Family Of Linear Models Research Articles

Using the Discrete Lindley Distribution to Deal with Over-dispersion in Count Data

Count data in environmental epidemiology or ecology often display substantial over-dispersion, and failing to account for the over-dispersion could result in biased estimates and underestimated standard errors. This study develops a new generalized linear model family to model over-dispersed count data by assuming that the response variable follows the discrete Lindley distribution. The iterative weighted least square is developed to fit the model. Furthermore, asymptotic properties of estimators, the goodness of fit statistics are also derived. Lastly, some simulation studies and empirical data applications are carried out, and the generalized discrete Lindley linear model shows a better performance than the Poisson distribution model.

Linear parameter-varying-based transition flight control design for a tilt-rotor aircraft

This paper presents the development of novel transition flight controllers for a class of urban air mobility aircrafts configured with a fixed-wing and six distributed electric rotor assemblies. Only the two tilt-rotors are utilized for thrust vectoring during transition flight from hovering to steady-level flight, while the four lift-rotors are modulated with aerodynamic lift induced by fixed-wing to maintain stable altitude-hold. Three tractable tilt-rotor articulation profiles are proposed by taking into account of various aircraft and hardware constraints. Given a predefined nominal tilting profile, a family of linear models is obtained by linearizing the nonlinear aircraft model at multiple tilt-rotor angular positions along the tilting profile. Using tilt-rotor angular position as a scheduling parameter, a discrete-time linear parameter-varying model can be constructed, which is then used to develop a novel transition flight control architecture that integrates the adaptive model predictive control law with feedforward effect of the dynamic reference compensation. The simulation results demonstrate the effectiveness of proposed transition flight controllers and its robustness subject to external disturbance.

Finite-time bounded control for quadrotors with extended dissipative performance using a switched system approach

In order to deal with the problem of attitude tracking control for quadrotors subject to time-varying inertia and external disturbances, a finite-time bounded switched linear parameter-varying (LPV) control method is presented. The attitude dynamics is described by two subsystems, where the inner angular-velocity system is used to track the desired angular velocities that are generated by the outer attitude-angle system. The angular-velocity system of quadrotors is modeled as a switched LPV model, where a family of linear models is developed to approximate the original nonlinear system and the LPV method is applied to model the time-varying inertia. Specially, a mode-dependent persistent dwell-time (MPDT) switching logic, which is more general than the typically used dwell-time (DT) or average dwell-time (ADT) switching logic, is adopted to govern the switching behaviors among these linear models. A state-feedback controller for the switched LPV error-tracking system is designed, which ensures both finite-time boundedness and extended dissipative performance. Finally, the developed theoretical results are verified by numerical simulation.

A Robust H∞ Control Approach for Blood Glucose Regulation in Type-1 Diabetes

Abstract The paper addresses the design of a H∞ closed-loop dedicated to Blood Glucose (BG) regulation for patients affected by Type-1 Diabetes Mellitus (T1DM). The closed-loop setup is standard, i.e. the H∞ feedback controller uses the information provided by a subcutaneous sensor to drive an insulin pump but as opposed to current existing solutions, it is proposed to assess the capabilities of a H∞ controller to be designed in a patient-independent way. For that purpose, the design is performed on a family of linear models in order to tackle the variability of a cohort of T1DM patients. Worst-case performance and robust margins are next computed with the help of the H∞/µ-analysis theory. The solution is finally assessed on the adult cohort of the high-fidelity UVA/Padova benchmark (v3.2), accepted by the US Food and Drug Administration (FDA) as a substitute for pre-clinical testing of control strategies.

A Control Solution for a Tethered Kite Trajectory Tracking With Application to Ship Propulsion

Abstract In the field of clean and green energy production systems, airborne wind energy (AWE) systems are really promising technologies. Replacing lightweight tethers with expensive towers, is an innovative solution to get energy from higher altitudes than classical wind turbines. But AWE systems can also be used to produce a traction force through a fast-flying airfoil, or kite. In this paper, the traction force is supposed to be used for ship propulsion. Such an application is permitted if the kite is kept on an appropriate trajectory. This paper thus considers the design of an automatic pilot for trajectory tracking. Its design requires a path-planning and a control strategies that are described here. In terms of control strategy, a robust CRONE controller is designed based on a family of linear models that stands for the nonlinear model of the kite and obtained numerically around several trajectories and for various flight conditions. Efficient trajectories for ship traction being periodic, a method involving tools dedicated to time-varying periodic systems is then used to validate the approach used for CRONE controller design.

