Special Issue "Algorithms for Reliable Estimation, Identification and Control II"

A special issue of Algorithms (ISSN 1999-4893).

Deadline for manuscript submissions: 15 March 2022.

Special Issue Editors

Dr. Andreas Rauh
E-Mail Website
Guest Editor
Prof. Luc Jaulin
E-Mail Website
Guest Editor
Lab-STICC, ENSTA Bretagne, 29806 Brest, France
Interests: Interval analysis; robotics
Dr. Julien Alexandre dit Sandretto
E-Mail Website
Guest Editor
ENSTA Paris, 91120 Palaiseau, France
Interests: interval analysis; state estimation; stochastic filtering techniques; robust control; optimization

Special Issue Information

Dear Colleagues,

The optimization of feedforward and feedback controllers with respect to predefined performance criteria is mainly studied. In particular, the enhancement and verification of their robustness concerning external disturbances and uncertain parameters are widespread aspects of current research activities. The same holds for the reliable estimation of non-measurable system states and the identification of parameters based on uncertain measurements. Possible applications of related optimization algorithms can be found not only in the frame of a control and estimator synthesis, but also in the field of reliable modeling and model-based analysis of measured data.

This Special Issue is a platform for the publication of novel algorithms in the frame of reliable and optimal estimation and control. Moreover, application-oriented aspects highlighting the practical applicability of theoretical approaches are highly welcome.

Possible topics of interest include the following:

  • Optimal and robust control of finite-dimensional systems;
  • Optimization and robustness analysis for partial differential equations;
  • Representation of epistemic and aleatory uncertainty by means of the following:
    • Interval analysis; and
    • Stochastic modeling procedures;
  • Structural optimization of controllers and state observers;
  • Parameter optimization and identification;
  • Stability analysis

Dr. Andreas Rauh
Prof. Luc Jaulin
Dr. Julien Alexandre dit Sandretto
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Algorithms is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Published Papers (6 papers)

Order results
Result details
Select all
Export citation of selected articles as:

Research

Article
An Algebraic Approach to Identifiability
Algorithms 2021, 14(9), 255; https://0-doi-org.brum.beds.ac.uk/10.3390/a14090255 - 27 Aug 2021
Viewed by 503
Abstract
This paper addresses the problem of identifiability of nonlinear polynomial state-space systems. Such systems have already been studied via the input-output equations, a description that, in general, requires differential algebra. The authors use a different algebraic approach, which is based on distinguishability and [...] Read more.
This paper addresses the problem of identifiability of nonlinear polynomial state-space systems. Such systems have already been studied via the input-output equations, a description that, in general, requires differential algebra. The authors use a different algebraic approach, which is based on distinguishability and observability. Employing techniques from algebraic geometry such as polynomial ideals and Gröbner bases, local as well as global results are derived. The methods are illustrated on some example systems. Full article
(This article belongs to the Special Issue Algorithms for Reliable Estimation, Identification and Control II)
Article
Experimental Validation of a Guaranteed Nonlinear Model Predictive Control
Algorithms 2021, 14(8), 248; https://0-doi-org.brum.beds.ac.uk/10.3390/a14080248 - 20 Aug 2021
Viewed by 567
Abstract
This paper combines the interval analysis tools with the nonlinear model predictive control (NMPC). The NMPC strategy is formulated based on an uncertain dynamic model expressed as nonlinear ordinary differential equations (ODEs). All the dynamic parameters are identified in a guaranteed way considering [...] Read more.
This paper combines the interval analysis tools with the nonlinear model predictive control (NMPC). The NMPC strategy is formulated based on an uncertain dynamic model expressed as nonlinear ordinary differential equations (ODEs). All the dynamic parameters are identified in a guaranteed way considering the various uncertainties on the embedded sensors and the system’s design. The NMPC problem is solved at each time step using validated simulation and interval analysis methods to compute the optimal and safe control inputs over a finite prediction horizon. This approach considers several constraints which are crucial for the system’s safety and stability, namely the state and the control limits. The proposed controller consists of two steps: filtering and branching procedures enabling to find the input intervals that fulfill the state constraints and ensure the convergence to the reference set. Then, the optimization procedure allows for computing the optimal and punctual control input that must be sent to the system’s actuators for the pendulum stabilization. The validated NMPC capabilities are illustrated through several simulations under the DynIbex library and experiments using an inverted pendulum. Full article
(This article belongs to the Special Issue Algorithms for Reliable Estimation, Identification and Control II)
Show Figures

