pressure sensors is needed to locate and isolate incidents. Four realistic simulation case studies demonstrating various properties of the observer are presented. Drilling incidents treated in the simulation case studies include packoff in the annulus, formation in-flows, loss of circulation, and various combinations of these. Although simulation results show that the developed observers successfully estimate properties of the incidents that they are tailored for, they do not constitute an incident-detection system for drilling. However, they provide a part of the data on which an overall incident-detection system can rely.

We design a leak detection, size estimation and localization algorithm for a branched pipe system, requiring flow and pressure measurements to be taken at the inlet and outlet boundaries, only. By showing that the pipe system model can be mapped into a system of coupled, linear hyperbolic PDEs (partial differential equations), with the parametric uncertainties caused by the leak appearing in a particular way, established methods can be applied to obtain state and parameter estimates. Analyzing the structure of the parametric uncertainties that appear in the obtained adaptive observer canonical form, we prove that total leak size can be estimated regardless of how leaks are distributed in the pipe network. Moreover, any number of point leaks can be located, provided they occur sufficiently separated in time.

We present a predictive feedback control method for a class of quasilinear hyperbolic systems with one boundary control input. Assuming exact model knowledge, convergence to the origin, or tracking at the uncontrolled boundary, are achieved in finite time. A robustness certificate is provided, showing that at least under more restrictive assumptions on the system coefficients, the control method has inherent robustness properties with respect to small errors in the model, measurements and control input. Rigorous, although conservative conditions on the time derivative of the initial condition and on the design parameter controlling the convergence speed are given to ensure global existence of the solution for initial conditions with arbitrary infinity-norm.

We present a novel streaming learning approach, utilizing a deep neural network (DNN) to learn from data available during operation to estimate at-bit density using drilling parameters. Since every wellbore is different, the relationship between drilling parameters and at-bit density varies. Equipment used, well trajectory, friction and bit wear are examples of conditions that affect this relationship and makes a pre-trained model unable to represent an accurate input/output mapping applicable to all wells. However, using delayed density log measurements, continuously supervising updates to the model is possible during operation. The algorithm has been tested on drilling data from wells on a field operated by Equinor and compared to a standard deep learning approach, where results show that a streaming learning approach outperforms the traditional method. Statistical analyses have been performed to verify the statistical significance and effect size on the data sets. Data visualizations using a t-distributed Stochastic Neighbor Embedding (t-SNE) indicate that the relationship between drilling parameters and density log indeed vary between wellbores, making generalizability an issue for a traditional supervised learning approach to this problem, and motivating a streaming learning approach. Using the proposed method, more accurate at-bit estimates can be made, providing preliminary indications ahead of the tool placed 20–30 m behind the bit, which, dependent on rate of penetration (ROP), will be available 20–120min later.

We design an adaptive observer for semi-linear 2 × 2 hyperbolic PDEs with parametric uncertainties in both state equations. The proposed method is an extension of a previous result where parametric uncertainties were only allowed in one of the system equation. We utilize partial state measurements of one of the distributed states to estimate the remaining unknown distributed state. The method can be applied to flow rate estimation in fluid flow systems where the pressure is measured.

We extend a previous result regarding adaptive control of a linear hyperbolic partial differential equation (PDE) with time-varying in-domain source coefficient in two ways. Firstly, we introduce a parametrization of the uncertain time-varying in-domain source coefficient that allows for a broader class of systems compared to previous result. Secondly, and more importantly, we introduce an uncertain scaling factor in the input boundary condition which is present in most applications, but wasn't handled in the previous result. All system parameters except the transport speed are uncertain and time-varying, although parametrizable as a linear combination of uncertain constants and certain time-variance. Closed-loop convergence of the state to the origin is proven, and performance is demonstrated for a numerical example. © 2020 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.

An adaptive observer design for a system of n + 1 coupled 1-D linear hyperbolic partial differential equations with an uncertain boundary condition is presented, extending previous results by removing the need for sensing collocated with the uncertainty. This modification is important and motivated by applications in oil & gas drilling where information about the down-hole situation is crucial in order to prevent or deal with unwanted incidents. Uncertainties are usually present down-hole while measurements are available top-side at the rig, only. Boundedness of the state and parameter estimates is proved in the general case, while convergence to true values requires bounded system states and, for parameter convergence, persistent excitation. The central tool for analysis is the infinitedimensional backstepping method applied in two steps, the first of which is time-invariant, while the second is time-varying induced by the time-varying parameter estimates.

