MIT NSL Reports on Adaptive Neurocontrol

[Rob Sanner]

	The following are the titles and abstracts of three reports we
have uploaded to the neuroprose archive.  Due to a large number of
recent requests for hardcopy reprints, these reports have now been
made available electronically.  They can also be obtained (under their
NSL reference number) by anonymous ftp at tlon.mit.edu in the pub
directory.
	These reports describe the results of research conducted at
the MIT Nonlinear Systems Laboratory during the past year into
algorithms for the stable adaptive tracking control of nonlinear
systems using gaussian radial basis function networks.
	These papers are potentially interesting to researchers in
both adaptive control and neural network theory. The research
described starts by quantifying the relation between the network size
and weights and the degree of uniform approximation accuracy a trained
network can guarantee. On this basis, it develops a _constructive_
procedure for networks which ensures the required accuracy. These 

constructions are then exploited for the design of stable adaptive
controllers for nonlinear systems.
	Any comments would be greatly appreciated and can be sent to
either rob at tlon.mit.edu or jjs at athena.mit.edu.

	  Robert M. Sanner and Jean-Jacques E. Slotine

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on neuroprose: sanner.adcontrol_9103.ps.Z

(NSL-910303, March 1991)
Also appears: Proc. American Control Conference, June 1991.

	Direct Adaptive Control Using Gaussian Networks 


	  Robert M. Sanner and Jean-Jacques E. Slotine

Abstract:
	A direct adaptive tracking control architecture is proposed
and evaluated for a class of continuous-time nonlinear dynamic systems
for which an explicit linear parameterization of the uncertainty in
the dynamics is either unknown or impossible.  The architecture
employs a network of gaussian radial basis functions to adaptively
compensate for the plant nonlinearities.  Under mild assumptions about
the degree of smoothness exhibited by the nonlinear functions, the
algorithm is proven to be stable, with tracking errors converging to a
neighborhood of zero.
	A constructive procedure is detailed, which directly
translates the assumed smoothness properties of the nonlinearities
involved into a specification of the network required to represent the
plant to a chosen degree of accuracy.  A stable weight adjustment
mechanism is then determined using Lyapunov theory.
	The network construction and performance of the resulting
controller are illustrated through simulations with an example system.

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on neuroprose: sanner.adcontrol_9105.ps.Z

(NSL-910503,  May 1991)

	Gaussian Networks for Direct Adaptive Control

	 Robert M. Sanner and Jean-Jacques E. Slotine
	
Abstract:
	This report is a complete and formal exploration of the ideas
originally presented in NSL-910303; as such it contains most of
NSL-910303 as a subset.  

	We detail a constructive procedure for a class of neural
networks which can approximate to a prescribed accuracy the functions
required for satisfaction of the control objectives.  Since this
approximation can be maintained only over a finite subset of the plant
state space, to ensure global stability it is necessary to introduce
an additional component into the control law, which is capable of
stabilizing the dynamics as the neural approximation degrades.  To
unify these components into a single control law, we propose a novel
technique of smoothly blending the two modes to provide a continuous
transition from adaptive operation in the region of validity of the
network approximation, to a nonadaptive operation in the regions where
this approximation is inaccurate. Stable adaptation mechanisms are
then developed using Lyapunov stability theory.
	Section 2 describes the setting of the control problem to be
examined and illustrates the structure of conventional adaptive
methods for its solution.  Section 3 introduces the use of
multivariable Fourier analysis and sampling theory as a method of
translating assumed smoothness properties of the plant nonlinearities
into a representation capable of uniformly approximating the plant
over a compact set.  This section then discusses the conditions under
which these representations can be mapped onto a neural network with a
finite number of components. Section 4 illustrates how these networks
may be used as elements of an adaptive tracking control algorithm for
a class of nonlinear systems, which will guarantee convergence of the
tracking errors to a neighborhood of zero.  Section 5 illustrates the
method with two examples, and finally, Section 6 closes with some
general observations about the proposed controller.

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on neuroprose: sanner.adcontrol_9109.ps.Z

(NSL-910901, Sept. 1991)
To appear: IEEE Conf. on Decision and Control, Dec. 1991. 


	Stable Adaptive Control and Recursive Identification
		Using Radial Gaussian Networks

	   Robert M. Sanner and Jean-Jacques E. Slotine

Abstract:
	Previous work has provided the theoretical foundations of a
constructive design procedure for uniform approximation of smooth
functions to a chosen degree of accuracy using networks of gaussian
radial basis functions.  This construction and the guaranteed uniform
bounds were then shown to provide the basis for stable adaptive
neurocontrol algorithms for a class of nonlinear plants.
	This paper details and extends these ideas in three
directions: first some practical details of the construction are
provided, explicitly illustrating the relation between the free
parameters in the network design and the degree of approximation error
on a particular set.  Next, the original adaptive control algorithm is
modified to permit incorporation of additional prior knowledge of the
system dynamics, allowing the neurocontroller to operate in parallel
with conventional fixed or adaptive controllers.  Finally, it is shown
how the gaussian network construction may also be utilized in
recursive identification algorithms with similar guarantees of
stability and convergence. The identification algorithm is
evaluated on a chaotic time series and demonstrates the predicted
convergence properties.