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110. An off-line approach for output feedback robust model predictive control

Author

Andrey Polyakov, Tingyu Lin, Xubin Ping, Xiaojuan Wang, and Baocang Ding

Subjects
Output feedback, Model predictive control, Computer Networks and Communications, Control and Systems Engineering, Computer science, Control theory, Applied Mathematics, Bounded function, Signal Processing, Table (database), Robust control, Invariant (mathematics), Off line
Abstract

For constrained linear parameter varying systems subject to bounded disturbances and noises, this article investigates an off-line output feedback robust model predictive control approach. The sub-observer gains with robust positively invariant sets, and sub-controller gains with robust control invariant sets are simultaneously off-line optimized and stored in a look-up table. According to real-time estimation error bounds and estimated states, the time-varying sub-observer gains and sub-controller gains are on-line searched. The proposed off-line output feedback robust model predictive control approach with the guarantee of nested robust positively invariant sets and robust control invariant sets in theory reduces the on-line computational burden.

Published
2021
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111. Generalized homogeneous control with integral action

Author

Yu Zhou, Andrey Polyakov, Gang Zheng, Finite-time control and estimation for distributed systems (VALSE), Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), Deformable Robots Simulation Team (DEFROST ), This work is partially supported by Chinese Science Council (CSC) 202006030019, the National Natural Science Foundation of China under Grant 62073081 and Grant 62050410352., Finite-time control and estimation for distributed systems [VALSE], and Deformable Robots Simulation Team [DEFROST ]

Subjects
integral control, finite-time, strict Lyapunov, Homogeneous system, Control and Systems Engineering, Mechanical Engineering, General Chemical Engineering, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, Biomedical Engineering, Aerospace Engineering, Electrical and Electronic Engineering, Industrial and Manufacturing Engineering
Abstract

A generalized homogeneous control with integral action for a multiple-input plant operating under uncertainty conditions is designed. The stability analysis is essentially based on a special version of the non-smooth Lyapunov function theorem for differential equations with discontinuous right-hand sides. A Lyapunov function for analysis of the closed-loop system is presented. For negative homogeneity degree, this Lyapunov function becomes a strict Lyapunov function allowing an advanced analysis to be provided. In particular, the maximum control magnitude and the settling-time of the closed-loop system are estimated and a class of disturbances to be rejected by the control law is characterized. The control parameters are tuned by solving a system of Linear Matrix Inequalities (LMIs), whose feasibility is proved at least for small (close to zero) homogeneity degrees. The theoretical results are illustrated by numerical simulations.

Published
2023
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113. An exact robust hyperexponential differentiator

Author

Denis Efimov, Andrey Polyakov, Konstantin Zimenko, Jian Wang, Finite-time control and estimation for distributed systems (VALSE), Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), ITMO University [Russia], College of Computer Science [Hangzhou] (HDU), and Hangzhou Dianzi University (HDU)

Subjects
[SPI.AUTO]Engineering Sciences [physics]/Automatic
Abstract

International audience; A simple differentiator is proposed, which is modeled by a second order time-varying linear differential equation. It is shown that for any signal of interest, whose second derivative is an essentially bounded function of time, the differentiation error converges to zero with a hyperexponential rate (faster than any exponential). An implicit discretization scheme of the differentiator is given, which preserves all main properties of the continuous-time counterpart. In addition, the differentiation error is robustly stable with respect to the measurement noise with a linear gain. The efficiency of the suggested differentiator is illustrated through comparison in numeric experiments with popular alternatives.

Published
2022

114. On simple design of a robust finite-time observer

Author

Artem N. Nekhoroshikh, Denis Efimov, Andrey Polyakov, Wilfrid Perruquetti, Igor B. Furtat, ITMO University [Russia], Finite-time control and estimation for distributed systems (VALSE), Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), Centrale Lille, Institute of Mechanical Engineering Problems [St. Petersburg] (IPME), and Russian Academy of Sciences [Moscow] (RAS)

Subjects
[SPI.AUTO]Engineering Sciences [physics]/Automatic
Abstract

International audience; This paper presents a novel observer that estimates the state of a linear system in the observer canonical form in finite time. Due to the specially selected dynamical gain, the proposed observer is easy to tune and, at the same time, it is robust to external perturbations (e.g., state disturbances and measurement noises). The tuning algorithm consists in solving a simple system of linear matrix inequalities with only two adjustable parameters. Theoretical results and a comparison with homogeneous and prescribed-time observers are illustrated by numerical simulation.