We solve a model reference adaptive control problem for a class of linear $ 2 \times 2$ hyperbolic partial differential equations (PDEs) with uncertain system parameters subject to harmonic disturbances, from a single boundary measurement anticollocated with the actuation. This is done by transforming the system into a canonical form, from which filters are designed so that the states can be expressed as linear combinations of the filters and uncertain parameters, a representation facilitating for the design of adaptive laws. A stabilizing controller is then combined with the adaptive laws to make the measured signal asymptotically track the output of a reference model. The reference model is taken as a simple transport PDE. Moreover, pointwise boundedness of all variables in the closed loop is proved, provided the reference signal is bounded. The theory is demonstrated in a simulation.

We present a new formulation of a convergence result for Lyapunov function candidates satisfying a differential inequality with integrable coefficients that often appears in adaptive control problems. Usually, Barbalat’s Lemma is invoked, requiring boundedness of the time derivative of the Lyapunov function candidate which can sometimes be hard to establish. By connecting results from the literature, an alternative route avoiding Barbalat’s Lemma is suggested.

We design two closely related state feedback adaptive control laws for stabilization of a class of 2 × 2 linear hyperbolic system of partial differential equations (PDEs) with constant but uncertain in-domain and boundary parameters. One control law uses an identifier, while the other is based on swapping design. We establish boundedness of all signals in the closed loop system, pointwise in space and time, and convergence of the system states to zero pointwise in space. The theory is demonstrated in simulations.

The heave motion of a floating rig induces pressure oscillations in the well when the heave compensators are disabled during connections. In this paper we discuss several factors affecting the achievable performance when rejecting such pressure oscillations by feedforward by controlling the opening of the topside choke. Here, the well is modeled as a semilinear hyperbolic system with a predictor-based control law that achieves exact pressure tracking at one location in the well in the nominal case. The focus is on wells with large friction (i.e. deep wells with high-viscosity drilling muds), where large control inputs are required at the topside choke. © 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd.

A model based method for kick and loss detection and attenuation in Managed Pressure Drilling is presented. The drilling system is modeled as a distributed parameter system combined with a reservoir flow equation containing reservoir pressure and the so-called productivity index as uncertain parameters. A swapping-based design for state and parameter estimation utilizing bottom-hole pressure measurements available via wired drill pipe is combined with a closed loop controller for kick and loss attenuation. The performance of the proposed method is compared to earlier results on kick attenuation in a simulation, showing significant improvement. © 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd.

In this paper, we solve an adaptive control problem for a class of $ 2 \times 2$ linear hyperbolic partial differential equations, where sensing and actuation are restricted to the boundary anticollocated with an uncertain parameter. This is done by combining a recently derived adaptive observer for the system states and the uncertain parameter, with an adaptive control law. Proof of $ L_2$ -boundedness for all signals in the closed loop is given, and the system states are proved to converge to zero pointwise in space. The theory is demonstrated in a simulation.

We consider the control and state estimation of a class of 2x2 semilinear hyperbolic systems with actuation and sensing collocated at one boundary. Our approach exploits the dynamics on the characteristic lines of the hyperbolic system. The control method using full-state feedback can be used for both stabilization of an equilibrium and tracking at an arbitrary point in the domain. The control objective is achieved globally in minimum time. A Lyapunov function is constructed to prove exponential convergence in the spatial supremum norm. For linear systems, the control input can be written explicitly as the inner product of kernels with the state, and turns out to be equivalent to the control input obtained from previously known backstepping methods. The observer achieves exact state estimation also in minimum time and, combined with the state-feedback controller, solves the output feedback control problem. The performance is demonstrated in a numerical example. © 2017. This is the authors’ accepted and refereed manuscript to the article. Locked until 5.7.2019 due to copyright restrictions. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/

