Philippe Neveux

A Polynomial Approach to Bias Aware Fixed-Lag Smoothing Problem

In the present technical note, a solution to the problem of fixed-lag smoothing of SISO systems in presence of a dynamical bias is presented in a polynomial framework. The bias aware smoothing problem is solved in three steps, namely, the design of the general structure of the smoother, the estimation of the dynamical bias by means of a deconvolution technique and, then, the combination of the previous results to obtain the bias aware fixed-lag smoother. Applied to an example, this approach shows its efficiency.

A Polynomial Approach to Robust Estimation of Uncertain Discrete-Time Systems

The robust estimation problem for uncertain discrete-time systems is treated in this paper considering parametric uncertainties in the polynomial framework. The estimator is the minimiser of a cost function written in a ∈-contaminated form. Uncertainties are not formally modelled. It is shown that, in the present context, the proposed approach can be connected to stochastic modelling of uncertainties. The optimal robust estimator is obtained by computing a spectral factorisation and by solving a single Diophantine equation. An example shows the efficiency of the proposed method.

Reducing the energy consumption of space heating in buildings: design of an optimal controller

Abstract The reduction of the energy consumption in buildings has become a priority in every developed country. Automatic control is one of the latest techniques introduced to this purpose. This paper describes the design of a new controller which controls the internal temperature of an individual dwelling by adjusting of the heating power. First, considering the intermittency the occupation, an optimal temperature trajectory in term of control cost has been computed. Second, introducing an augmented state representation, a state feedback law has been calculated. Third, since this law required an inaccessible state, a Kalman estimator has been introduced to estimate this state. Introducing a deconvolution problematic in its design, a “virtual feed forward” based on estimation has been introduced to balance the external disturbances. Fourth, in order to take into account the control saturation of the heating system, an anti-windup compensator has been introduced to the controller. Finally, the controller has been tested in simulation on an experimental building and the interest of the virtual feed forward has been illustrated.

Robust H∞ filtering by means of lead-lag controller

Abstract In the present paper, a new strategy for robust filtering problem of linear time-invariant (LTI) continuous time system is proposed. The key idea consists in generalizing the structure of a linear state estimator of the Luenberger class. As a matter of fact, the closed loop form of this class of state estimator can be assimilated to a closed loop control problem. Then, the standard correction term can be viewed as a Proportional controller. In this paper, we propose a more general form of controller in order to obtain the robustness. An example shows the efficiency of the proposed approach.

Deconvolution for slowly time-varying systems 3D cases

In the present work, we discuss an extension of the deconvolution techniques of Sekko [20] and Neveux [18] to 3D signals. The signals are assumed to be degraded by electronic linear systems, in which parameters are slowly time-varying such as sensors or other storage systems. For this purpose, Sekko & al. [20] developed a structure that has been adapted to time-varying systems [18] in order to produce an inverse filter with constant gain. This latter method was applied successfully to ordinary images [23]. The treatment of omnidirectional images requires working on the unit sphere. Therefore, the problem should be cast in 3D. In the 3D case, the deconvolution method [18] can be applied after some manipulations. The Heinz-Hopf fibration offers the possibility to consider that the sphere is similar to a torus. The advantage of this approach is that Kalman filtering can be applied and omnidirectional images projected on the sphere can be deconvolved.

Bias-aware Kalman filtering by mixing H 2 and H ∞ approaches

In the present article, an alternative methodology is presented to tackle the filtering problem in presence of unknown bias. The basic idea is to construct an H∞ estimator of the estimation error due to the unknown bias. The bias aware filter can be implemented by means of two filters, namely the standard H2 Kalman filter and the H∞ estimation error estimator. On the other hand, the bias aware filter can also be implemented as a single filter. Depending on users need, one or the other implementation can be done.

Robust ε-contaminated filter for discrete-time systems

The robust filtering problem for uncertain discrete-time systems is treated in this paper. An ϵ-contaminated framework is adopted to design the robust filter in presence of model uncertainties. The result is presented in term of Toeplitz matrix equations. The proposed approach does not require a formal modelling of uncertainties. Meanwhile, the ϵ-contaminated robust filter is equivalent to the minimum variance filter with a stochastic representation of the uncertainties. An example shows the effectiveness of the approach.

A simple method for estimating space-dependent parameters in soil science

Abstract The problem of parameter estimation for a distributed parameter system (DPS) is treated. The DPS under consideration appears in Soil Science where it models a measurement method of the soil water content (namely Time Domain Reflectometry (TDR)). The model consists in a set of partial differential equation (PDE) known as the telegraphist equation. The measurement method provides the current at only one position. This increases the complexity of the parameter estimation problem. The solution proposed takes advantage of a property of the measured signal. Compared to existing solutions, the proposed technique has a very reduced computational burden. Examples show its ability to estimate space-dependent parameters with a reasonable confidence interval and a reduced computational burden compared to existing solutions.

H∞ and H2 bias aware filters for continuous-time Lipschitz systems

Abstract In the present paper, the bias aware estimation problem is treated for continuous-time Lipschitz systems. The strategy adopted differs from the usual Two-Stage strategy by the fact that the bias is not estimated. This approach permits to obtain filters with same complexity of estimators with no bias which is not the case for Two-Stage estimators. The estimators are obtained by solving a single Riccati equation. An example shows the efficiency of the proposed approach.

H∞ smoother for Lipschitz nonlinear systems

Abstract In the present paper, the H ∞ fixed-interval smoothing problem is treated in the context of continuous-time Lipschitz nonlinear systems. The problem is solved by the combination of a forward and a backward H ∞ filters. In order to fulfill this objective, the original H ∞ smoothing problem is split into two subproblems of H ∞ filtering, namely, the H ∞ forward and backward filtering. The solution is obtained in terms of Riccati equations. The proposed approach shows its efficiency on a synthetic example.