Published
2022

131. Homogeneous Finite-time Tracking Control on Lie Algebra so(3)

Author

Yu Zhou, Andrey Polyakov, Gang Zheng, Finite-time control and estimation for distributed systems (VALSE), Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), and Deformable Robots Simulation Team (DEFROST )

Subjects
[INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering
Abstract

International audience; An attitude tracking problem for a full-actuated rigid body in 3-D is studied using a model of rotation dynamics on the Lie group SO(3). A generalized homogeneous control is adopted to achieve tracking of a smooth attitude trajectory in a finite-time. The attitude dynamics on the Lie algebra so(3) is utilized to design the homogeneous control, since SO(3) is not a vector space. A switch control is proposed for achieving global finite-time tracking by combining a global asymptotic control with local homogeneous control. The simulations illustrate the performance of the proposed control algorithm.

Published
2022

133. Sliding mode control applied to a square-back Ahmed body

Author

Franck Kerhervé, Jean-Pierre Richard, Wafik Abassi, Laurent Keirsbulck, Marc Lippert, Maxime Feingesicht, Baptiste Plumjeau, Camila Chovet, Andrey Polyakov, Jean-Marc Foucaut, Laboratoire d'Automatique, de Mécanique et d'Informatique industrielles et Humaines - UMR 8201 (LAMIH), Université de Valenciennes et du Hainaut-Cambrésis (UVHC)-Centre National de la Recherche Scientifique (CNRS), Chalmers University of Technology [Göteborg], Turbulence Incompressible et Contrôle (TIC ), Département Fluides, Thermique et Combustion (FTC), Institut Pprime (PPRIME), Université de Poitiers-ENSMA-Centre National de la Recherche Scientifique (CNRS)-Université de Poitiers-ENSMA-Centre National de la Recherche Scientifique (CNRS)-Institut Pprime (PPRIME), Université de Poitiers-ENSMA-Centre National de la Recherche Scientifique (CNRS)-Université de Poitiers-ENSMA-Centre National de la Recherche Scientifique (CNRS), Finite-time control and estimation for distributed systems (VALSE), Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Ecole Centrale de Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Ecole Centrale de Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mécanique des Fluides de Lille – Kampé de Fériet - UMR 9014 (LMFL), Ecole Centrale de Lille-ONERA-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Arts et Métiers Sciences et Technologies, HESAM Université (HESAM)-HESAM Université (HESAM), Université de Valenciennes et du Hainaut-Cambrésis (UVHC)-Centre National de la Recherche Scientifique (CNRS)-INSA Institut National des Sciences Appliquées Hauts-de-France (INSA Hauts-De-France), Université de Poitiers-ENSMA-Centre National de la Recherche Scientifique (CNRS), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), Centrale Lille, Laboratoire de Mécanique de Lille - FRE 3723 (LML), Université de Lille, Sciences et Technologies-Centrale Lille-Centre National de la Recherche Scientifique (CNRS), Laboratoire d'Automatique, de Mécanique et d'Informatique industrielles et Humaines - UMR 8201 [LAMIH], Turbulence Incompressible et Contrôle [TIC ], Finite-time control and estimation for distributed systems [VALSE], Laboratoire de Mécanique des Fluides de Lille – Kampé de Fériet - UMR 9014 [LMFL], Institut Pprime [PPRIME], Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 [CRIStAL], and Laboratoire de Mécanique de Lille - FRE 3723 [LML]

Subjects
Computer science, bilinear time-delay model, General Physics and Astronomy, 02 engineering and technology, 01 natural sciences, Sliding mode control, [SPI.AUTO]Engineering Sciences [physics]/Automatic, [SPI.MECA.MEFL]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Fluids mechanics [physics.class-ph], 010305 fluids & plasmas, External flow, [SPI]Engineering Sciences [physics], flow control, sliding mode control, drag reduction unsteadiness of separated flows, 0203 mechanical engineering, Control theory, 0103 physical sciences, Aerodynamic drag, Trailing edge, ComputingMilieux_MISCELLANEOUS, Mathematical Physics, Mechanics, Lift (force), Flow control (fluid), 020303 mechanical engineering & transports, Particle image velocimetry, Drag
Abstract

