Modified Nested Saturated Control for Uncertain Multiple Integrators With High-Order Nonlinear Perturbation

This article studies the global asymptotic stability problem of multiple integrators subject to uncertain parameters and high-order nonlinear perturbation. By introducing a modified saturation function with positive tunable parameters, three types of modified nested saturated controllers with different parameter assignments are proposed to handle the uncertain integrators with high-order nonlinear perturbation. The specific mechanism of the modified nested saturated controllers with different parameter assignments, in which control parameters appear before states, saturation functions, or saturation levels, is comprehensively analyzed. With the help of a modified saturation function, the global convergence domain of each state can be kept invariable in the saturation reduction analysis. Meanwhile, a large saturation level is obtained by adjusting positive tunable parameters. Combining with derivatives calculation and $M$ -matrix-based comparison theory, proposed saturated control schemes are utilized to handle the considered system. Finally, an active magnetic bearing (AMB) system is revisited as an uncertain mechanical system and used to verify the feasibility of the proposed control designs.