Abstract This works is concerned with the finite-time optimal stabilization problem for a class of switched non-strict-feedback nonlinear systems whose powers are possibly different positive odd rational numbers in the sense the powers of each subsystem might differ from others. It is well known that high-order nonlinear systems are intrinsically challenging as feedback linearization and backstepping method successfully developed for low-order systems fail to work. To this purpose, the nested saturation homogeneous controller is constructively devised to achieve global finite-time stability. Furthermore, the corresponding design parameters are optimized by minimizing a well-defined cost function, and thus an optimal controller being independent of switching signals is obtained. Simulation results are eventually provided to validate the effectiveness of the proposed control scheme.

中文翻译：

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切换高阶有理功率非线性系统的全局有限时间镇定

摘要 本文研究一类开关非严格反馈非线性系统的有限时间最优镇定问题，其功率可能是不同的正奇有理数，因为每个子系统的功率可能与其他子系统不同。众所周知，高阶非线性系统本质上具有挑战性，因为为低阶系统成功开发的反馈线性化和反推方法无法正常工作。为此，构造性地设计了嵌套饱和齐次控制器以实现全局有限时间稳定性。此外，通过最小化明确定义的成本函数来优化相应的设计参数，从而获得独立于开关信号的最优控制器。