John L' Junkins

1
John L. Junkins

• Intelligent Systems
• 1st Annual TiiMS URETI Review Meeting
• University of Houston
• July 14 15, 2003

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Team Members

• Kamesh Subbarao, Post Doctoral Researcher
• Puneet Singla, PhD Candidate
• Ben Mertz, Undergraduate Summer Intern
• Collaborations with
• John Valasek, Othon Rediniotis, et al

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Research Objectives/Deliverables Year One

• 1. Develop Multi-Resolution Input/Output Modeling
  Methods for Systems With Embedded Sensing and
  Actuation (ESA)
• 2. Develop Adaptive Control Approaches For
  Nonlinear ESA Systems with Large Model
  Uncertainty
• 3. Validate the Formulations Developed in 1. and
  2. by Application to the Synthetic Jet Actuator
  Wing Experiment (Collaborate with Valasek and
  Rediniotis)

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Overview Results for Objective 1, 2 and
3(details on following slides)

• Objective 1 (Input/output modeling for ESA
  systems)
• Developed mathematical models for representing
  the synthetic jet actuator influence of
  aerodynamic forces using Radial Basis Function
  Networks (RBFN) gt Several Significant Advances.
• Objective 2 (adaptive control for ESA systems)
• Developed an Adaptive Controller that includes
  real-time adaptation of RBFN based adaptive
  controller to track prescribed pitch motions.
• Objective 3 (validation/experimentation with SJA
  wing)
• Preliminary modeling studies are underway with
  static, free dynamic and sinusoidal pitching
  motion data.
• Interfaced the dSPACE, MATLAB and SIMULINK
  hardware and software with the SJA hardware.
• Identification Experiments and Controller
  Implementation (collaboration with Valasek and
  Rediniotis).

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Motivation

• To achieve the TiiMS vision, we need to advance
  multi-resolution modeling and control
  technologies that enable us to build adaptive,
  intelligent, shape controllable micro and macro
  structures with embedded sensing and actuation
  for advanced aerospace systems.
• Ultimately, we need modeling and control methods
  that enable multi-resolution
• aggregation of sensed information and
• distribution of control input information to
  achieve desired dynamics.
• Develop modeling tools for characterizing
  physical behavior at multiple length and time
  scales.
• Lack of unified physics-based modeling approaches
  to derive macro models from those at micro and
  nano level.
• Mechanics/Physics methodologies presently fall
  short cant yet derive macro and micro dynamical
  models from quantum mechanics models applicable
  at scales smaller than pico.
• While waiting for the evolution of physics-based
  models, we are pursuing multi-resolution,
  adaptive input/output modeling approaches to
  capture macro static and dynamic models directly
  from experiments
• gt use these models as the basis for adaptive
  control.

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Motivation, Continued

• Primary Long Range Interest Design an
  Intelligent Control Structure integrating the
  functions of all the flight control actuators,
  reconfigurability, and also adapting efficiently
  over different flight regimes accommodate
  uncertainty. Over the near term
• Active flow control by embedding sensors and
  actuators at achievable scales on the wing.
• For the near-term, use
• MEMs scale sensing
• and actuation to
• accomplish proof of
• concept demonstrations
• and to challenge the
• modeling and control
• methodologies.
• Obtain a mapping between pressure distribution
  over the wing and synthetic jet actuators (SJAs).
• Mapping between the input and output of SJAs is
  unknown and known to be nonlinear in nature.
• Un-steady effects make it impossible to capture
  the physics fully from static experiments.
• Obtain a mapping between the SJA actuation
  parameters (frequency, direction, etc. for each
  actuator) and the resulting aerodynamic lift,
  drag, and moment.

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Modeling and Control of High Dimensioned Systems
John Junkins, John Valasek et al

• Team with Rediniotis and Lagoudas to define
  initial problems having distributed sensing and
  actuation.
• Establish open loop adaptive approximation
  methods capable of multi-scale representation.
• Establish closed loop adaptive approximation and
  control formulations
• Develop algorithms and interface to proof of
  concept experiments,

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Artificial Neural Networks and related I/O
Mapping e.g., Modeling SJA Influence on
Aerodynamics

