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Miroslav Krstic - One of the best experts on this subject based on the ideXlab platform.
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Extremum Seeking Feedback With Wave Partial Differential Equation Compensation
Journal of Dynamic Systems Measurement and Control, 2020Co-Authors: Tiago Roux Oliveira, Miroslav KrsticAbstract:Abstract This paper addresses the compensation of wave actuator dynamics in scalar Extremum seeking (ES) for static maps. Infinite-dimensional systems described by partial differential equations (PDEs) of wave type have not been considered so far in the literature of ES. A distributed-parameter-based control law using back-stepping approach and Neumann actuation is initially proposed. Local exponential stability as well as practical convergence to an arbitrarily small neighborhood of the unknown Extremum Point is guaranteed by employing Lyapunov–Krasovskii functionals and averaging theory in infinite dimensions. Thereafter, the extension for wave equations with Dirichlet actuation, antistable wave PDEs as well as the design for the delay-wave PDE cascade are also discussed. Numerical simulations illustrate the theoretical results.
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Stochastic Extremum Seeking for Dynamic Maps With Delays
IEEE Control Systems Letters, 2019Co-Authors: Damir Rusiti, Tiago Roux Oliveira, Giulio Evangelisti, Matthias Gerdts, Miroslav KrsticAbstract:We address a Newton-based Extremum seeking algorithm for maximizing higher derivatives of unknown maps in the presence of known time delays. Different from all previous works on this topic, we employ stochastic instead of periodic perturbations, allow arbitrarily long output delays and consider a dynamic map to be optimized. We incorporate a novel predictor feedback for delay compensation and show local exponential stability along with convergence to a small neighborhood of the unknown Extremum Point. For the purpose of the proof, we apply a backstepping transformation and averaging theory in infinite dimensions for stochastic systems. Moreover, simulations highlight the effectiveness of the proposed predictor-feedback scheme.
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ACC - Gradient Extremum Seeking with Time-Varying Delays
2018 Annual American Control Conference (ACC), 2018Co-Authors: Tiago Roux Oliveira, Damir Rusiti, Mamadou Diagne, Miroslav KrsticAbstract:This paper presents a gradient Extremum seeking algorithm to cope with locally quadratic static maps under time-varying delays. Dealing with non constant delays has a strong impact in the predictor design in terms of the associated transport partial differential equation (PDE) with variable convection speeds as well as the conditions imposed on the delay regarding its arbitrary duration but bounded variation. A new predictor design with a perturbation-based estimate of the unknown Hessian of the map must be introduced to accommodate this variable nature of the delays, which can arise both in actuation and sensing paths. Local exponential stability and convergence to a small neighborhood of the unknown Extremum Point are rigorously detailed. This result is achieved by using backstepping transformation and averaging in infinite dimensions. Numerical simulations are given to illustrate the effectiveness of the proposed predictor-based Extremum seeking control for time-delay compensation.
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Predictor Feedback for Extremum Seeking with Delays
Advances in Delays and Dynamics, 2017Co-Authors: Tiago Roux Oliveira, Miroslav KrsticAbstract:In this paper, we derive the design and analysis for scalar gradient Extremum seeking (ES) subject to arbitrarily long input–output delays, by employing a predictor with a perturbation-based estimate of the Hessian. Exponential stability and convergence to a small neighborhood of the unknown Extremum Point can be guaranteed. This result is carried out using backstepping transformation and averaging in infinite dimensions. Generalization of the results for Newton-based ES is also indicated. Some simulation examples are presented to illustrate the performance of the delay-compensated ES control scheme.
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Gradient Extremum Seeking with Delays
IFAC-PapersOnLine, 2015Co-Authors: Tiago Roux Oliveira, Miroslav KrsticAbstract:Abstract In this paper, we derive the design and analysis for scalar gradient Extremum seeking control (ESC) subject to arbitrarily long input-output delays, by employing a predictor with a perturbation-based estimate of the Hessian. Exponential stability and convergence to a small neighborhood of the unknown Extremum Point can be guaranteed. This result is carried out using backstepping transformation and averaging in infinite dimensions. Some simulation examples are presented to illustrate the performance of the delay-compensated ESC scheme.
Tiago Roux Oliveira - One of the best experts on this subject based on the ideXlab platform.
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Extremum Seeking Feedback With Wave Partial Differential Equation Compensation
Journal of Dynamic Systems Measurement and Control, 2020Co-Authors: Tiago Roux Oliveira, Miroslav KrsticAbstract:Abstract This paper addresses the compensation of wave actuator dynamics in scalar Extremum seeking (ES) for static maps. Infinite-dimensional systems described by partial differential equations (PDEs) of wave type have not been considered so far in the literature of ES. A distributed-parameter-based control law using back-stepping approach and Neumann actuation is initially proposed. Local exponential stability as well as practical convergence to an arbitrarily small neighborhood of the unknown Extremum Point is guaranteed by employing Lyapunov–Krasovskii functionals and averaging theory in infinite dimensions. Thereafter, the extension for wave equations with Dirichlet actuation, antistable wave PDEs as well as the design for the delay-wave PDE cascade are also discussed. Numerical simulations illustrate the theoretical results.
