Source Seeking for Quad-Rotor Aircraft With Actuator Dynamic Uncertainties via Small-Gain Approach

This paper investigates the source seeking problem for quad-rotor aircraft system in the presence of actuator dynamic uncertainties and presents the semi-global asymptotic practical stability for the closed-loop extremum-seeking system. A new hierarchical two-layer extremum-seeking control framework is presented which consists of a slow quasi-steady-state extremum-seeking algorithm and a fast transient-state dynamics reference-tracking system, the notion of input-to-output practical stability is adopted to describe the performance of different subsystems. Compared to the existing results, this paper eliminates the need for the assumption that the controlled system must exhibit exponential stability at a specific equilibrium point or manifold. By leveraging the nonlinear small-gain theorem and incorporating a robust parameter design approach under small-gain condition, the semi-global practical stability of the overall system is ensured, even in the presence of uncertainties in the actuator dynamics. Finally, the effectiveness of the proposed method is verified through physical experiment and numerical simulation. Note to Practitioners—The rapid advancement of control and optimization algorithms for autonomous systems has significantly broadened the deployment of drones and autonomous ground vehicles across a wide range of industrial and societal domains. These technologies offer promising solutions to complex control problems in applications such as precision agriculture, disaster response, and industrial automation. However, real-world physical systems are often subject to dynamic uncertainties, unmodeled dynamics, and external disturbances, which can result in conservative control strategies and degraded system performance. Therefore, the development of robust and adaptive control methods that can accommodate diverse environmental conditions and inherent system constraints remains a fundamental challenge in control engineering. This study addresses the source-seeking problem for drones operating in spatially distributed signal fields. A novel theoretical framework is proposed to mitigate the restrictive assumptions commonly imposed by conventional extremum-seeking algorithms on the tracking performance of controlled systems. By leveraging this relaxed formulation, the scalability and applicability of perturbation-based extremum-seeking control are significantly enhanced for drones with heterogeneous performance characteristics. To validate the proposed method, physical experiments are conducted in outdoor environments. The results demonstrate the ability of drones to autonomously navigate toward and localize signal sources in the presence of modeling uncertainties and external disturbances. These findings highlight the practical relevance of the proposed approach to real-world source-seeking tasks, such as fire source localization, hazardous gas leak detection, and related applications. Future research will explore the extension of this framework to cooperative multi-agent source-seeking tasks to further improve the efficiency, scalability, and robustness of autonomous localization systems.