Linearization of discrete-time control system by state transformation

This paper presents necessary and sufficient linearizability conditions by state transformation for discrete-time multi-input nonlinear control system under the mild assumption on the surjectivity property and describes how to find the state transformation when it exists. The conditions are formulated in terms of backward shifts of vector fields, defined by the system dynamics. The conditions are compared with those that allow additionally the regular static state feedback. The theory is illustrated by two examples

Adaptive backstepping sliding mode control for heavy-weight airdrop operations

This paper proposes an adaptive backstepping sliding mode flight control method that is compatible with heavyweight cargo airdrop. The goal is to maintain the plane states during cargo extraction process, in the presence of uncertainties of both constant and time-varying types, as well as matched and unmatched types. A backstepping sliding mode flight control law with parameter adaptation is presented based on the plane-cargo dynamics in strict-feedback form. The control approach consists in having an adaptation law that approximates the disturbance and uncertain aerodynamic function, which is separated from the complex nonlinearities. Also, the adaptation algorithm with projection can bound the estimated function. This ensures the robustness of the controller against time-varying disturbance and uncertainty. The convergence performance and robustness property of the control law are proved by the Lyapunov theory. The control effect is evaluated on a transport plane performing a maximum load airdrop task in a number of simulation scenarios

Projection-Based Adaptive Backstepping Control of a Transport Aircraft for Heavyweight Airdrop

An autopilot inner loop that combines backstepping control with adaptive function approximation is developed for airdrop operations. The complex nonlinear uncertainty of the aircraft-cargo model is factorized into a known matrix and an uncertainty function, and a projection-based adaptive approach is proposed to estimate this function. Using projection in the adaptation law bounds the estimated function and guarantees the robustness of the controller against time-varying external disturbances and uncertainties. The convergence properties and robustness of the control method are proved via Lyapunov theory. Simulations are conducted under the condition that one transport aircraft performs a maximum load airdrop task at a height of 82 ft, using single row single platform mode. The results show good performance and robust operation of the controller, and the airdrop mission performance indexes are satisfied, even in the presence of ±15% uncertainty in the aerodynamic coefficients, ±0.01 rad/s pitch rate disturbance, and 20% actuators faults