A phenomenological model for percussive drilling systems is proposed in this paper to explain the experimentally demonstrated existence of an optimal weight-on-bit (WOB), for which the rate of penetration (ROP) is maximized. Several hypotheses have been previously proposed to explain this universal characteristic of percussive drilling, including increased wear of the bit, reduced indexing, and poor cleaning of debris under excessive WOB. Motivated by experimental evidence, we instead consider an increase of the pseudo-stiffness of the bit-rock interface (BRI) with increasing WOB, and investigate its effect on the impact energy transmitted to the rock. The 1D model approximates the dynamics underlying the drilling process by assuming that the impact of the hammer generates a longitudinal wave in the bit. It is shown that the BRI pseudo-stiffness influences the incident wave and associated energy transmitted from the bit to the rock. As a consequence, the drilling efficiency is affected by the dependence of the BRI stiffness on the WOB. The model indicates that there exist optimal conditions for the energy transfer from the bit to the rock in terms of the impedance ratio and the BRI stiffness/WOB. Thus it confirms that there is a sweet spot as seen in practice, which suggests that the root cause of the existence of a sweet spot in the ROP-WOB relationship lies in the nature of the BRI laws, rather than with issues related to bit indexing, bit wear, and/or cleaning of the debris. © Springer-Verlag GmbH Austria, part of Springer Nature 2020. This is a post-peer-review, pre-copyedit version of an article. The final authenticated version is available online at: DOI:https://doi.org/10.1007/s00603-020-02232-x

We solve an adaptive boundary control problem for an 1-D linear hyperbolic partial differential equation (PDE) with an uncertain in-domain source parameter and uncertain transport speed using boundary sensing only. Convergence of the parameters to their true values is achieved in finite-time. Since linear hyperbolic PDEs are finite-time convergent in the non-adaptive case, finite-time parameter convergence leads to the system state converging in finite-time. This is achieved by combining a recently derived transport speed estimation scheme using boundary sensing only, with the swapping scheme for hyperbolic PDEs and a least-squares identifier of an event-triggering type. The method is demonstrated in simulations. © 2020 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.

Recently, the first result on backstepping-based adaptive control of a 1-D linear hyperbolic partial differential equation (PDE) with an uncertain transport speed was presented. The system also had an uncertain, constant in-domain coefficient, and the derived controller achieved convergence to zero in the L ∞ -sense in finite time. In this paper, we extend that result to systems with a spatially varying in-domain coefficient, achieving asymptotic convergence to zero in the L ∞ -sense. Additionally, for the case of having a constant in-domain coefficient, the new method is shown to have a slightly improved finite-time convergence time. The theory is illustrated in simulations. © 2020 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.

We construct a method of dealing with the problem of overparameterization in model reference adaptive control (MRAC) of 2 ×2 linear hyperbolic partial differential equations (PDEs). The method is based on linear interpolation of the uncertain parameters. The proposed method is demonstrated in simulations of the fluid mechanics of a drilling system, and compared to a previously derived, overparameterized MRAC scheme, showing improved tracking and convergence properties. © 2020 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.

Early kick/loss detection is a crucial part of safe well control, and it plays a major role in the reduction of risk and non-productive time in drilling. In conventional drilling, topside sensing is used for early kick/loss detection. Recently, Venturi flowmeter based online return flow estimation has been introduced for this purpose by the authors. In managed pressure drilling, both topside sensing and bottomside sensing can be used for kick/loss detection. Therefore, a topside return flow estimator with a bottomside well pressure and flow estimator is combined to provide a complete kick/loss detection and estimation scheme for managed pressure drilling systems. This allows improved kick/loss detection. In addition, a closed-loop kick/loss attenuation controller is used to illustrate the estimation scheme.

We design an adaptive model-based observer for state and parameter estimation in 2 × 2 semi-linear hyperbolic systems with uncertain parameters where we assume that one of the two distributed states is available through distributed sensing. The uncertainties appear in the equation for the unmeasured distributed state and may be non-linear in the unmeasured state, although linearly parameterized. The adaptive law is designed using a Lyapunov approach and expressed in terms of known signals by utilizing the specific model structure which gives rise to a general solution strategy valid for a large class of non-linear source terms. © 2019 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.

In this paper, we use swapping design filters to bring systems of $n+1$ partial differential equations of the hyperbolic type to static form. Standard parameter identification laws can then be applied to estimate unknown parameters in the boundary conditions. Proof of boundedness of the adaptive laws are offered, and the results are demonstrated in simulations.