International audience; We consider the first closed-loop separation control experiment on an Ahmed body using a robust, model-based strategy called "sliding mode control" (SMC). The goal is to reduce and further maintain the aerodynamic drag of the square-back Ahmed body flow at Re h = 9 × 10 4 (based on the body height). This study also investigates the practical feasibility of this approach which shows a great promise for industrial applications. The flow is manipulated by a slotted jet placed on the top trailing edge, combined with a predefined angle direction, and sensed by a drag balance. Base pressure and lift measurements are also obtained in real-time. The interaction between the air jet actuator and the mean near-wake flow are depicted by means of Particle Image Velocimetry. In order to compare this closed-loop strategy we first present two open-loop ones. Continuous blowing is initially used to directly influence the recirculation area and hence achieve a reduction in the drag. Approximately a drag reduction of 8% is accomplished making this approach the "optimal case" control strategy. However, because steady blowing mechanisms lead to the highest energy consumption scheme, this strategy will only serve as the first open-loop control reference. The second open-loop strategy involves three periodic forcing frequencies, St A = 0.0765, 0.135 & 0.405. The influence of these frequencies on the near-wake, and its further drag modification, will be further examined. The proposed sliding mode control (closed-loop strategy) is applied to the same Ahmed body configuration and compared to the open-loop cases. It will be designed on the basis of a simplified input-output model which was recently defined for another flow control application. Last, a second experiment is conducted so to show the disturbance rejection of the controller, corroborating the robustness and efficiency of this control approach. Its limitations and difficulties on an experimental setup are also discussed. SMC is able to reduce and maintain the drag to a desire set-point regardless external flow perturbations. Our control strategy was recently used in another context (flow reattachement on a wing) with the same robustness. These successes make guess it is applicable to multiple experimental and industrial contexts.

Published
2020
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134. A Switching Controller for a Class of MIMO Bilinear Systems With Time Delay

Author

Emilia Fridman, Tonametl Sanchez, Andrey Polyakov, Laurentiu Hetel, Universidad Nacional Autónoma de México (UNAM), Finite-time control and estimation for distributed systems (VALSE), Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), Department of Electrical Engineering, Tel Aviv University [Tel Aviv], Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), Universidad Nacional Autónoma de México = National Autonomous University of Mexico (UNAM), Tel Aviv University (TAU), and ANR-18-CE40-0008,DIGITSLID,Différentiateurs et commandes homogènes par modes glissants multivalués en temps discret: l'approche implicite(2018)

Subjects
0209 industrial biotechnology, Computer science, switched control, MIMO, 02 engineering and technology, State (functional analysis), Stability (probability), Computer Science Applications, Nonlinear system, 020901 industrial engineering & automation, Control and Systems Engineering, Control theory, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, bilinear systems, Trajectory, Electrical and Electronic Engineering, Constant (mathematics), Finite set, time-delay systems
Abstract

In this paper, we propose a state-dependent switching controller for multiple-input multiple-output (MIMO) bilinear systems with constant delays in both the state and the input. The control input is assumed to be restricted to take only a finite number of values. The stability analysis of the closed loop is based on a Lyapunov–Krasovskii functional, and the design is reduced to solve a system of linear matrix inequalities. The controller can be designed by considering (state) delay-dependent or delay-independent conditions.

Published
2020
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135. Finite- and Fixed-Time Nonovershooting Stabilizers and Safety Filters by Homogeneous Feedback

Author

Andrey Polyakov, Miroslav Krstic, Finite-time control and estimation for distributed systems (VALSE), Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), University of California [San Diego] (UC San Diego), and University of California (UC)

Subjects
Control and Systems Engineering, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, FOS: Electrical engineering, electronic engineering, information engineering, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Systems and Control (eess.SY), Electrical and Electronic Engineering, Electrical Engineering and Systems Science - Systems and Control, Computer Science Applications
Abstract

International audience; Non-overshooting stabilization is a form of safe control where the setpoint chosen by the user is at the boundary of the safe set. Exponential non-overshooting stabilization, including suitable extensions to systems with deterministic and stochastic disturbances, has been solved by the second author and his coauthors. In this paper we develop homogeneous feedback laws for fixed-time nonovershooting stabilization for nonlinear systems that are input-output linearizable with a full relative degree, i.e., for systems that are diffeomorphically equivalent to the chain of integrators. These homogeneous feedback laws can also assume the secondary role of 'fixed-time safety filters' (FxTSf filters) which keep the system within the closed safe set for all time but, in the case where the user's nominal control commands approach to the unsafe set, allow the system to reach the boundary of the safe set no later than a desired time that is independent of nominal control and independent of the value of the state at the time the nominal control begins to be overridden.

