# Robust Adaptive Control for Nonlinear Aircraft System with Uncertainties
## 1 Introduction  
Uncertain nonlinear system control is a challenging topic in the field of control theory and application. Fundamental control methods for nonlinear systems include the back-stepping approach [1], feedback control [2], and sliding mode control [3]. Additionally, adaptive control has attracted much attention due to its capacity to accommodate system uncertainties. Various adaptive strategies have been developed for uncertain nonlinear systems, such as adaptive optimal control [4], immersion and invariance (I & I) adaptive control [5], adaptive neural control [6], and adaptive sliding mode control [7]. Model reference adaptive control (MRAC) is an important area in aircraft system control research. MRAC architecture was developed in the 1950s [8] for the design of aircraft autopilot to deal with uncertainties during the flight period. This control scheme has been extensively investigated in aerospace engineering [9; 10; 11; 12], since the controller design does not rely excessively on accurate plant models. In standard MRAC, high adaptive gains are generally employed to achieve fast adaptation in the existence of system uncertainties. However, this leads to high-frequency oscillations in system responses, which can be a potential threat to system stability. Specifically, high-performance safety-critical aircraft require the designed controller to have the ability to guarantee the transient performance of the system while achieving fast adaptation. In the MRAC structure, the tracking error between a real uncertain plant and the selected reference model plays a decisive role in the performance of the adaptive controller, in that the controller parameters are adjusted online for the update law, which is designed on the basis of tracking errors. When large uncertainties exist in the aircraft system, such as control surface failure, aerodynamic coefficient changes, or unexpected external disturbances, high adaptive gains are applied to rapidly reduce system tracking errors in order to achieve fast adaptation, which offsets the impact of uncertainties. Highadaptive gains, however, may introduce high-frequency components into the control response, and a closed-loop system with poor transient behavior in the early stage of adaptation will in turn suffer from issues of actuator saturation [13], unmodeled dynamics [14], and even instability of the system [15]. In view of this defect of MRAC, great efforts have been made to deal with the problem. Multiple models and switching strategies [16] were developed to improve the transient response of the adaptive control by choosing a model that best approximates the plant for the controller. A combined/composite-model-reference adaptive control system was reported [17; 18; 19], which used prediction errors to formulate adaptive laws; flight test results confirmed a noticeable improvement in transient performance with high adaptive gains. [PERSON] et al. investigated the \(L_{1}\) adaptive control method [20; 21], wherein the high-frequency components in a control signal can be filtered out by a low-pass filter. A low-frequency learning adaptive control scheme [22; 23] was also proposed to improve transient performance while achieving fast adaptation. An observer-based adaptive control scheme [24; 25], in which an error feedback item is introduced to the reference model, was verified to be a practical approach for improving transient behavior. However, this resulted in changing the well-designed reference model, which meant that the desired reference signal to be tracked had to be revised. In this paper, a robust adaptive control for handling control effectiveness uncertainty, matched plant uncertainty, and external disturbance uncertainty of an aircraft is presented. The main contribution of this paper is the improved tracking performance of a model reference adaptive control system.