G. Goffaux

Continuous - discrete interval observers for monitoring microalgae cultures

Algorithms estimating unmeasured component concentrations play a key role in bioprocess applications where only a few on‐line measurements are usually available. In this article, interval observers are designed to provide guaranteed intervals for the key components involved in cultures of microalgae. In contrast with most of the published studies focusing on continuous‐time measurements, this study considers discrete‐time measurements with possibly long and irregular sampling and defines predictors based on model equations and state transformations to ensure the enclosure of the state variables between two measurement times. The methods are validated with experimental data where the remaining inorganic nitrogen and the microalgal internal quota are estimated.

Design of a Robust Nonlinear Receding-Horizon Observer - Application to a biological system

The objective of this study is to design a robust receding-horizon observer for systems described by nonlinear models with uncertain parameters. Robustification in the presence of model uncertainties naturally leads to the formulation of a nonlinear min-max optimization problem, which can either be solved numerically or which can be converted to a simpler minimization problem using linearization along a nominal trajectory and recent results in linear robust receding-horizon estimation. This method is first evaluated in simulation and then with real-life experimental data collected from continuous cultures of phytoplankton.

Vehicle Positioning by a Confidence Interval Observer - Application to an Autonomous Underwater Vehicle

State estimation methods allow the vehicle position and velocity to be reconstructed by combining information from sensors and vehicle model. From a security point of view, position and velocity have to be known with a high level of confidence in order, for example, to avoid vehicle collision. In this paper, a confidence interval observer is developed to enclose positioning variables with some confidence degree (or integrity level). For this purpose, the algorithm is divided in two parts. First, a predictor, based on the vehicle dynamics, is derived to estimate bounds on state variables with lower bounded integrity. Then, at each measurement time, confidence intervals from the sensors are combined with union and intersection operations to satisfy the integrity level. The shortest non-empty intervals are chosen among the safe intervals. Finally, to quantify the reliability of estimation, a security measure is defined by the probability of having one faulty estimation in some period of time and is related to the integrity level objective. This method is illustrated with simulation tests based on an autonomous underwater vehicle described by a nonlinear model.

Discrete-time interval observers applied to cultures of phytoplankton

Abstract Based on intervals bounding the uncertain initial conditions, inputs, model parameters and measurements, interval observers provide guaranteed intervals for the state trajectory. However, most of the published studies focus on methods relying on continuous-time on-line measurements, or at least, with relatively fast sampling. In this study, interval state estimation methods are proposed in the situation, quite common in biological systems, where measurements are only available at discrete, and possible rare, times. The attention is focused on defining predictors preserving the boundedness of the state variables between two measurement times assuming bounded uncertainties. The methods are tested with experimental data from continuous cultures of the green algae Dunaliella tertiolecta.

Design of a Robust Nonlinear Receding-Horizon Observer - First-Order and Second-Order Approximations

The objective of this study is to design a robust receding-horizon observer for systems described by nonlinear models with uncertain parameters. Robustification in the presence of model uncertainties naturally leads to the formulation of a nonlinear min-max optimization problem, which can be converted to a simpler minimization problem using approximation along a nominal trajectory. In this study, the suitability of first-order and second-order approximations is investigated. These methods are evaluated in simulation and with experimental data from continuous cultures of phytoplankton.

Parameter Identification to Enforce Practical Observability of Nonlinear Systems

The sensitivity of measurements to unmeasured state variables strongly affects the rate of convergence of a state estimator. To overcome potential observability problems, the approach has been to identify the model parameters so as to reach a compromise between model accuracy and system observability. An objective function that weighs the relative importance of these two objectives has been proposed in the literature. However, this scheme relies on an extensive heuristic search to select the weighting coefficients. This paper proposes an objective function that is the product of measures of these two objectives, thus alleviating the need for the trial-and-error selection of the weighting coefficient. The proposed identification procedure is evaluated using both simulated and experimental data, and with different observer structures.

Design of a confidence interval observer—Application to vehicle positioning

Abstract State estimation methods allow the vehicle position and velocity to be reconstructed by combining information from sensors and vehicle model. From a security point of view, position and velocity have to be known with a high level of confidence in order, for example, to avoid vehicle collision. In this paper, a confidence interval observer is developed to enclose positioning variables with some confidence degree (or integrity level). Based on a vehicle model and intervals bounding, with some associated probability, the uncertain initial conditions, inputs, model parameters and measurements, a predictor provides intervals for the state estimate trajectory between two measurement times. At each measurement time, confidence intervals from the sensors and the predictor are combined with union and intersection operations so as to satisfy the specified integrity level. Finally, the shortest non-empty intervals are chosen among the safe intervals. This method is illustrated with simulation tests based on an autonomous underwater vehicle described by a nonlinear model.

Robust filtering techniques applied to train positioning

Abstract State estimation methods allow the vehicle position and velocity to be reconstructed by combining information from sensors and vehicle modelling. In a railway application, measurement signals from several sensors are available at asynchronous times, e.g., signals from odometers, radars and accelerometers. A Kalman filter can be easily designed based on a linear discrete-time model. However, in the train security package, only one accelerometer is available and moreover, this accelerometer is sensitive to rail track gradient. To circumvent the problem of estimation bias, a robust filter is developed, which takes uncertainties on the acceleration measurements and asynchronous data into account.