Published
2022
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136. Quadrotor stabilization under time and space constraints using implicit PID controller

Author

Siyuan Wang, Andrey Polyakov, Gang Zheng, Finite-time control and estimation for distributed systems (VALSE), Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), Institut National des Sciences Appliquées (INSA), and Deformable Robots Simulation Team (DEFROST )

Subjects
Computer Science::Robotics, robust, Computer Networks and Communications, Control and Systems Engineering, Computer Science::Systems and Control, constraint, Applied Mathematics, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, Signal Processing, MathematicsofComputing_NUMERICALANALYSIS, quadrotor, Nonlinear
Abstract

International audience; In this paper, the quadrotor stabilization under time and state constraints is studied. The objective is to design a nonlinear controller under time and state constraint for quadrotor. The nonlinear quadrotor model is built by the Euler-Lagrange approach while ignoring the Coriolis terms, hub moment and force. Based on quadrotor's dynamic model, a nonlinear feedback controller is designed for the quadrotor stabilization under time and state constraints. This feedback is an implicit PID controller where the feedback gains are obtained from LMIs (Linear matrix inequalities). LMI system characterizing the system stability and convergence properties is built based on convex embedding approach and implicit Lyapunov function method. To demonstrate the application prospects of implicit PID controller, robustness analysis is provided to show the property of implicit PID controller under external disturbance. The key novelty of this paper is that the implicit PID controller is proven feasible for applying to the quadrotor under time and state constraints, which is also the main outcome.

Published
2022

137. Finite-time stabilization under state constraints

Author

Artem N. Nekhoroshikh, Denis Efimov, Andrey Polyakov, Wilfrid Perruquetti, Igor B. Furtat, National Research University of Information Technologies, Mechanics and Optics [St. Petersburg] (ITMO), Finite-time control and estimation for distributed systems (VALSE), Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), Centrale Lille, and Centrale Lille Institut (CLIL)

Subjects
[SPI.AUTO]Engineering Sciences [physics]/Automatic
Abstract

International audience; The problem of finite-time stabilization of linear systems under state and control input constraints in the presence of external disturbances is addressed. The proposed control is designed such that the closed-loop system is 1) superstable, when system trajectories risk to violate the state constraints, and 2) homogeneous with a negative degree, otherwise. While the former property ensures the fulfillment of the state and control constraints, the latter implies finite-time stability. The robustness of the control scheme with respect to disturbances is studied. Theoretical results are supported by numerical simulations.

Published
2021
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138. On energetically optimal finite-time stabilization

Author

Andrey Polyakov, Denis Efimov, Xubin Ping, Finite-time control and estimation for distributed systems (VALSE), Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), and Xidian University

Subjects
[INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering
Abstract

International audience; The problem of finite-time stabilization of a linear plant with an optimization of both a settling time and an weighted/averaged control energy is studied using the concept of generalized homogeneity. It is shown that the optimal finite-time stabilizing control in this case can be designed solving a simple linear algebraic equation. Some issues of a practical applicability and a robustness of the obtained control law are studied.

