10.1.  INTRODUCTION

Advances in technology and modeling in commercially available software
make possible highly accurate simulations of aircraft and their environmental
interactions. With increased on-board computational resources, this allows
for the design of sophisticated nonlinear controllers that exploit these simulations
online, in order to achieve high-performance autonomous control of
vehicles capable of rapid adaptation and aggressive maneuvering. In this
chapter, we describe a method for helicopter control through the use of the
FlightLab simulator [1] coupled with nonlinear control techniques. FlightLab
is a commercial software product developed by Advanced Rotorcraft Technologies.
Details on the modeling capabilities of FlightLab are given in Section 10.2.2. A
challenge in using FlightLab and similar flight simulators to design controllers is that
the governing dynamic equations are not readily available (i.e., the aircraft
represents a ‘‘black-box’’ model). This precludes the use of most traditional
nonlinear control approaches that require an analytic model. Our methodology is
based on the model predictive control (MPC) approach [2,3]. MPC is an
optimization-based framework for learning a stabilizing control sequence that
minimizes a specified cost function. For general nonlinear systems, this requires a
numerical optimization procedure involving iterative forward (and backward)
simulations of the model dynamics. The resulting control sequence represents an
"open-loop" control law, which can then be reoptimized online at periodic update
intervals to improve robustness.

Our approach to MPC, referred to as model predictive neural control
(MPNC), utilizes a combination of a state-dependent Riccati equation
(SDRE) controller and an optimal neural controller. In contrast to traditional
MPC, the architecture implements an explicit feedback controller. The
SDRE technique [4,5] is an improvement over traditional linearization-based
linear quadratic (LQ) controllers (SDRE control will be elaborated on in a
later section). SDRE design, however, requires an analytic representation of
an aircraft model. To provide an analytic representation, the numeric simulator
model is approximated by a six-degree-of-freedom (6DOF) rigid-body
dynamic model, providing a set of governing equations at each time instant
necessary to design the SDRE. In our framework, the SDRE controller
provides an initial stabilizing controller, and it is then augmented by a neural
network (NN) controller. The NN controller is optimized online using a
calculus of variations approach to minimize the MPC cost function. Note that
this differs from either (a) the use of a NN for system identification of the
nonlinear plant as part of a traditional MPC approach (see reference 6) or
(b) the use of a NN for error feedback to account for model uncertainty (see
references 7 and 8). We also make use of the SDRE solution to provide a
control Lyapunov function (CLF) for use in a receding horizon approach to
MPC. In addition, we explore a number of numeric approximations in order
to improve the computational performance of the approach. The basic
framework of our approach has been described in references 9 and 10.