Data-Efficient Extremum-Seeking Control Using Kernel-Based Function Approximation
Extremum-seeking control (ESC) is widely used in optimization problems where the system dynamics are unknown. However, traditional ESC methods suffer from slow convergence and high data requirements due to their reliance on continuous perturbation signals. This blog explores a novel data-efficient ESC approach
using kernel-based function approximation, significantly improving convergence speed while reducing the number of required measurements.
Challenges in Traditional ESC
Conventional ESC relies on small perturbations added to system inputs to estimate gradients, requiring frequent measurements. This process is inefficient because:
- It slows down convergence due to time-scale separation constraints.
- Measurement costs are high, especially in resource-intensive applications.
- Repeated perturbations cause transient effects that may lead to system instability.
A Kernel-Based Approach to ESC
The proposed method introduces a kernel-based function approximation to predict the system’s underlying cost function in real-time, eliminating the need for frequent perturbations. Key features of this approach include:
- Online function approximation: Uses previously collected input-output data to construct an accurate cost function estimate.
- Reduced measurement dependency: Updates parameters only when a cost reduction is guaranteed, avoiding unnecessary measurements.
- Improved convergence rate: Achieves faster optimization compared to traditional ESC methods.
Stability and Performance Analysis
The research provides a rigorous stability analysis, ensuring that the system remains within a stable operating range during optimization. Simulations on a multi-input nonlinear system demonstrate:
- Faster convergence than standard ESC techniques.
- Lower computational and measurement overhead, making it practical for real-world applications.
- Scalability to complex systems, such as robotics and industrial automation.
Conclusion
This new ESC method revolutionizes extremum-seeking optimization by leveraging kernel-based learning to minimize data usage and accelerate convergence. As industries strive for smarter and more adaptive control systems, data-efficient approaches like this pave the way for robust, cost-effective solutions.
What are your thoughts on integrating machine learning techniques into real-time control applications?
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