The problem considered in this paper is that of controlling downhole pressure during oil and gas well drilling, with a particular focus on handling gas kicks leading to two-phase gas–liquid flow conditions. We identify a first-order approximation to the infinite-dimensional system which captures the dominating mode of the pressure dynamics in the frequency range of interest, while the high-frequency pressure dynamics are represented by a multiplicative uncertainty. This approximation is then modified to accommodate the changes to the dynamics introduced by the two-phase flow. The linearized plant has an open-loop time constant which varies between 2 and 600 s depending on operating point and gas distribution in the well. Robust controller design is then performed using linear matrix inequalities (LMIs) via a polytopic norm-bounded description of both the high-frequency multiplicative, and the low-frequency parametric uncertainty. It is shown that, in order to achieve acceptable performance over such a large range of open loop time constants, a time-varying controller gain is required. The main contribution of the paper is to achieve this control objective systematically by formulating the control design problem as an LMI optimization problem. Then optimal solutions of the LMI problem can be obtained in polynomial time by using modern interior point method (IPM) numerical solution algorithms.

The aim of this paper is to achieve a model for prediction of cerebral palsy based on motion data of young infants. The prediction is formulated as a classification problem to assign each of the infants to one of the healthy or with cerebral palsy groups. Unlike formerly proposed features that are mostly defined in the time domain, this study proposes a set of features derived from frequency analysis of infants' motions. Since cerebral palsy affects the variability of the motions, and frequency analysis is an intuitive way of studying variability, suggested features are suitable and consistent with the nature of the condition. In the current application, a well-known problem, few subjects and many features, was initially encountered. In such a case, most classifiers get trapped in a suboptimal model and, consequently, fail to provide sufficient prediction accuracy. To solve this problem, a feature selection method that determines features with significant predictive ability is proposed. The feature selection method decreases the risk of false discovery and, therefore, the prediction model is more likely to be valid and generalizable for future use. A detailed study is performed on the proposed features and the feature selection method: the classification results confirm their applicability. Achieved sensitivity of 86%, specificity of 92% and accuracy of 91% are comparable with state-of-the-art clinical and expert-based methods for predicting cerebral palsy.

This paper presents a modification to L 1 adaptive control that allows for disturbances entering at the output and application of this control strategy to Managed Pressure Drilling with harmonic disturbances representing the heave motion of a floating drilling rig. By incorporating the disturbance at the output into the closed-loop reference model, it is shown that the L 1 adaptive control structure can be left unchanged while the original transient performance bounds are preserved. It is further shown that rejection of the output disturbance can be taken care of entirely in the filter design step of L 1 adaptive control using the internal model principle. A systematic filter design procedure based on LMIs is provided, that requires only one tuning parameter to be adjusted by the designer. The control design is applied to disturbance attenuation and set-point tracking in the so-called heave problem in oil well drilling. We present experimental results of control system tests in a medium size test facility emulating a 900 m long well.

We solve an adaptive control problem for n + 1 hyperbolic systems using collocated sensing and control, extending recent results for adaptive control of 2 × 2 systems and systems with non-collocated sensing and control. The boundary condition has an affine form with both unknown reflective and additive parameters and can be used to model well–reservoir interactions in oil and gas drilling where properties of the reservoir are unknown. Boundedness of the system states in the L 2 -norm, and convergence to a steady state profile satisfying a control objective relevant to the drilling application, are proved. The state estimation error is shown to converge to zero in the L 2 -norm and one of the boundary parameter estimates (modelling the reservoir pressure in the drilling application) is shown to converge to the true parameter value. The design is illustrated in a simulation example.

In this paper we derive a minimum time convergent bilateral observer for a 2×2 system of linear coupled first-order 1-D hyperbolic PDEs. First, a Volterra integral transformation is combined with a Fredholm integral transformation to derive a minimum time collocated observer for a class of 2+2 systems (four coupled PDEs). Then, it is shown that the 2 ×2 system (two coupled PDEs) can be transformed to a 2+2 system via an invertible coordinate transformation. The 2×2 bilateral observer is subsequently obtained from the 2+2 minimum time collocated observer, and it is shown that it has convergence time equal to the theoretical minimum time for bilateral sensing. The performance of the 2×2 bilateral observer is demonstrated in a simulation and compared to a previously derived observer using only unilateral sensing. © 2019 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.

