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This work was supported by the National Natural Science Foundation of China (Grant Nos. 12172266, 12272283, 12472023), the Fundamental Research Funds for the Central Universities (Grant No. ZYTS25192)，Shaanxi Fundamental Science Research Project for Mathematics and Physics (Grant No. 23JSZ010), GL was supported by National Science Centre, Poland under the project SHENG-2, No. 2021/40/Q/ST8/00362.
In this paper, the finite-time adaptive high-energy orbit control of an asymmetric multistable galloping energy harvester (GEH) is studied by combining the minimum parameter learning (MPL) method and the Radial Basis Function neural network (RBFNN). Firstly, an asymmetric multistable GEH is introduced and the nonlinear dynamical model is formulated. Then, the finite-time adaptive sliding mode control method based on the MPL-based RBFNN is designed for the high-energy orbit control of the harvester, in which the nonlinear external interference and the model uncertainty are considered. During the practical design of an adaptive sliding mode controller, the hyperbolic tangent function replaces the conventional switching function, effectively solving the buffeting problem resulting from high switching gain in sliding mode control. In addition, the model uncertainty of the asymmetric multistable GEH is approximated by an RBFNN-based method, and the weight of RBFNN is replaced by a single parameter derived by the MPL method, which reduces the volatility of trajectory tracking. According to Lyapunov stability theory, the stability of the designed controller is proved. Finally, numerical results demonstrate that the controller exhibits strong robustness and adaptability in handling unknown dynamics and external disturbances. The controller can switch the harvester from a low-energy orbit to a high-energy orbit after a short time, and maintain the stable motion at the high-energy orbit after the control process finished. The error can also be controlled within an acceptable range, which greatly improves the energy harvesting efficiency of the harvester.
