Prescribed dual-layer multi-time-scale control for uncertain nonaffine aircraft models with actuator saturation

A cascade control law is designed to address the tracking control problem for a class of non-strict feedback cascade systems, represented by the fixed-wing aircraft altitude model, under multiple adverse constraints including uncertainties, actuator saturation, and nonaffine characteristics. This control law consists of multiple serially connected practical prescribed-time (PPT) sub-controllers with identical structures, whose internal components are also PPT convergent, thereby forming an inner-outer dual-layer multi-time-scale structure. This structure facilitates the active shaping of closed-loop system characteristics through the specification of convergence times. For input saturation, the extended state influenced by the control input is treated as a virtual control variable. This variable is utilized as a bridge to construct an anti-saturation auxiliary dynamic system, overcoming the difficulty of directly using the actual control input for saturation compensation in nonaffine systems. Additionally, a high-gain filter with PPT convergence properties is designed, which dynamically solves for the actual control input from the virtual control variable and allows for explicit adjustment of the solution speed. The closed-loop convergence analysis is provided without relying on the time-scale separation assumption, and numerical simulations as well as hardware-in-the-loop simulations validate the feasibility and superiority of the proposed controller.