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MED - Extremum Seeking for Static Maps with Unknown Hessian Signs
2019 27th Mediterranean Conference on Control and Automation (MED), 2019Co-Authors: Aline Lopes Dibo, Tiago Roux OliveiraAbstract:Extremum seeking control aims at determining and keeping the output of a nonlinear map on its unknown Extremum Point. In the literature, despite of considering an unknown objective function in the real-time optimization problem, it is mandatory to know whether the Extremum Point is a maximum or a minimum, which is characterized by means of the Hessian signs in case of static scalar maps. This paper proposes the process of Extremum seeking occurs independently of the Hessian sign information. The key idea is to combine the classical Extremum seeking approach with a switching monitoring function. The switching algorithm will drive the closed-loop system to the unknown Extremum, neglecting if it is a maximum or a minimum. In addition, simulation results show the robustness properties of the proposed recipe under changes of the Hessian signs occurring “on-the-fly” fashion as well as its adaptability to solve distinct online minimizing and maximizing problems in sequence.
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Stochastic Extremum Seeking for Dynamic Maps With Delays
IEEE Control Systems Letters, 2019Co-Authors: Damir Rusiti, Tiago Roux Oliveira, Giulio Evangelisti, Matthias Gerdts, Miroslav KrsticAbstract:We address a Newton-based Extremum seeking algorithm for maximizing higher derivatives of unknown maps in the presence of known time delays. Different from all previous works on this topic, we employ stochastic instead of periodic perturbations, allow arbitrarily long output delays and consider a dynamic map to be optimized. We incorporate a novel predictor feedback for delay compensation and show local exponential stability along with convergence to a small neighborhood of the unknown Extremum Point. For the purpose of the proof, we apply a backstepping transformation and averaging theory in infinite dimensions for stochastic systems. Moreover, simulations highlight the effectiveness of the proposed predictor-feedback scheme.
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ACC - Gradient Extremum Seeking with Time-Varying Delays
2018 Annual American Control Conference (ACC), 2018Co-Authors: Tiago Roux Oliveira, Damir Rusiti, Mamadou Diagne, Miroslav KrsticAbstract:This paper presents a gradient Extremum seeking algorithm to cope with locally quadratic static maps under time-varying delays. Dealing with non constant delays has a strong impact in the predictor design in terms of the associated transport partial differential equation (PDE) with variable convection speeds as well as the conditions imposed on the delay regarding its arbitrary duration but bounded variation. A new predictor design with a perturbation-based estimate of the unknown Hessian of the map must be introduced to accommodate this variable nature of the delays, which can arise both in actuation and sensing paths. Local exponential stability and convergence to a small neighborhood of the unknown Extremum Point are rigorously detailed. This result is achieved by using backstepping transformation and averaging in infinite dimensions. Numerical simulations are given to illustrate the effectiveness of the proposed predictor-based Extremum seeking control for time-delay compensation.
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Predictor Feedback for Extremum Seeking with Delays
Advances in Delays and Dynamics, 2017Co-Authors: Tiago Roux Oliveira, Miroslav KrsticAbstract:In this paper, we derive the design and analysis for scalar gradient Extremum seeking (ES) subject to arbitrarily long input–output delays, by employing a predictor with a perturbation-based estimate of the Hessian. Exponential stability and convergence to a small neighborhood of the unknown Extremum Point can be guaranteed. This result is carried out using backstepping transformation and averaging in infinite dimensions. Generalization of the results for Newton-based ES is also indicated. Some simulation examples are presented to illustrate the performance of the delay-compensated ES control scheme.
Damir Rusiti - One of the best experts on this subject based on the ideXlab platform.
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Stochastic Extremum Seeking for Dynamic Maps With Delays
IEEE Control Systems Letters, 2019Co-Authors: Damir Rusiti, Tiago Roux Oliveira, Giulio Evangelisti, Matthias Gerdts, Miroslav KrsticAbstract:We address a Newton-based Extremum seeking algorithm for maximizing higher derivatives of unknown maps in the presence of known time delays. Different from all previous works on this topic, we employ stochastic instead of periodic perturbations, allow arbitrarily long output delays and consider a dynamic map to be optimized. We incorporate a novel predictor feedback for delay compensation and show local exponential stability along with convergence to a small neighborhood of the unknown Extremum Point. For the purpose of the proof, we apply a backstepping transformation and averaging theory in infinite dimensions for stochastic systems. Moreover, simulations highlight the effectiveness of the proposed predictor-feedback scheme.
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ACC - Gradient Extremum Seeking with Time-Varying Delays
2018 Annual American Control Conference (ACC), 2018Co-Authors: Tiago Roux Oliveira, Damir Rusiti, Mamadou Diagne, Miroslav KrsticAbstract:This paper presents a gradient Extremum seeking algorithm to cope with locally quadratic static maps under time-varying delays. Dealing with non constant delays has a strong impact in the predictor design in terms of the associated transport partial differential equation (PDE) with variable convection speeds as well as the conditions imposed on the delay regarding its arbitrary duration but bounded variation. A new predictor design with a perturbation-based estimate of the unknown Hessian of the map must be introduced to accommodate this variable nature of the delays, which can arise both in actuation and sensing paths. Local exponential stability and convergence to a small neighborhood of the unknown Extremum Point are rigorously detailed. This result is achieved by using backstepping transformation and averaging in infinite dimensions. Numerical simulations are given to illustrate the effectiveness of the proposed predictor-based Extremum seeking control for time-delay compensation.