• Issues and Qualitative Ideas
• The central difficulty lies in choosing
  appropriate basis functions (physics model always
  best!)
• Brute force method gt choose a complete
  (infinite) set of basis functions
• But such an estimator will have far too many
  parameters to determine from limited number of
  observations. lt impractical esp for use in
  adaptive control.
• Alternatively, we can use prior knowledge of the
  problems approximate physics to only learn only
  the unknown model error.
• In past two decades, Artificial Neural Networks
  (ANNs) have emerged in some areas of pattern
  classification, signal processing, dynamical
  modeling and control.
• Neural networks have shown in some applications,
  ability to learn behavior where traditional
  modeling is difficult or impossible. gt
  But the ANN approach is most definitely not a
  panacea!
• The traditional ANNs still have serious
  short-comings
• Abstraction gt the estimated weights do not have
  physical significance
• Interpolation versus Extrapolation
• gt How do we know when a given model is
  sufficiently well-supported by the network having
  converged, and utilizing sufficiently dense and
  accurate measurements neighboring the desired
  evaluation point?
• Issues Affecting Practical Convergence
• gt A priori learning versus on-line adaptation?
• gt When the ANN architecture is fixed a priori,
  then the family of solvable problems is
  implicitly constrained this suggests the
  architecture should be learned.

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Motivation for RBF Networks

• RBFN are special two layer NN with node influence
  characteristics described by radial basis
  functions.
• The Gaussian function is an ideal choice for
  basis functions because each response can be
  confined to local dominance.
• Major Advantages
• Lives in the space of inputs gt enables
  physical interpretation of the parameters.
• The network geometry and number of nodes can be
  adapted for efficiency. More generally,
  non-circular Gaussian functions should be used.
• Covers theorem A complex pattern
  classification problem or input/output problem
  cast in a high-dimensional space is more likely
  to be approximately linearly separable than in a
  low-dimensional space.
• the bad news is that high
  parametric dimensionality is not exactly an
  advantage!
• Multilayer Neural networks (MLP) and RBFN can
  serve as Universal Approximators.
• MLP performs a global and distributed
  approximation whereas
• RBFN gives a global approximation but with
  locally dominant basis functions
• MLP have been found to have slower convergence
  rates compared to RBFN.
• RBFN can converge locally where many local
  measurements exist.
• Adapting the architecture of RBFN leads to a new
  class of approximators suitable for
  multi-resolution approximation applications.

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Radial Basis Functions

• To construct a RBFN, we need to tune the RBF
  parameters.
• Resource Allocating Network (RAN) The learning
  process for RAN involves allocation of new hidden
  units as well as adjusting the network
  parameters.
• To adjust the network parameters, a Sequential
  version of Least Squares (essentially an
  Algebraic Extended Kalman Filter) is used.
• A pruning strategy is based upon the contribution
  of a hidden unit for N successive data points has
  also been developed to control the growth of
  network.

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Multi Resolution Algorithm

• While the RAN algorithm has been very successful
  in a few applications, ...
• The network size can grow indefinitely because
• The choice of (fixed) basis function shapes and
  initial distribution over the state space may
  bear no correlation to the function to be
  represented.
• No provision for a-priori sizing of the network
• To attempt to overcome the above, a pruning
  strategy is used a-posteriori, but
• The number of basis functions required may never
  converge.
• No means for adaptively reshaping, scaling, and
  rotation of basis functions lt root difficulty.
• It is principally an on-line learning algorithm
  (but not well-suited to high-dim real time
  control).

We introduce the following modifications to
RBFN/RAN approach

• The network size is initially kept limited by
  judicious location of the RBFs via a Directed
  Connectivity Graph approach.
• Allows a-priori adaptive sizing of the network
  for off-line learning.
• Zeroth Order Network Pruning comes for free
  because of the Connectivity Graph.
• Direction dependent Scaling and Rotation of
  basis functions is provided for
• maximal trend sensing with minimal parameter
  representations.
• Adaptation of the network parameters done to
  account for on-line tuning.
• Other ideas are being explored gt ways to reduce
  dimensionality gt localized learning

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Multi Resolution Algorithm (MRA-RBFN)

• Step 1 Find the interior extremum points of the
  given surface-data.
• Step 2 Divide the input space into several
  subspaces of equally spaced 1-D arrays so that
  the extremum points do not fall on the boundary
  of any sub-region.
• Step 3 Find the relative maximum and minimum in
  each region.
• Step 4 Make a directed graph of all the maximum
  points sorted in descending order and call it M.
• Step 5 Make a directed graph of all the minimum
  points sorted in ascending order and call it N.
• Step 6 Choose 1st point in M and N as a
  candidate for Gaussian center and function values
  as the weight of those Gaussian functions.
• Step 7 For these points find the associated
  covariance matrix (P) with the help of local
  mask. (Initial estimates are obtained by looking
  at the second moments of the data)
• Step 8 Initialize rij Pij and s 0.
• Step 9 Learn unknown RBFN parameters using
  Recursive Least Squares or Sequential Least
  Squares using the complete data set.
• Step 10 Check if estimated parameter vector
  satisfies the inequality constraints.
• Step 11 Check the estimation error residuals. If
  they do not satisfy the required accuracy then
  choose the next point in sets M and N as the
  Gaussian center and follow from step 7.

