Conventional perturbation-based extremum seeking control (ESC) employs a slow time-dependent periodic signal to find an optimum of an unknown plant. To ensure stability of the overall system, the ESC parameters are selected such that there is sufficient time-scale separation between the plant and the ESC dynamics. This approach is suitable when the plant operates at a fixed time-scale. In case the plant slows down during operation, the time-scale separation can be violated. As a result, the stability and performance of the overall system can no longer be guaranteed. In this paper, we propose an ESC for periodic systems, where the external time-dependent dither signal in conventional ESC is replaced with the periodic signals present in the plant, thereby making ESC time-invariant in nature. The advantage of using a state-based dither is that it inherently contains the information about the rate of the rhythmic task under control. Thus, in addition to maintaining time-scale separation at different plant speeds, the adaptation speed of a time-invariant ESC automatically changes, without changing the ESC parameters. We illustrate the effectiveness of the proposed time-invariant ESC with a Van der Pol oscillator example and present a stability analysis using averaging and singular perturbation theory.
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Quasi-Stochastic Approximation: Design Principles With Applications to Extremum Seeking Control
From the summary: The goal of this article is two-fold: survey the emerging theory of QSA (quasi-stochastic approximation) and its implication to design, and explain the intimate connection between QSA and ESC (extremum seeking control). The contributions go in two directions: ESC algorithm design can benefit by applying concepts from QSA theory, and the broader research community with interest in gradient-free optimization can benefit from the control theoretic approach inherent to ESC.
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- Award ID(s):
- 1935389
- PAR ID:
- 10477050
- Publisher / Repository:
- IEEE Control Systems Magazine
- Date Published:
- Journal Name:
- IEEE Control Systems
- Volume:
- 43
- Issue:
- 5
- ISSN:
- 1066-033X
- Page Range / eLocation ID:
- 111 to 136
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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