Published
2021

139. State observation in microbial consortia: A case study on a synthetic producer‐cleaner consortium

Author

Alex dos Reis de Souza, Denis Efimov, Andrey Polyakov, Jean‐Luc Gouzé, Eugenio Cinquemani, Finite-time control and estimation for distributed systems (VALSE), Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Université de Lille-Centrale Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centrale Lille-Centre National de la Recherche Scientifique (CNRS), Biological control of artificial ecosystems (BIOCORE), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire d'océanographie de Villefranche (LOV), Institut national des sciences de l'Univers (INSU - CNRS)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Institut de la Mer de Villefranche (IMEV), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Institut national des sciences de l'Univers (INSU - CNRS)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Institut de la Mer de Villefranche (IMEV), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Université Côte d'Azur (UCA), Analyse, ingénierie et contrôle des micro-organismes (MICROCOSME), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université Grenoble Alpes (UGA), Institut National de Recherche en Informatique et en Automatique (Inria), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), Laboratoire d'océanographie de Villefranche (LOV), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Modeling, simulation, measurement, and control of bacterial regulatory networks (IBIS), Laboratoire Adaptation et pathogénie des micro-organismes [Grenoble] (LAPM), Centre National de la Recherche Scientifique (CNRS)-Université Joseph Fourier - Grenoble 1 (UJF)-Centre National de la Recherche Scientifique (CNRS)-Université Joseph Fourier - Grenoble 1 (UJF)-Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut Jean Roget, and ANR-20-CE45-0014,Ctrl-AB,Optimisation et controle de la productivité d'un écosystème algues-bactéries(2020)

Subjects
0303 health sciences, 0209 industrial biotechnology, observability, Mechanical Engineering, General Chemical Engineering, Biomedical Engineering, Aerospace Engineering, bioprocess, 02 engineering and technology, Industrial and Manufacturing Engineering, 03 medical and health sciences, [SPI]Engineering Sciences [physics], 020901 industrial engineering & automation, Control and Systems Engineering, microbial consortia, state estimation, Electrical and Electronic Engineering, ComputingMilieux_MISCELLANEOUS, 030304 developmental biology
Abstract

International audience; In this article, the problem of state estimation of a microbial consortium is discussed. This microbial consortium is composed of two strains, called producer and cleaner, in continuous culture. The producer strain grows by consuming glucose, while the cleaner grows by consuming the acetate excreted by the producer and toxifies the environment. Considering two available measurements, the total biomass and a fluorescent reporter, an observability analysis is cast and state estimators are proposed for each state component of this system. Although the system is shown to be detectable using solely the total biomass as measurement, the advantage of measuring the fluorescent reporter on the observer design is highlighted. A numerical experiment illustrates the methodology.

Published
2021
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140. Generalized Homogenization of Linear Observers: Theory and Experiment

Author

Gang Zheng, Siyuan Wang, Andrey Polyakov, Finite-time control and estimation for distributed systems (VALSE), Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), Deformable Robots Simulation Team (DEFROST ), and ANR-18-CE40-0008,DIGITSLID,Différentiateurs et commandes homogènes par modes glissants multivalués en temps discret: l'approche implicite(2018)

Subjects
0209 industrial biotechnology, Mechanical Engineering, General Chemical Engineering, 010102 general mathematics, Biomedical Engineering, Aerospace Engineering, 02 engineering and technology, 01 natural sciences, Industrial and Manufacturing Engineering, 020901 industrial engineering & automation, Control and Systems Engineering, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, 0101 mathematics, Electrical and Electronic Engineering
Abstract

International audience; A procedure of upgrading a linear observer to homogeneous (nonlinear) one is proposed and validated by experiment. The nonlinear observer design is based on the the concept of a linear geometric homogeneity. The simple procedure developed to apply the homogeneous nonlinear observer is based on the parameters provided by the linear observer, which is potential for many applications to improve their performance. A saturation function is introduced to guaranteed the improvement of estimation quality. Finally the theoretical results are confirmed by the QDrone platform of Quanser T M .

Published
2021
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141. Robust Stabilization of Control Affine Systems with Homogeneous Functions

Author

Denis Efimov, Andrey Polyakov, and Konstantin Zimenko

Subjects
0209 industrial biotechnology, Class (set theory), Homogeneity (statistics), 020208 electrical & electronic engineering, Homogeneous function, 02 engineering and technology, Linear matrix, Nonlinear control, symbols.namesake, 020901 industrial engineering & automation, Control and Systems Engineering, Control system, 0202 electrical engineering, electronic engineering, information engineering, symbols, Applied mathematics, Affine transformation, Control (linguistics), Mathematics
Abstract

The stabilization problem of the affine control system ẋ = f0(x)+∑i=1muifi(x) with homogeneous functions f0, fi is studied. This class of systems is of interest due to the robust properties of homogeneity and the fact that many affine systems can be approximated by or transformed to the class under consideration. An advantage of the introduced design method is that the tuning rules are presented in the form of linear matrix inequalities. Performance of the approach is illustrated by a numerical example.