This paper demonstrate the feasibility and illustrates some challenges of applying extremum seeking control to online optimization of the drilling process. Specifically, we consider the problem of finding the hook-load (and consequently the weight on bit) which optimizes the rate of penetration while drilling. To this end, a phenomenological drilling model is presented which includes the bit foundering that occurs at too high weight on bit. We then propose an Extremum Seeking (ES) controller architecture which can be used in conjunction with existing auto-driller systems. The effectiveness of this ES architecture is illustrated by simulation examples with the presented model. publishedVersion

A scheme for fast kick estimation in managed pressure drilling is presented. The reservoir pressure and production index are estimated by utilizing information in a fast traveling shock wave induced by an unexpected rise in reservoir pressure. A least squares estimation problem is formulated from an early-lumping approach based on a reduced order drift-flux model. The Levenberg-Marquardt scheme is applied to solve the non-linear least-squares problem. The estimation scheme is tested with simulated top-side flow measurements from a two-phase drift flux model. © 2019 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.

One of the challenges when applying managed pressure drilling (MPD) offshore on a floating rig is the wave-induced heaving motion of the rig. During drillstring extensions, the drillstring is rigidly attached to the rig and follows the rig’s heaving motion. This induces pressure oscillations in the well that can violate pressure margins, in particular in rough conditions and when margins are tight. In order to enable drilling operations under such conditions, the pressure oscillations are to be attenuated by use of a controllable valve installed in the bottomhole assembly (BHA) at the bottom of the drillstring. The subject of this paper is the controller design for the valve flow based on measurements of the BHA movement and downhole pressure. Using a frequency-domain approach, the control law is designed to, in case of downwards BHA movement, reduce the valve flow to compensate the mud being displaced by the BHA and the flow due to mud clinging to the moving drillstring. Controlling the valve flow in such a manner creates large differential pressures over the valve that can potentially destabilize the BHA motion, which must be taken into consideration in the control design. Stability and performance of the closed-loop system are verified in simulations using a high-fidelity model of the drilling mud and elastic drillstring. © 2019 Published by Elsevier Ltd. Under a Creative Commons CC-BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/).

We derive an adaptive output-feedback stabilizing controller for a system of 2 × 2 linear hyperbolic partial differential equations (PDEs) with delayed, anti-collocated sensing and control. This is done by using a series of transformations to show that the system is equivalent to delay-free systems for which such controllers have been derived. The only required knowledge of the system is the system's transport delays, the sensor and actuation delays and the sign of the product of the actuation and sensing scaling constants. The theory is verified in a simulation. © 2018 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.

Most model-based control and estimation techniques put limitations on the structure and complexity of the models to which they are applied. This has motivated the development of simplified models of gas-liquid two-phase flow for control and estimation applications. This paper reviews the literature for such models with a focus on applications from the field of drilling. The models are categorized in terms of complexity and the physical interpretation of the simplifications employed. A simulation study is used to evaluate their ability to qualitatively represent dynamics of 3 different gas-liquid scenarios encountered in drilling, based on which conclusions are drawn. © 2016. This is the authors’ accepted and refereed manuscript to the article. LOCKED until 5.7.2018 due to copyright restrictions. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/

We develop an adaptive observer that estimates boundary parameters and the system states in general heterodirectional linear systems of m+n coupled hyperbolic partial differential equations. The observer uses boundary sensing only, and is based on the swapping design, where filters are constructed that can be used to express the system states as linear static combinations of the unknown parameters and the filters states. Standard parameter identification laws can then be applied. Proof of boundedness of the estimates is offered, and sufficient conditions ensuring exponential convergence to their true values is derived. The theory is verified in a simulation.

We design a leak detection system consisting of an adaptive observer based on a set of two coupled one dimensional first order hyperbolic partial differential equations governing the flow dynamics. It is assumed that measurements are only available at the inlet and outlet of the pipe. Convergence properties are provided showing that the leak size estimation problem can be tackled independently from how the leak is distributed along the pipe. This is key to obtaining a simple estimation scheme for the leak location. Simulations are provided to demonstrate the ability of the system to detect, quantify and locate leaks.