Electro-Thermal and Aging Lithium-Ion Cell Modelling with Application to Optimal Battery Charging

This paper deals with optimal charging versus aging minimization for lithium-ion batteries. The optimal charging strategy proposed involves charging controllers whose design relies on a battery model. The model, especially designed for automotive battery management systems applications, is recalled in this paper. It provides the voltage response of a cell to an input current. It also models side reactions that produce degradation mechanisms and thus decrease battery performance. Side reaction modelling involves taking into account the temperature cell variations, which are thus also modelled. The association of the three above-mentioned sub-models leads to an electro-thermal battery aging model used to design an optimal charging strategy that simultaneously takes into account the minimization of charging time and maximization of battery lifetime. Thus, to achieve a charging controller that manages battery health, an appropriate charging trajectory was computed by solving an optimization problem minimizing aging. Then, a charge control loop was designed. The nonlinear behavior of the battery was taken into account through the linearization of the electro-thermal aging model in different operating conditions. To take into account the resulting linear model family, the CRONE design methodology was used. The principles of this methodology are recapped and the design of the charging control loop is explained. The efficiency of the resulting charge controller is illustrated by several simulations.

Controller Gains of an Inverted Pendulum are Influenced by the Visual Feedback Position.

In this study we experimentally test and model the control behavior of human participants when controlling inverted pendulums of different dynamic lengths, and with visual feedback of varying congruence to these dynamic lengths. Participants were asked to stabilize the inverted pendulum of L = 1 m and L = 4 m, with visual feedback shown at various distances along the pendulum. We fit a family of linear models to the control input (cart velocity) applied by participants. We further tested the models by predicting this control input for a pendulum with dynamic length L = 2 m and comparing the prediction to the experimental data. We show that the sum of proportional error correction and a term inversely proportional to visual feedback gain can well describe the control in human participants.

Bayesian Analysis for Parameters of Multivariate tFA model with Simulation

In many kinds of pollution, such as economic and environmental pollution, the researchers use the normal linear model to present their data studies. That selection may be inaccurate because the data of those studies do not vacate from outlier observations, which have great effect on the estimation problem even if they are processed or removed from the sample study. These processes lead to facts defacement to the decision maker. For that reason, the non-normal linear models has been found out to combat that matter. That error term in these models belongs to the family of probability distributions which resist outliers, for example, the multivariate t and mixture normal distributions. The factor analysis model belongs to the family of linear models and because the multivariate data sets do not vacate outliers .For this reason this paper is concerned with studying the t factor analysis model. The model analyzed by Bayesian technique in which the common factors are treated as fixed and random variables . We supposed that all parameters of both two models were unknown and their prior distributions belong to conjugate families. The number of extracted factors in factor analysis models cannot be determined a prior .On this foundation, in Bayesian analysis, these factors are treated as random variables. We obtained a posterior probability criterion to choose the number of extracted factors for the two models. We choose the number of factors in which they must be entered, and the model which they have maximum posterior probability. All results that we concluded were applied to empirical data sets which are generated by simulation in two different sample sizes (n=50,100) at different values of the degrees of freedom for the distribution of the error term. Also, we selected different forms of factor loading matrix and variance matrix of error term. Matlab (7.9) language is used in data generation and analysis

Gain-Scheduled Autopilot Design and Validation for an Experimental Guided Projectile Prototype

This paper investigates the design and validation of a gain-scheduled skid-to-turn autopilot for an experimental canard-guided, fin-stabilized 80-mm-guided projectile prototype in a hardware-in-the-loop (HIL) wind tunnel-based setup. The projectile dynamics are a priori unknown and are determined from open-loop system identification experiments conducted on the test setup. To this end, a nonlinear airframe model is discussed and considered for linearization around equilibrium operating points. The linear model parameters are estimated from several data collection experiments, resulting in a family of linear models. This knowledge is leveraged in a second step to compute a family of robustly stable multiobjective disturbance-rejection and reference-tracking controllers, which are implemented on the HIL test setup using a zero-pole gain interpolation scheme. The time-domain performance of the autopilot is finally assessed by the means of numerical simulations and experimental results gathered from the test setup, demonstrating the excellent suitability of the proposed approach.

Robust Control of a Tandem Helicopter with Variable Payload

The present work aims at showing that structured H∞ synthesis can tune a unique controller for a tandem helicopter with different payload configurations. First, the rotorcraft dynamics is modeled, including the variable payload and its impact on the centre of mass and inertia. The controller architecture imposed by the manufacturer’s autopilot is then presented. In order to tune this controller, the design problem is cast in the framework of structured H∞ synthesis, in particular by using Matlab function systune, whose multi-model synthesis capabilities are exploited. The synthesis is performed on a family of linear models obtained by linearising the tandem helicopter dynamics in hover conditions for different mass and payload configurations. The controller is then validated on a nonlinear simulation of the rotorcraft dynamics.