Published
2020
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142. On finite-time stability of sub-homogeneous differential inclusions

Author

Andrey Polyakov, Wilfrid Perruquetti, Youness Braidiz, and Denis Efimov

Subjects
0209 industrial biotechnology, Observer (quantum physics), 020208 electrical & electronic engineering, Mathematical analysis, Ode, 02 engineering and technology, Extension (predicate logic), Stability (probability), Section (fiber bundle), Nonlinear system, 020901 industrial engineering & automation, Differential inclusion, Control and Systems Engineering, Homogeneity (physics), 0202 electrical engineering, electronic engineering, information engineering, Mathematics
Abstract

Sub-homogeneity property is introduced and is related to a differential inclusion (DI). It is shown that a nonlinear ordinary differential equation (ODE), which may not admit a homogeneous approximation, can be transformed into a sub-homogeneous DI (which is a homogeneous extension of the original ODE). Using this homogeneous extension, one can directly recover finite-time stability property for some particular classes of nonlinear systems. In the last section, such a sub homogeneity property is used to design a nonlinear finite-time observer.

Published
2020
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143. On fixed-time stability of a class of nonlinear time-varying systems

Author

Youness Braidiz, Andrey Polyakov, Denis Efimov, and Wilfrid Perruquetti

Subjects
Lyapunov function, 0209 industrial biotechnology, Class (set theory), Homogeneity (statistics), 020208 electrical & electronic engineering, 02 engineering and technology, Stability (probability), Section (fiber bundle), symbols.namesake, Nonlinear system, Stability conditions, 020901 industrial engineering & automation, Control and Systems Engineering, Fixed time, 0202 electrical engineering, electronic engineering, information engineering, symbols, Applied mathematics, Mathematics
Abstract

Fixed-time stability of a class of nonlinear time-varying systems is investigated using the introduced notions of sub- and sup-homogeneity. These concepts allow the systems (even if they do not admit homogeneous approximations) to be analyzed using the homogeneity of their extensions. Then, finite-time and fixed-time stability properties can be recovered. The proposed stability conditions are not based on Lyapunov arguments. In the last section, an example illustrates the obtained results.

Published
2020
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145. Adaptive Discontinuous Control for Homogeneous Systems Approximated by Neural Networks

Author

Andrey Polyakov, Mariana Ballesteros, Alexander S. Poznyak, Isaac Chairez, Denis Efimov, Centro de Investigacion y de Estudios Avanzados del Instituto Politécnico Nacional (CINVESTAV), Finite-time control and estimation for distributed systems (VALSE), Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), Instituto Politechnico National (IPN), and Instituto Politecnico Nacional [Mexico] (IPN)

Subjects
Lyapunov stability, 0209 industrial biotechnology, Adaptive control, Neural Networks, Computer simulation, Artificial neural network, Computer science, Homogeneity (statistics), Computer Science::Neural and Evolutionary Computation, 020208 electrical & electronic engineering, System Identification, System identification, Homogeneous function, 02 engineering and technology, Discontinuous Control, Adaptive Control, Nonlinear system, symbols.namesake, 020901 industrial engineering & automation, Homogeneous systems, Control and Systems Engineering, Control theory, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, 0202 electrical engineering, electronic engineering, information engineering, symbols
Abstract

International audience; This study is devoted to the design of an adaptive discontinuous control based on differential neural networks (DNNs) for a class of uncertain homogeneous systems. The control is based on the universal approximation properties of artificial neural networks (ANNs) applied on a certain class of homogeneous nonlinear functions. The adaptation laws for the DNNs parameters are obtained with the application of the Lyapunov stability theory and the homogeneity properties of the approximated nonlinear system. The stability analysis of the closed loop system with the proposed controller is presented. The estimation error in the approximation of the uncertain homogeneous functions is considered in the stability analysis. The performance of the controller is illustrated by means of a numerical simulation of a homogeneous model.