We derive a full state feedback law and a state observer for a class of disturbance rejection problems for n+1 linear coupled partial differential equations (PDEs). The disturbance enters the system at one boundary, while the actuation and sensing are limited to the opposite boundary. We solve this by separately designing a state feedback controller and an observer, and show that they can be combined into an output feedback control law that rejects the effect of the disturbance with exponential decay. The performance of output feedback controller is demonstrated in a simulation.

We solve a tracking problem for general heterodirectional linear 1-D hyperbolic partial differential equations. A full state feedback controller and an observer generating full state estimates from sensing co-located with the actuation are designed. Both converge in finite, minimum time. The two are then combined into an output feedback law achieving tracking in finite time given by the sum of the convergence times of the controller and observer.

Keeping the pressure within predefined bounds is essential for the safety of managed pressure drilling operations, but drill string movements can induce pressure fluctuations that violate these margins. We extend previous results on disturbance rejection for a 2 x 2 hyperbolic model of the fluid dynamics in the borehole. We perform a simulation study, in which we illustrate the controller performance for heave induced oscillations and compare it to the previously available controller. The stochasticity of sea waves induces limitations on the achievable performance. Further, the controller is applied to intended string movements, where control can be used to remove conservative limitations on the speed of the movement.

We aim at predicting cerebral palsy at an early stage using normal video camera.A new motion segmentation method is proposed that benefits from prior knowledge.A particle matching technique is used to reduce the dependency on prior knowledge.The proposed method segments the objects, infants body parts, with high performance.The method is tested on a standard benchmark and outperforms the previous methods. Motion segmentation refers to the task of segmenting moving objects subject to their motion in order to distinguish and track them in a video. This is a challenging task in situations where different objects share similar movement patterns, or in cases where one object is occluded by others in part of the scene. In such cases, unsupervised motion segmentation fails and additional information is needed to boost the performance. Based on a formulation of the clustering task as an optimization problem using a multi-labeled Markov Random Field, we develop a semi-supervised motion segmentation algorithm by setting up a framework for incorporating prior knowledge into the segmentation algorithm. Prior knowledge is given in the form of manually labelling trajectories that belong to the various objects in one or more frames of the video. Clearly, one wishes to limit the amount of manual labelling in order for the algorithm to be as autonomous as possible. Towards that end, we propose a particle matching procedure that extends the prior knowledge by automatically matching particles in frames over which fast motion or occlusion occur. The performance of the proposed method is studied through a variety of experiments on videos involving fast and complicated motion, occlusion and re-appearance, and low quality film. The qualitative and quantitative results confirm reliable performance on the types of applications our method is designed for.

As oil exploration and development costs rise, the oil industry increases its efforts to improve oil recovery (IOR) from existing fields. IOR is achieved mainly by drilling more wells, but drilling in partially depleted reservoirs is challenging due to narrow pressure margins. Offshore drilling in harsh environments, such as the North Sea, presents additional challenges, since the heaving motion from a floating rig induces large surge and swab pressures in the well. This brief suggests a remedy for this problem using automatic control of well pressure. Taking advantage of an experimental lab facility recently completed at NTNU, a model of the drilling system is developed using subspace identification methods. The model serves as a basis for state estimation and controller design using model predictive control. Applying the controller to the lab facility, pressure oscillations are suppressed by 70%-90% compared with the open-loop case, depending on the period of the heave motion. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works nb_NO

We extend recent results regarding disturbance rejection control of n+m linear hyperbolic partial differential equations (PDEs) in a number of ways: 1) We allow spatially varying coefficients; 2) The disturbance is allowed to enter in the interior of the domain, and; 3) Rejection is achieved in minimum time. Additionally, we solve a tracking problem, where the tracking objective is achieved in finite, minimum time. We use a recently derived Fredholm transformation technique in addition to infinite-dimensional backstepping in our design. © 2018 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.

We derive a state-feedback controller for a scalar 1-D linear hyperbolic partial differential equation (PDE) with a spatially-and time-varying interior-domain parameter. The resulting controller ensures convergence to zero in a finite time d 1 , corresponding to the propagation time from one boundary to the other. The control law requires predictions of the in-domain parameter a time d 1 into the future. The state-feedback controller is also combined with a boundary observer into an output-feedback control law. Lastly, under the assumption that the interior-domain parameter can be decoupled into a time-varying and a spatially-varying part, a stabilizing adaptive output-feedback control law is derived for an uncertain spatially varying parameter, stabilizing the system in the L 2 -sense from a single boundary measurement only. All derived controllers are implemented and demonstrated in simulations. © 2018 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.

