Multi‐parametric extremum seeking‐based iterative feedback gains tuning for nonlinear control

Benosman, Mouhacine

doi:10.1002/rnc.3547

Cited by 15 publications

(10 citation statements)

References 36 publications

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“…which gives the iterative update equations (9). In hardware, sufficiently large 0 and small Δ, result in convergence of the kind we prove analytically for (11). With the approach described above, from the iteratively updated parameters' point of view, in the limit as Δ → 0, the overall system and update dynamics take on a continuous, two time scale (t, ) form:…”

Section: Problem Setup and Es Backgroundmentioning

confidence: 84%

Extremum seeking for optimal control problems with unknown time‐varying systems and unknown objective functions

Scheinker

2020

Adaptive Control & Signal

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Summary We consider the problem of optimal feedback control of an unknown, noisy, time‐varying, dynamic system that is initialized repeatedly. Examples include a robotic manipulator which must perform the same motion, such as assisting a human, repeatedly and accelerating cavities in particle accelerators which are turned on for a fraction of a second with given initial conditions and vary slowly due to temperature fluctuations. We present an approach that applies to systems of practical interest. The method presented here is model independent; does not require knowledge of the objective function; is robust to measurement noise; is applicable for any set of initial conditions; is applicable to simultaneously controlling an arbitrary number of parameters; and may be implemented with a broad range of continuous or discontinuous functions such as sine or square waves. For systems with convex cost functions we prove that our algorithm will produce controllers that approach the minimal cost. For linear systems we reproduce the cost minimizing linear quadratic regulator optimal controller that could have been designed analytically had the system and cost function been known. We demonstrate the effectiveness of the algorithm with simulation studies of noisy and time‐varying systems.

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Section: Problem Setup and Es Backgroundmentioning

confidence: 84%

Extremum seeking for optimal control problems with unknown time‐varying systems and unknown objective functions

Scheinker

2020

Adaptive Control & Signal

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“…[15][16][17] Besides, although the literature 17 also provides an alternative IFT method, which requires only two gradient experiments per one-step optimization, it requires identification of a model of the linearized closed-loop system around its operating trajectory, instead. Another approach is proposed in the literature 18 based on the multiparametric extremum seeking (MES) method. The MES method allows to require only one gradient experiment per one-step optimization.…”

Section: Introductionmentioning

confidence: 99%

Iterative feedback tuning for Hamiltonian systems based on variational symmetry

Satoh

Fujimoto

2019

Intl J Robust & Nonlinear

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Summary This paper proposes a novel iterative feedback tuning (IFT) for Hamiltonian systems, which can describe a practically important class of nonlinear systems. Hamiltonian systems have a special property called variational symmetry, and it can be used to estimate the input‐output mapping of the variational adjoint for certain input‐output mappings of the systems. First, we derive a modified variational symmetry to adapt to the gradient estimation of an optimal control–type cost function with respect to adjustable parameters of a controller. Second, we provide an IFT algorithm based on the property, which generates the optimal parameters minimizing the cost function by iteration of experiments. The proposed algorithm requires less number of experiments to estimate the gradient than the conventional IFT methods for nonlinear systems. We also provide a method to optimize the elements of the dissipation matrix, which does not directly appear in the Hamiltonian function, by equipping a dynamic feedback of the generalized coordinate. Moreover, we provide an IFT algorithm considering parameter constraints so that the parameters can be optimized within a prescribed search range. Finally, a numerical simulation of a two‐link robot manipulator including a comparison with the conventional IFT methods demonstrates the effectiveness of the proposed method.

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“…While the issue of zero dynamics has been widely researched in the past decades, robustness of uncertainties has not gained such a significant attention according to [2]. Results concerning parametric uncertainties can be found in the adaptive control literature, where the controller design usually relies on the utilization of Lyapunov functions [3], [4]. While stability of the system can be guaranteed in such a way, the design procedure might be cumbersome in systems where it is nontrivial to find a proper Lyapunov function.…”

Section: Introductionmentioning

confidence: 99%

Continuous time Robust Fixed Point Transformations based control

2019

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The Robust Fixed Point Transformation based control proved to be beneficial in controlling nonlinear systems with structural or parametric discrepancies. The method was originally formalized in discrete time, using local deformations to alter the input trajectory in order to diminish the uncertainties. A continuous time counterpart is introduced in this paper, which also connects the method to the feedback linearization principle. Such a formalism should make it possible for one to use tools from the classical continuous time literature to analyse the properties and convergence of the method. The theory is demonstrated by controlling angiogenic inhibition of tumor growth using the minimal model.

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Multi‐parametric extremum seeking‐based iterative feedback gains tuning for nonlinear control

Cited by 15 publications

References 36 publications

Extremum seeking for optimal control problems with unknown time‐varying systems and unknown objective functions

Extremum seeking for optimal control problems with unknown time‐varying systems and unknown objective functions

Iterative feedback tuning for Hamiltonian systems based on variational symmetry

Continuous time Robust Fixed Point Transformations based control

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