Published
2020
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146. Homogeneous Observer Design for Linear MIMO Systems

Author

Denis Efimov, Artem Kremlev, Andrey Polyakov, and Konstantin Zimenko

Subjects
0209 industrial biotechnology, Observer (quantum physics), Degree (graph theory), Homogeneity (statistics), 020208 electrical & electronic engineering, 02 engineering and technology, State (functional analysis), Stability (probability), 020901 industrial engineering & automation, Compact space, Control and Systems Engineering, Control theory, Robustness (computer science), 0202 electrical engineering, electronic engineering, information engineering, Canonical form, Mathematics
Abstract

The paper is devoted to the problem of state observation (particularly, in finite time) of linear MIMO systems. The presented nonlinear observer does not require system transformation to a canonical form and guarantees finite-time (asymptotic with a fixed-time attraction of any compact set containing the origin) stability of observation error equation if homogeneity degree is negative (positive). The proposed observer is robust in input-to-state sense with respect to disturbances and measurement noises. Performance of the observer is illustrated by a numerical example.

Published
2020
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147. A Consistent Discretisation method for Stable Homogeneous Systems based on Lyapunov Function

Author

Andrey Polyakov, Denis Efimov, and Tonametl Sanchez

Subjects
Lyapunov function, Surface (mathematics), 0209 industrial biotechnology, Discretization, 020208 electrical & electronic engineering, 02 engineering and technology, symbols.namesake, Nonlinear system, 020901 industrial engineering & automation, Rate of convergence, Control and Systems Engineering, Homogeneous, Stability theory, 0202 electrical engineering, electronic engineering, information engineering, symbols, Applied mathematics, Mathematics
Abstract

In this paper we propose a discretisation scheme for continuous and asymptotically stable homogeneous systems. This method is based on the dynamics of the system projected on a level surface of a homogeneous Lyapunov function. The discretisation method is explicit and preserves the convergence rate of the continuous-time system.

Published
2020
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148. Observer-Based Robust Control of a Continuous Bioreactor with Heterogeneous Community

Author

Jean-Luc Gouzé, Alex dos Reis de Souza, Denis Efimov, Andrey Polyakov, Finite-time control and estimation for distributed systems (VALSE), Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), Biological control of artificial ecosystems (BIOCORE), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire d'océanographie de Villefranche (LOV), Institut national des sciences de l'Univers (INSU - CNRS)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Institut de la Mer de Villefranche (IMEV), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Institut national des sciences de l'Univers (INSU - CNRS)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Institut de la Mer de Villefranche (IMEV), and Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)

Subjects
0209 industrial biotechnology, Observer (quantum physics), Computer science, 020208 electrical & electronic engineering, Control (management), Robust control, Bioreactor, 02 engineering and technology, Limiting, [SPI.AUTO]Engineering Sciences [physics]/Automatic, 020901 industrial engineering & automation, Biochemical process, Control and Systems Engineering, Control theory, 0202 electrical engineering, electronic engineering, information engineering, Observer based, Observer-based control
Abstract

International audience; This work addresses the problem of robust control of the continuous bioreactor-namely the chemostat-using an observer-based approach. We design a control law aiming to regulate the growth of a certain species and to stabilize the output-a growth-associated product of interest-in a prescribed level. In addition, to avoid the single-species dogma (which takes only one species into account for control design), we add to the microbial community unknown species competing for the limiting substrate. Finally, this control architecture is able to maintain the productivity, despite this competing heterogeneity (or biodiversity) of the community.

Published
2020
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149. METHOD OF FORMING NOMENCLATURE AND NUMBER OF SPARE PARTS FOR MAINTENANCE AND REPAIR OF SPECIAL MACHINES OF MILITARY PURPOSE

Author

Andrey Polyakov

Subjects
020303 mechanical engineering & transports, 0203 mechanical engineering, Computer science, Spare part, 021105 building & construction, 0211 other engineering and technologies, 02 engineering and technology, Hardware_REGISTER-TRANSFER-LEVELIMPLEMENTATION, Nomenclature, Manufacturing engineering
Abstract

The system for the maintenance and repair of special military vehicles (SMV) is a complex system. The study of such systems is based primarily on system analysis and synthesis. The complexity of the study of the system of maintenance and repair of the SMV is due to the weak formalization of the processes and data on the impact of the operating time and duration of the period of time the SMV is in operation on the likelihood of their failure-free operation. To improve the efficiency of the functioning of the existing system of maintenance and repair of the SMV, a method for the formation of the nomenclature and the number of spare parts has been proposed.

Published
2019
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