Integration of Adaptive Estimation and Adaptive Control Design for Uncertain Nonlinear Systems

Abstract

This paper presents a method to integrate adaptive estimation and adaptive control designs for a class of uncertain nonlinear systems having both parametric uncertainties and unmodeled dynamics. The method is based on Lyapunov-like stability analysis of all the errors in the closed-loop system. The adaptive estimator considered is a linear, time-varying Kalman filter augmented by the output of an observer neural network. The observer neural network compensates the nominal Kalman filter for modeling errors. The estimated states are used in the construction of an adaptive control solution that is based on approximate feedback linearization augmented with the outputs of an adaptive neural network controller. The presented approach is then applied to a vision-based formation flight control problem. The objective is for a follower aircraft to maintain range from a maneuvering leader aircraft using a monocular fixed camera for passive sensing of the leader's relative motion. In the implementation, the states of the adaptive estimator are estimates of line-of-sight variables and the outputs of the observer neural network are estimates of the leader acceleration. The adaptive control solution considered is an integrated guidance and control design that includes online adaptation to unmodeled nonlinearities such as the unknown leader aircraft acceleration and parametric uncertainties in the own-aircraft aerodynamic derivatives. Simulation results using a nonlinear 6DOF simulation model of a fixed-wing UAV are presented to illustrate the feasibility and efficacy of the approach.2 presented in Ref. [6][7][8][9] for full relative degree systems. The approach presented in this paper differs from that in Ref. [3,[5][6][7][8][9] in two significant aspects. The approaches in Ref. [3,[5][6][7][8][9] all require knowledge of the dimension of the complete state vector of the system. The approach developed in this paper is applicable to systems with unmodeled dynamics, and does not require knowledge of the dimension of the complete state vector. An adaptive observer is built to estimate only the modeled states of the system. In addition, the approaches in Ref. [3,[5][6][7][8][9] permit augmentation only of a linear time-invariant observer with a NN. In this paper, we consider augmentation of a linear, time-varying observer with a NN. These extensions in theory are important to allow application in certain guidance and flight control applications. For example in applications such as missile intercept guidance, target tracking and vision-based formation flight, not all the states are available for feedback and the target dynamics are the poorly modeled or unmodeled.The problem of leader-follower formation flight in which the follower aircraft is equipped with only an onboard camera to track the leader aircraft is quite challenging. This problem requires simultaneous sensor data processing, state estimation and tracking control in the presence of unmodeled disturbances (leader acceleration) and measurement uncertainties. Sensor data pr...

Optimal control and line‐of‐sight guidance formation flight

“…Nonlinear control of multiple UAVs in close‐coupled formation flight and 6‐DOF nonlinear simulation of vision‐based formation flight have been studied in Corey and Sahjendra (2000), and Sattigeri et al (2005), respectively. Adaptive control design and its application to the formation flight have been examined in Kutay et al (2005), Misovec (2002), and Sattigeri et al (2007).…”