Aerospace Science and Technology 12 (2008) 248–255 www.elsevier.com/locate/aescte Neural network based adaptive output feedback augmentation of existing controllers Nakwan Kim a,∗ , Anthony J. Calise b a Chungnam National University, Department of Aerospace Engineering, 220 Gung-dong, Yuseong-gu, Daejeon 305-764, South Korea b Georgia Institute of Technology, School of Aerospace Engineering, 270 Ferst Drive, Atlanta, GA 30332, USA Received 26 June 2006; received in revised form 28 May 2007; accepted 2 July 2007 Available online 6 July 2007 Abstract This paper describes an approach for augmenting a linear controller with a neural network based adaptive element in output feedback setting. The approach is applicable to non-affine nonlinear systems with parametric uncertainty and unmodeled dynamics. Stability of the adaptive control system is ensured using Lyapunov direct method. A numerical example of guided munitions illustrates the efficacy of the approach.  2007 Elsevier Masson SAS. All rights reserved. Keywords: Adaptive control; Neural network; Output feedback; Guided munitions 1. Introduction As an aerial vehicle requires high maneuverability in a wide flight envelope, a flight controller needs to deal with nonlinear- ity and uncertainty unless the aircraft is precisely modeled at high cost. Nonlinearity can be handled by employing feedback linearization which transforms a nonlinear plant into linear time invariant form. In terms of uncertainty, adaptive control is a vi- able choice and has drawn a great deal of interest in dealing with uncertainty. However, the conventional adaptive control is limited to linearly-parameterized uncertainty. The difficulty lies in finding an appropriate linear parameterization of the uncer- tainty. The limitation can be overcome by introducing neural network (NN) which is capable of parameterizing nonlinear uncertainty. Therefore, the combination of feedback lineariza- tion and NN based adaptive control became a popular method to cope with nonlinearity and uncertainty in control systems [18,21,26]. This method has been successful in applications to flight vehicles, robot manipulators, and experimental devices in a state feedback setting [1,3,10]. Extensions of the methods to state observer-based output feedback controls are treated in [14,20]. However, these designs are limited to systems with full * Corresponding author. Tel.: +82 42 821 6689; fax: +82 42 825 9225. E-mail address: nkim@cnu.ac.kr (N. Kim). relative degree less than or equal to two. These limitations in- herent in state observer-based design are removed in a direct adaptive approach [2] and in an error observer-based approach [13]. There are other methods of augmenting with NNs such as integrator backstepping [6,11] in strict feedback systems and sliding mode control [5,8] using a sliding manifold. The methods combining feedback linearization and NN re- quires one to design a new inversion controller unless the exist- ing controller architecture is already based on inversion. Con- sidering that the majority of existing controllers are not based on inversion, it is desirable to augment the existing control sys- tems with a NN based adaptive element. Adaptive augmentation with a linear controller is introduced in a state feedback setting in [22]. The efficiency of this approach is corroborated in an application to attitude control of a spacecraft in [24]. It is ex- tended to output feedback setting in a direct adaptive approach in [4,25] and in an error-observer approach in [15]. This pa- per proposes an approach for a simple reference model which has the same relative degree as the true plant as depicted in Fig. 1. This approach differs from the approaches in [4,15,22, 24,25] in that the reference model does not require knowledge of the existing controller. The reference model is constructed to represent the ideal response characteristics of the closed-loop system. NN augmentation of an existing controller is used to force the plant output to track the reference model trajectory. 1270-9638/$ – see front matter  2007 Elsevier Masson SAS. All rights reserved. doi:10.1016/j.ast.2007.07.001