Offset-free multi-model economic model predictive control for changing economic criterion

Economic Model Predictive Controllers, consisting of an economic criterion as stage cost for the dynamic regulation problem, have shown to improve the economic performance of the controlled plant. However, throughout the operation of the plant, if the economic criterion changes – due to variations of prices, costs, production demand, market fluctuations, reconciled data, disturbances, etc. – the optimal operation point also changes. In industrial applications, a nonlinear description of the plant may not be available, since identifying a nonlinear plant is a very difficult task. Thus, the models used for prediction are in general linear. The nonlinear behavior of the plant makes that the controller designed using a linear model (identified at certain operation point) may exhibit a poor closed-loop performance or even loss of feasibility and stability when the plant is operated at a different operation point. A way to avoid this issue is to consider a collection of linear models identified at each of the equilibrium points where the plant will be operated. This is called a multi-model description of the plant. In this work, a multi-model economic MPC is proposed, which takes into account the uncertainties that arise from the difference between nonlinear and linear models, by means of a multi-model approach: a finite family of linear models is considered (multi-model uncertainty), each of them operating appropriately in a certain region around a given operation point. Recursive feasibility, convergence to the economic setpoint and stability are ensured. The proposed controller is applied in two simulations for controlling an isothermal chemical reactor with consecutive-competitive reactions, and a continuous flow stirred-tank reactor with parallel reactions.

The generalised isodamping approach for robust fractional PID controllers design

ABSTRACTIn this paper, we present a novel methodology to design fractional-order proportional-integral-derivative controllers. Based on the description of the controlled system by means of a family of linear models parameterised with respect to a free variable that describes the real process operating point, we design the controller by solving a constrained min–max optimisation problem where the maximum sensitivity has to be minimised. Among the imposed constraints, the most important one is the new generalised isodamping condition, that defines the invariancy of the phase margin with respect to the free parameter variations. It is also shown that the well-known classical isodamping condition is a special case of the new technique proposed in this paper. Simulation results show the effectiveness of the proposed technique and the superiority of the fractional-order controller compared to its integer counterpart.

An Affine Parameter Dependent Controller of an Helicopter for Various Forward Velocity Conditions

In this paper, we address the design of a controller that accomplishes stabilization and reference tracking at various flight conditions by using linear helicopter models. The suggested controller is in the form of an H-infinity gain-scheduler, and is used for stabilization and reference tracking for the 4 axis (heave, pitch, roll and yaw) autopilot. Based on the linear models given for the Puma helicopter, an approximate affine parameter dependent model has been built. Then, a linear parameter dependent controller is synthesized which stabilizes the affine parameter dependent helicopter model. By doing so, a single controller achieves stabilization and reference tracking of a family of linear models by scheduling the controller gains based on the online measurement of the scheduling parameter, which is the forward velocity. Moreover, the affine parameter dependent controller is fitted into the linear models. It is observed that this single parameter dependent controller successfully stabilizes a family of linear helicopter model at different forward flight conditions.

An Affine Parameter Dependent Controller for an Autonomous Helicopter at Different Flight Conditions

In this paper we address the design of a controller that achieves stabilization and reference tracking at different flight conditions for an unmanned helicopter. The controller proposed is in the form of an H-infinity gain-scheduler, and is used for stabilization and reference tracking, for the 4 axis autopilot. (heave, pitch, roll and yaw control) A nonlinear helicopter model has been built, trimmed and linearized at different flight conditions. Based on the linearized models an approximate affine parameter dependent model has been constructed. Then, a linear parameter dependent controller is synthesized which stabilizes the affine parameter dependent helicopter model. By doing so, a single controller achieves stabilization and reference tracking of a family of linear models by scheduling the controller gains based on the online measurement of the scheduling parameter, which is the forward velocity. Moreover, the affine parameter dependent controller is fitted into the nonlinear helicopter model. It is seen that this single parameter dependent controller successfully stabilizes the nonlinear helicopter model at different flight conditions.

Lossless predictive coding for images with Bayesian treatment.

Adaptive predictor has long been used for lossless predictive coding of images. Most of existing lossless predictive coding techniques mainly focus on suitability of prediction model for training set with the underlying assumption of local consistency, which may not hold well on object boundaries and cause large predictive error. In this paper, we propose a novel approach based on the assumption that local consistency and patch redundancy exist simultaneously in natural images. We derive a family of linear models and design a new algorithm to automatically select one suitable model for prediction. From the Bayesian perspective, the model with maximum posterior probability is considered as the best. Two types of model evidence are included in our algorithm. One is traditional training evidence, which represents the models’ suitability for current pixel under the assumption of local consistency. The other is target evidence, which is proposed to express the preference for different models from the perspective of patch redundancy. It is shown that the fusion of training evidence and target evidence jointly exploits the benefits of local consistency and patch redundancy. As a result, our proposed predictor is more suitable for natural images with textures and object boundaries. Comprehensive experiments demonstrate that the proposed predictor achieves higher efficiency compared with the state-of-the-art lossless predictors.