We design an adaptive controller for a 2 × 2 linear hyperbolic PDE with uncertain boundary parameters where measurements are taken at both boundaries, while only one boundary is actuated. The uncertainty, which appears in the un-actuated boundary, is in a bilinear form, which allows us to use bilinear adaptive laws for which parameter estimate convergence is guaranteed under a simple, a priori verifiable, persistence of excitation criterion. The control objective is boundary set-point regulation where the set-point is dependent on one of the unknown parameters. Stability is proved in the L 2 -sense and all signals in the closed loop are shown to be bounded. © 2018 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.

We consider a scalar 1-D linear hyperbolic partial differential equation (PDE) for which infinite-dimensional backstepping controllers have previously been designed based on boundary actuation and sensing, and incorporate first order actuator and sensor dynamics into the design. Two observer designs are proposed, and combined with a state-feedback into output-feedback control laws which render the origin of the closed-loop system exponentially stable with arbitrary convergence rate. The theory is verified in simulations.

In this technical note, we develop a full state feedback law for disturbance rejection in systems described by linear 2 × 2 partial differential equations of the hyperbolic type, with the disturbance modelled as an autonomous, finite dimensional linear system affecting the PDE's left boundary, and actuation limited to the right boundary. The effect of the disturbance is rejected at an arbitrary point in the domain within a finite time. The performance is demonstrated through simulation.

This paper presents a modification to L 1 adaptive control that allows for disturbances entering at the output and application of this control strategy to Managed Pressure Drilling with harmonic disturbances representing the heave motion of a floating drilling rig. By incorporating the disturbance at the output into the reference model, it is shown that the Li adaptive control structure can be left unchanged while the original transient performance bounds are preserved. It is further shown that rejection of the output disturbance can be taken care of entirely in the filter design step of Li adaptive control using the internal model principle. A systematic filter design procedure based on LMIs is provided, that requires only one tuning parameter to be adjusted by the designer. The control design is applied to disturbance attenuation and set-point tracking in the so-called heave problem in oil well drilling. We present experimental results of control system tests in a medium size test facility emulating a 900 m long well.

We solve the problem of controlling a class of one-dimensional semilinear 2 × 2 hyperbolic systems to the origin in minimum time using actuation at both boundaries of the domain. The control method can also be used to solve a class of tracking problems. For the special case of time-invariant linear systems, the state-feedback control law can be written explicitly as the inner product of kernels with the state. We further design an observer to estimate the distributed state from measurements at both boundaries, also in minimum time. The state-feedback controller and observer are combined to solve the output-feedback control problem. A numerical example is given to demonstrate the controller performance. © 2018 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.

Many interesting problems in the oil and gas industry face the challenge of responding to disturbances from afar. Typically, the disturbance occurs at the inlet of a pipeline or the bottom of an oil well, while sensing and actuation equipment is installed at the outlet, only, kilometers away from the disturbance. The present paper develops an output feedback control law for such cases, based on modelling the transport phenomenon as a 2 $\times$ 2 linear partial differential equation (PDE) of hyperbolic type and the disturbance as a finite-dimensional linear system affecting the left boundary of the PDE. Sensing and actuation are co-located at the right boundary of the PDE. The design provides a separation principle, allowing a disturbance attenuating full-state feedback control law to be combined with an observer. The results are applied to a relevant problem from the oil and gas industry and demonstrated in simulations.

A model-based in-/out-flux detection scheme for managed pressure drilling is presented. We apply a globally exponentially stable adaptive observer which estimates the unknown states and parameters of the hydraulic system and in particular quantifies the magnitude of the in-/out-flux and its location in the well. While the observer can be used purely as an in-/out-flux detection system, the paper also presents a simple controller that automatically and effectively stops an in-/out-flux. This novel control scheme departs from common practice for automatic managed pressure drilling, which is to regulate down-hole pressure to some predetermined set point. Experimental results and realistic simulations with a state-of-the-art simulator are provided to show the effectiveness of the method.