Global Universal Finite-Time Stabilizing Control for Feedforward Nonlinear Systems With Non-Parametric Uncertainty: A Non-Nested Strategy

The global stabilization control issue concerning a class of general upper-triangular nonlinear systems subject to non-parametric uncertainties is dealt with in this paper by constructing a nonsmooth dynamic nonrecursive state-feedback controller. The major challenge in handling such systems is that they cannot be stabilized through the conventional feedback linearization approaches. The investigated strategy does not involve a nested process, commonly seen in existing methods, but rather constructs a homogeneous stabilizer directly via a low-gain design, which greatly facilitates the design of the controller and the analysis of global stability. Meanwhile, by developing a dual-layer adaptive low-gain online updating law, the system with unknown homogeneous nonlinearity growth conditions under consideration can be flexibly stabilized. A numerical simulation and an application to the nonlinear liquid level control resonant circuit system are implemented in this paper to demonstrate the efficacy of the built framework. Note to Practitioners—Upper-triangular model construction is commonly found in practical systems, such as the nonlinear liquid level control resonant circuit system and the planar vertical take-off and landing (PVTOL) system. In these applications, there are inevitably uncertainties within model construction, e.g., internal parameter perturbations and external disturbances. They pose challenges to achieving the control goals of rapid and precise stabilization or regulation for the system. The common strategies for handling upper-triangular systems are recursive nested control and integral feedforward techniques, etc. However, for practical engineers, these strategies are hard to operate due to the complex design process and numerous design parameters to be tuned. Fortunately, nonrecursive strategies have been frequently mentioned in recent years for more convenient engineering implementation. These strategies typically feature simple controller forms, fewer control parameters and are easy to tune, which is of great significance for rapidly and precisely controlling practical systems with various uncertainties. Based on the dynamic low-gain domination strategy, a nonsmooth nonrecursive finite-time controller has been proposed in this paper under the condition that the nonlinearities growth rate is unknown. Finally, through a complex numerical simulation and an application to the nonlinear liquid level control resonant circuit system with parametric uncertainties, the effectiveness of the proposed nonrecursive algorithm has been verified.