Linear models‐based LPV modelling and control for wind turbines

AbstractThe non‐linear behaviour of wind turbines demands control strategies that guarantee the robustness of the closed‐loop system. Linear parameter‐varying (LPV) controllers adapt their dynamics to the system operating points, and the robustness of the closed loop is guaranteed in the controller design process. An LPV collective pitch controller has been developed within this work to regulate the generator speed in the above rated power production control zone. The performance of this LPV controller has been compared with two baseline control strategies previously designed, on the basis of classical gain scheduling methods and linear time‐invariant robust H∞ controllers. The synthesis of the LPV controller is based on the solution of a linear matrix inequalities system, proposed in a mixed‐sensitivity control scenario where not only weight functions are used but also an LPV model of the wind turbine is necessary. As a contribution, the LPV model used is derived from a family of linear models extracted from the linearization process of the wind turbine non‐linear model. The offshore wind turbine of 5 MW defined in the Upwind European project is the used reference non‐linear model, and it has been modelled using the GH Bladed 4.0 software package. The designed LPV controller has been validated in GH Bladed, and an exhaustive analysis has been carried out to calculate fatigue load reductions on wind turbine components, as well as to analyse the load mitigation in some extreme cases. Copyright © 2014 John Wiley & Sons, Ltd.

One-layer robust MPC: a multi-model approach

In this paper, an MPC that explicitly integrates the RTO structure into the dynamic control layer is presented. In particular, a robust MPC is proposed, which takes into account the uncertainties that arise from the difference between nonlinear and linear models, by means of a multi-model approach: a finite family of linear models is considered, which operate appropriately in a moderate-to-large region around a given operating point. In this way, each linear model provides an enough accurate description of the system. Feasibility and stability conditions are preserved. Moreover, the real plant converges to the optimal point that optimizes the economic cost function.

Bayesian Analysis of Mixture of Normal Factor Analysis Model

Factor analysis model belongs to a family of linear models and because the multivariate data sets do not vacate outliers . For this reason , this paper is concerned with Bayesian analysis of mixed normal factor analysis model . The mixture normal distribution treats the observations of a sample as they are taken from two different populations and none from single population . The model is analyzed when the common factor is (stochastic and non-stochastic) variable . We suppose that all the parameters of the model are unknown , some of them have prior distributions belong to the conjugate family.

Disentangling the complexity of infectious diseases: Time is ripe to improve the first-line statistical toolbox for epidemiologists

Because many biological processes related to the dynamics of infectious diseases are caused by complex interactions between the environment, the host(s) and the agent(s), the necessity to address the methodological implications of this inherent complexity has recently emerged in epidemiology. Most epidemiologists now acknowledge that most human infectious diseases are likely to have complex dynamics. However, this knowledge still percolates with difficulty in their statistical “modus operandi”. Indeed, for the study of complex systems, the traditional first-line statistical toolbox of epidemiologists (mainly built around the Generalized Linear Model family), despite its undeniable practicality and robustness, has structural limitations deprecating its usefulness. Three major sources of complexity neglected or not taken into account by this first-line statistical toolbox and having deep statistical implications are the multi-level organization of data, the non-linear relationships between variables and the complex interactions between variables. Three promising candidates to incorporate along with traditional tools for a new first-line statistical toolbox more suitable to apprehend these sources of complexity are the generalized linear mixed models, the generalized additive models, and the structural equation models. The aforementioned methodologies have the advantage to be generalizations of GLM models and are relatively easy to implement. Their assimilation and implementation would thus be greatly facilitated for epidemiologists. More globally, this text underlines that an improved use of other methods as such described here compared to traditional ones has to be performed to better understand the complexity challenging epidemiologists every day. This is particularly true in the field of infectious diseases for which major public health challenges will have to be addressed in the coming decades.

Gain scheduled continuous-time model predictive controller with experimental validation on AC machine

Linear controllers with gain scheduling have been successfully used in the control of nonlinear systems for the past several decades. This paper proposes the design of gain scheduled continuous-time model predictive controller with constraints. Using induction machine as an illustrative example, the paper will show the four steps involved in the design of a gain scheduled predictive controller: (i) linearisation of a nonlinear plant according to operating conditions; (ii) the design of linear predictive controllers for the family of linear models; (iii) gain scheduled predictive control law that will optimise a multiple model objective function with constraints, which will also ensure smooth transitions (i.e. bumpless transfer) between the predictive controllers; (iv) experimental validation of the gain scheduled predictive control system with constraints.