Christian Ebenbauer - One of the best experts on this subject based on the ideXlab platform.
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ECC - A family of Extremum seeking laws for a unicycle model with a moving target: theoretical and experimental studies
2018 European Control Conference (ECC), 2018Co-Authors: Victoria Grushkovskaya, Simon Michalowsky, Alexander Zuyev, Max May, Christian EbenbauerAbstract:In this paper, we propose and practically evaluate a class of gradient-free control functions ensuring the motion of a unicycle-type system towards the Extremum Point of a time- varying cost function. We prove that the unicycle is able to track the Extremum Point, and illustrate our results by numerical simulations and experiments that show that the proposed control functions exhibit an improved tracking performance in comparison to standard Extremum seeking laws based on Lie bracket approximations.
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Extremum Seeking for Time-Varying Functions using Lie Bracket Approximations
IFAC-PapersOnLine, 2017Co-Authors: Victoria Grushkovskaya, Christian Ebenbauer, Hans-bernd Dürr, Alexander ZuyevAbstract:Abstract The paper presents a control algorithm that steers a system to an Extremum Point of a time-varying function. The proposed Extremum seeking law depends on values of the cost function only and can be implemented without knowing analytical expression of this function. By extending the Lie brackets approximation method, we prove the local and semi-global practical uniform asymptotic stability for time-varying Extremum seeking problems. For this purpose, we consider an auxiliary non-autonomous system of differential equations and propose asymptotic stability conditions for a family of invariant sets. The obtained control algorithm ensures the motion of a system in a neighborhood of the curve where the cost function takes its minimal values. The dependence of the radius of this neighborhood on the bounds of the derivative of a time-varying function is shown.
J.a. Masad - One of the best experts on this subject based on the ideXlab platform.
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Optimization methods with structural dynamics applications
Computers & Structures, 1997Co-Authors: J.a. MasadAbstract:Abstract Two efficient and numerically exact methods for the analysis and computation of derivatives and Extremum Points of variable coefficients differential eigenvalue problems are presented. The methods are applied to optimize the shape of a nonuniform beam such that its fundamental natural frequency is a maximum. One of the methods consists of deriving an analytical expression for the rate of change of the eigenvalue with respect to a free parameter of the variable coefficients differential eigenvalue problem. The expression is then set to zero to analyze the Extremum Point or is used within an iteration scheme to drive the eigenvalue to its maximum or minimum value. The second method is a “one-shot” method which augments the original and differentiated systems by trivial equations for the rates of change of free parameters and solves the resulting nonlinear system subject to the original and differentiated boundary conditions as well as the associated normalization conditions.
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Computational methods for differential eigensystems
Computers & Structures, 1997Co-Authors: J.a. Masad, Balakumar BalachandranAbstract:Abstract Two methods are presented here for analyses of differential eigensystems with variable coefficients and homogeneous boundary conditions. These methods can be used to compute derivatives and Extremum Points of eigenvalues with respect to the chosen free parameters in the considered system. In one method, adjoint equations and solvability conditions are used to derive expressions for the derivatives of eigenvalues with respect to the free parameters in the design vector, and this expression is used to determine an Extremum Point with the help of an iteration scheme. In another method, the differential eigensystem is augmented with additional differential equations corresponding to the free parameters, and the augmented (nonlinear) system subjected to the original and differential boundary conditions is solved in one step. Both of these computational methods are illustrated with examples from structural mechanics.
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Analysis and Computation of Extremum Points with Application to Boundary-Layer Stability
Journal of Computational Physics, 1996Co-Authors: J.a. MasadAbstract:A method for analysis and computation of derivatives and Extremum Points of variable-coefficients differential eigenvalue problems is presented. The method utilizes the orthogonality of the adjoint eigenfunctions to the homogenous part of the once or more differentiated problem to derive an analytical expression for the rate of change of eigenvalue with respect to a free parameter. The Extremum Point can be analyzed and computed by setting and driving, respectively, the first rate of change of the eigenvalue with respect to the free parameters to zero. Higher order derivatives can be computed by solving, sequentially, sets of inhomogeneous two-Point boundary value problems. The method is applied to analyze and compute the most amplified inviscid instability wave in two-dimensional compressible boundary layers and the most amplified viscous instability wave in three-dimensional incompressible boundary layers. It is shown analytically that while the most-amplified spatial instability wave in two-dimensional incompressible boundary layer is two dimensional, the corresponding most amplified wave in three-dimensional boundary layer is generally oblique. It is also shown analytically that the most-amplified disturbance in three-dimensional boundary layer is generally a traveling disturbance. Furthermore, it is shown analytically that the inviscid growth rate is an Extremum Point.
