Extremum-seeking control for optimization of time-varying steady-state responses of nonlinear systems

Abstract

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Nondisturbing Extremum Seeking Control for Multiagent Industrial Systems

“…However, boundedness of the solutions can still be guaranteed. This stability result is similar to the ones in [14, Corollary 13] and [16,Theorem 14].…”

Uniform quasi-convex optimisation via Extremum Seeking

“…The early researches on the Extremum Seeking (ES) date bake to 1920s [1] and since then this strategy has been extensively exploited to solve several optimisation problems in electronics [2], mechatronics [3], mechanics [4], aerodynamics [5], thermohydraulics [6], and thermoacoustic [7]. Some of the most popular ES schemes are those proposed in [8,9], which represent the subject of the proposed analysis, although a remarkable variety of schemes were proposed, such as the adoption of an integral action in [10], the use of a cost function's parameter estimator [11,12], the introduction of an observer [13], the extension to fractional derivatives in [3], the use of a predictor to compensate output delays in [14], the implementation of a Newton-based algorithm avoiding the Hessian matrix inversion [15,16], and the concurrent use of a simplex-method to find the global minimiser [17].…”

Uniform non-convex optimisation via Extremum Seeking

“…The early research on the Extremum Seeking (ES) dates back to the 1920s [1] and since then this strategy has been extensively exploited to solve several optimisation problems in electronics [2], mechatronics [3], mechanics [4], aerodynamics [5], thermohydraulics [6], and thermoacoustic [7]. Some of the most popular ES schemes are those proposed in [8], [9], which represent the subject of the proposed analysis, although a remarkable variety of schemes were proposed, such as the adoption of integral action in [10], the use of a cost function's parameter estimator [11], [12], the introduction of an observer [13], the extension to fractional derivatives in [3], the use of a predictor to compensate output delays in [14], the implementation of a Newton-based algorithm avoiding the Hessian matrix inversion [15], [16], and the concurrent use of a simplex-method to find the global minimiser [17].…”