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Abstract This article presents an extremum‐seeking control (ESC) algorithm for unmodeled nonlinear systems with known steady‐state gain and generally non‐convex cost functions with bounded curvature. The main contribution of this article is a novel gradient estimator, which uses a polyhedral set that characterizes all gradient estimates consistent with the collected data. The gradient estimator is posed as a quadratic program, which selects the gradient estimate that provides the best worst‐case convergence of the closed‐loop Lyapunov function. We show that the polyhedral‐based gradient estimator ensures the stability of the closed‐loop system formed by the plant and optimization algorithm. Furthermore, the estimated gradient provably produces the optimal robust convergence. We demonstrate our ESC controller through three benchmark examples and one practical example, which shows our ESC has fast and robust convergence to the optimal equilibrium.
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Improving the Performance of a Hierarchical Traffic Flow Control Framework Using Lyapunov-Based Switched Newton Extremum Seeking
Abstract The primary aim of this research paper is to enhance the effectiveness of a two-level infrastructure-based control framework utilized for traffic management in expansive networks. The lower-level controller adjusts vehicle velocities to achieve the desired density determined by the upper-level controller. The upper-level controller employs a novel Lyapunov-based switched Newton extremum seeking control approach to ascertain the optimal vehicle density in congested cells where downstream bottlenecks are unknown, even in the presence of disturbances in the model. Unlike gradient-based approaches, the Newton algorithm eliminates the need for the unknown Hessian matrix, allowing for user-assignable convergence rates. The Lyapunov-based switched approach also ensures asymptotic convergence to the optimal set point. Simulation results demonstrate that the proposed approach, combining Newton’s method with user-assignable convergence rates and a Lyapunov-based switch, outperforms gradient-based extremum seeking in the hierarchical control framework.
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- Award ID(s):
- 2130704
- PAR ID:
- 10481923
- Publisher / Repository:
- ASME
- Date Published:
- Journal Name:
- ASME Letters in Dynamic Systems and Control
- Volume:
- 3
- Issue:
- 4
- ISSN:
- 2689-6117
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1115/1.4064088