Figure 1

Article
Iterative Solution of Linear Matrix Inequalities for the Combined Control and Observer Design of Systems with Polytopic Parameter Uncertainty and Stochastic Noise
Algorithms 2021, 14(7), 205; https://0-doi-org.brum.beds.ac.uk/10.3390/a14070205 - 07 Jul 2021
Viewed by 788
Abstract
Most research activities that utilize linear matrix inequality (LMI) techniques are based on the assumption that the separation principle of control and observer synthesis holds. This principle states that the combination of separately designed linear state feedback controllers and linear state observers, which [...] Read more.
Most research activities that utilize linear matrix inequality (LMI) techniques are based on the assumption that the separation principle of control and observer synthesis holds. This principle states that the combination of separately designed linear state feedback controllers and linear state observers, which are independently proven to be stable, results in overall stable system dynamics. However, even for linear systems, this property does not necessarily hold if polytopic parameter uncertainty and stochastic noise influence the system’s state and output equations. In this case, the control and observer design needs to be performed simultaneously to guarantee stabilization. However, the loss of the validity of the separation principle leads to nonlinear matrix inequalities instead of LMIs. For those nonlinear inequalities, the current paper proposes an iterative LMI solution procedure. If this algorithm produces a feasible solution, the resulting controller and observer gains ensure robust stability of the closed-loop control system for all possible parameter values. In addition, the proposed optimization criterion leads to a minimization of the sensitivity to stochastic noise so that the actual state trajectories converge as closely as possible to the desired operating point. The efficiency of the proposed solution approach is demonstrated by stabilizing the Zeeman catastrophe machine along the unstable branch of its bifurcation diagram. Additionally, an observer-based tracking control task is embedded into an iterative learning-type control framework. Full article
(This article belongs to the Special Issue Algorithms for Reliable Estimation, Identification and Control II)
Show Figures

Figure 1

Article
Interval Extended Kalman Filter—Application to Underwater Localization and Control
Algorithms 2021, 14(5), 142; https://0-doi-org.brum.beds.ac.uk/10.3390/a14050142 - 29 Apr 2021
Cited by 2 | Viewed by 685
Abstract
The extended Kalman filter has been shown to be a precise method for nonlinear state estimation and is the facto standard in navigation systems. However, if the initial estimated state is far from the true one, the filter may diverge, mainly due to [...] Read more.
The extended Kalman filter has been shown to be a precise method for nonlinear state estimation and is the facto standard in navigation systems. However, if the initial estimated state is far from the true one, the filter may diverge, mainly due to an inconsistent linearization. Moreover, interval filters guarantee a robust and reliable, yet unprecise and discontinuous localization. This paper proposes to choose a point estimated by an interval method, as a linearization point of the extended Kalman filter. We will show that this combination allows us to get a higher level of integrity of the extended Kalman filter. Full article
(This article belongs to the Special Issue Algorithms for Reliable Estimation, Identification and Control II)
Show Figures

Figure 1

Article
Union and Intersection Operators for Thick Ellipsoid State Enclosures: Application to Bounded-Error Discrete-Time State Observer Design
Algorithms 2021, 14(3), 88; https://0-doi-org.brum.beds.ac.uk/10.3390/a14030088 - 14 Mar 2021
Cited by 1 | Viewed by 887
Abstract
Thick ellipsoids were recently introduced by the authors to represent uncertainty in state variables of dynamic systems, not only in terms of guaranteed outer bounds but also in terms of an inner enclosure that belongs to the true solution set with certainty. Because [...] Read more.
Thick ellipsoids were recently introduced by the authors to represent uncertainty in state variables of dynamic systems, not only in terms of guaranteed outer bounds but also in terms of an inner enclosure that belongs to the true solution set with certainty. Because previous work has focused on the definition and computationally efficient implementation of arithmetic operations and extensions of nonlinear standard functions, where all arguments are replaced by thick ellipsoids, this paper introduces novel operators for specifically evaluating quasi-linear system models with bounded parameters as well as for the union and intersection of thick ellipsoids. These techniques are combined in such a way that a discrete-time state observer can be designed in a predictor-corrector framework. Estimation results are presented for a combined observer-based estimation of state variables as well as disturbance forces and torques in the sense of an unknown input estimator for a hovercraft. Full article
(This article belongs to the Special Issue Algorithms for Reliable Estimation, Identification and Control II)
Show Figures

Figure 1

Article
Transformation of Uncertain Linear Systems with Real Eigenvalues into Cooperative Form: The Case of Constant and Time-Varying Bounded Parameters
Algorithms 2021, 14(3), 85; https://0-doi-org.brum.beds.ac.uk/10.3390/a14030085 - 08 Mar 2021
Cited by 1 | Viewed by 773
Abstract
Continuous-time linear systems with uncertain parameters are widely used for modeling real-life processes. The uncertain parameters, contained in the system and input matrices, can be constant or time-varying. In the latter case, they may represent state dependencies of these matrices. Assuming bounded uncertainties, [...] Read more.
Continuous-time linear systems with uncertain parameters are widely used for modeling real-life processes. The uncertain parameters, contained in the system and input matrices, can be constant or time-varying. In the latter case, they may represent state dependencies of these matrices. Assuming bounded uncertainties, interval methods become applicable for a verified reachability analysis, for feasibility analysis of feedback controllers, or for the design of robust set-valued state estimators. The evaluation of these system models becomes computationally efficient after a transformation into a cooperative state-space representation, where the dynamics satisfy certain monotonicity properties with respect to the initial conditions. To obtain such representations, similarity transformations are required which are not trivial to find for sufficiently wide a-priori bounds of the uncertain parameters. This paper deals with the derivation and algorithmic comparison of two different transformation techniques for which their applicability to processes with constant and time-varying parameters has to be distinguished. An interval-based reachability analysis of the states of a simple electric step-down converter concludes this paper. Full article
(This article belongs to the Special Issue Algorithms for Reliable Estimation, Identification and Control II)
Show Figures

Figure 1

Back to TopTop