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Approximation of Test Surface by Adaptive
Gaussian RBFN
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Approximation of Test Surface by Adaptive
Gaussian RBFN
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Multi Resolution Algorithm (MRA-RBFN)
Modeling Approach

• Features of the Radial Basis Functions
• Direction dependent Scaling (ensured
• by using ellipsoidal functions)
• Rotation of the basis functions
• This is ensured through a unique
• parameterization of the R matrix.

R is an n X n positive definite symmetric matrix
One only needs to construct the upper/lower
triangular matrix. The symmetry is explicitly
enforced.
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Multi Resolution Algorithm (MRA-RBFN)
To enforce Positive Definiteness and Symmetry of
R Parameter Projection is employed to enforce
the above, whenever the inequality is violated
during the Kalman Updates.

• Learning Algorithm - Sequential Least Squares

pk is (n2)(n3)/2 vector of unknown parameters
of RBF network.
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Multi Resolution Algorithm (MRA-RBFN)

• Further, the sensitivities of the outputs with
  respect to the parameters are obtained as
  follows,

This Algorithm was tested on a variety of test
functions. We present some results from the
studies, importantly a test case for function
Approximation and a Dynamical System
Identification experiment.
Case 1
Case 2
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Modeling Results
Case 1 Using RAN (Circular Gaussians RBFs)
Test Surface and Approximated Surface
87 Gaussian Centers gt slow convergence, 500
RBFs reqd for acceptable approx.
Approximated contours of MRAN approximation
Contours of true surface
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Modeling Results
Case 1 (using MRA-RBFN)
Estimation needed 32 basis functions to learn
the whole surface to order of magnitude higher
precision Measured Data (True Surface)

MRA-RBFN Estimated Surface
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Modeling Results Case 1
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Modeling ResultsCase 2 Nonlinear Discrete
System Identification

• Nonlinear discrete system in S. Tan, J. Hao, and
  J. Vandewalle, Identification of nonlinear
  discrete-time multivariable dynamical system by
  RBF neural networks, IEEE Int. Conf. on Neural
  Networks, pp. 3250-3255, Orlando, FL, 1994.

• Training Data - 200 uniformly distributed random
  input signals, u, between -2 and 2.
• Testing data set - Sequence of periodic inputs

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Modeling ResultsCase 2 Nonlinear Discrete
System Identification
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Modeling and Control of High Dimensioned Systems
John Junkins, John Valasek et al

• Team with Rediniotis and Lagoudas to define
  initial problems having distributed sensing and
  actuation.
• Establish open loop adaptive approximation
  methods capable of multi-scale representation.
• Establish closed loop adaptive approximation and
  control formulations
• Develop algorithms and interface to proof of
  concept experiments,

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High Level Schematic for Closed Loop Flow Control
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Subsystem Modeling - 1

• SJA Aero Model
• Current capability w.r.t to the SJA model is
  limited to producing pitching moment only. (HW
  augmentation for plunge control is underway)

Control Methodology to generate a desired Moment
at a particular AoA
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Subsystem Modeling - 2
Control Methodology
In an open loop sense observe the following,

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Static Approximation of Synthetic Jet Actuator
Lift, Drag and Moment Coefficients vs SJA
Frequency (wSJA) and Angle of Attack (a)
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Control Law - 1
Single degree of freedom pitch dynamics
Where, is the AoA, M is the Mach Number, q
is the Pitch rate, q is the wing loading, c is
the chord and J is the Moment of Inertia. ()r
correspond to the reference values.
Control Objective Track a prescribed trajectory,
ar and qr using the synthetic jet actuation
frequency as the control input. This translates
to generating an equivalent moment to achieve the
task.
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Control Law - 2
Consider an approximation of
thats modeled as follows

• The Higher Order Terms (HOT) are approximated
  using the Radial Basis Function
• Networks.
• The linear terms are included to approximate the
  behavior at low AoA when the
• contributions due to HOT are small.

