Flexible Convergence Rate for Quadratic Programming-Based Control Lyapunov Functions

• Published in: Proceedings of the IEEE Conference on Decision & Control pp. 8845 - 8851
• Main Authors: Dihel, Logan, Hyun, Nak-Seung Patrick
• Format: Conference Proceeding
• Language: English
• Published: IEEE 16.12.2024
• Subjects: Attitude control; Closed loop systems; Control Lyapunov Functions; Convergence; Costs; Feedback Control; Geometric Control; Lyapunov methods; Nonlinear systems; Quadratic programming; Quadrotors; Safety; Tuning
• ISSN: 2576-2370
• DOI: 10.1109/CDC56724.2024.10886305

For many systems, there is an objective to minimize control effort while also providing a fast convergence rate. In the past decade, quadratic programming (QP) and control Lyapunov functions (CLF) have been combined to create online feedback controllers which minimize control effort subject to convergence rate guarantees. However, these convergence rate guarantees can sometimes be too slow, or require strong conditions for the closed loop system. Similarly, an existing controller may provide a fast convergence rate, but require too much control effort. In this paper, we introduce a flexible exponentially stabilizing CLF condition, which admits various convergence rates. This relaxation allows a novel QP-based controller with a state-dependent tuning parameter to adaptively tune between the convergence rate and control effort. We show the QP-based controller can be applied to any exponentially stabilizing CLF, and the solution is piecewise continuous with exponential convergence guarantees. A comparative study to other control types such as min-norm based control and geometric control for attitude tracking on \mathrm{SO}(3) is shown to validate the trade-off benefits of using the proposed flexible CLF control.