Global robust stabilisation of a general ANCBC systems with heterogeneous and asymmetric actuator saturation

In this paper, we aim at resolving the global stabilisation of a general Asymptotically Null Controllable with Bounded Controls system, addressing both asymmetric heterogeneous saturation characteristics and disturbance rejection requirements. To this end, we propose a new control algorithm that integrates high-gain technique with a nonlinear control algorithm subject to a re-designed saturation function. First, the saturation level vector of the re-designed saturation function operates in a decentralised manner, thereby directly addressing heterogeneous saturation constraints. Second, each dimension of the saturation vector dynamically adjusts itself through dual distinct mechanisms, separately avoiding upper-bound and lower-bound saturation in asymmetric saturation scenarios. Third, the high-gain technique actively attenuates additive input disturbances, delivering enhanced robustness against input additive disturbances. We conduct theoretical analysis from both state feedback and output feedback perspectives, yielding sufficient conditions for global robust stabilisation. Finally, numerical simulations are provided to verify the theoretical results.