Rotation, Elliptical Gaussian Angle lt 45 degrees
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Control Law - 3
Tracking error dynamics
However, to account for above we modify the
control law as,
and ensures closed loop stability with
arbitrarily small tracking errors as time goes to
infinity.
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Control Law - 4
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Control Law - 5
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System Identification Experiment
Persistency of Excitation in the Input Spectrum
Data Acquisition
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dSPACE

• Provides complete
  solutions for Functional
• Prototyping and Electronic Control Unit (ECU)
• Software Development
• dSPACE allows generation,
  modulation and recording of
  the necessary input voltage corresponding to
  the specified signals.
• Sensor data can be directly
• read into a data file for further
• processing

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Experimental Adaptive Control Results
The SGA Wing Experiment is ongoing it is
expected that ce will successfully close
all control loops during summer 03. Some
problems with the controllability at small angles
of attack and current power supplies are being
addressed with design modifications. Collaboratin
g with Kurdila, Ko, Akella, and Strganac, we
have conducted experiments that show the
adaptive the control approach is effective in
suppressing aeroelastic flutter over wide range
of speed and parameter variations as compared
to several competing approaches, this was the
most effective as regards robustness with respect
to model errors.
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Results/Directions

• A Promising set of analytical, computational and
  experimental research activity is bearing
  significant fruit
• Adaptive Radial Basis Network for Input/Output
  Modeling
• Adaptive Control Approach that includes real time
  adaptation of RBFN
• Aerodynamic modeling experimental
  infrastructure.
• First control implementation on the SJA wing
  experiment nearly complete
• Aero modeling, SJA i/o models control
  software/hardware implementation
• Simulations indicate impending success
• Directions
• The Experiments for SJA wing control
• Complete implementation (MATLAB SIMULINK
  dSPACE)
• SJA Wing design architecture needs to be extended
• Soft large a restraints!, Controllability at
  small a, power supply issues
• Extend configuration to permit Plunge Motion
  Control.
• Multiple SJAs Distributed actuation
  Distributed Sensing Reconfigurability
• Refine the RBF Network Approximation Theory and
  Algorithms gt enhanced methods to localize
  learning and manage dimensionality
• Improve the algorithms for localization and
  controlling the input/output model dim.
• Investigate methods to characterize the
  confidence/uncertainty of local approximation.

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Education and Outreach

• Postdoctoral Research Associates
• Kamesh Subbarao gt U. of TX. / Arlington, Sept.
  03
• Graduate Students
• Puneet Singla, PhD candidate
• Hee Eun Lee, MS candidate
• Curriculum Integration
• Estimation and controls methodology gt AERO 626
• Frequent seminars and lab tours for graduate and
  undergraduate students.

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Education and Outreach

• Undergraduate Students
• Ben Mertz, Rose Hulman Inst. of Tech.
• Summer Research Intern
• in HS, winner of the 96 Red Hacker Award gt
• Other Participants
• Visiting Scientist Dr. James D. Turner, AmDyn,
  Inc.
• Computational Mechanics
• High Dimensioned Systems, Symbolic Methods,
  Automatic Differentiation
• Molecular Dynamics

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Education and Outreach

• Activities with Sponsor and Industries
• Have collaborated with Richard Pappa/NASA LRC to
  propose a novel Optical Diagnostic System for
  future generation Solar Sails. This resulted in
  a successful 2.3M NASA funded proposal to
  validate the methodology, to initiate in August,
  2003.
• We held our first board meeting in College
  Station during the Spring of 2003, we have had
  extensive discussions with board chair Malcolm R.
  ONeill, with regard to the overall goals and
  organization of TiiMS.
• Subsequent to broad discussions with board member
  Joe Tillerson/Sandia National Laboratory, we have
  had technical discussions with Rush
  Robinett/Sandia, George James/NASA JSC and Bob
  Nellums/Sandia, regarding optical sensing
  research applicable to measuring deformation of
  thin films.
• Dr. James D. Turner, AmDyn Inc., is spending one
  month (July, 2003) collaborating on analysis of
  high dimensioned dynamical systems.

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Publications/Presentations

• J. Junkins,Accommodating Nonlinearity and Model
  Error in Dynamics, Stability, and Control
  Analysis of Mechanical Systems, 2003 Den Hartog
  Keynote Lecture, ASME Design Engineering
  Technical Conferences, Chicago, September
  2-6,2003.
• J. Ko, J., T. Strganac, J. Junkins, M. Akella,
  and A. Kurdila, Structured Model Reference
  Adaptive Control for Wings with Structural
  Nonlinearity, Journal of Vbration and Control,
  Vol 8, pp553-337, 2002.
• P. Singla, K. Subbarao, O. Rediniotis, J. Junkins
  "Intelligent Radial Basis Function Networks For
  Multiresolution Modeling Application to
  Synthetic Jet Actuation and Flow Control"
  accepted for 42nd AIAA Aerospace Sciences Meeting
  and Exhibit Reno, Nevada, 5 - 8 Jan 2004.
• in preparation
• K. Subbarao, P. Singla, J. Junkins, "Direction
  Dependent Scaling and Rotation of RBF Networks
  Applied to Function Approximation.
• K. Subbarao, P. Singla, J Junkins, "Nonlinear
  Predictive Methods For Non-Affine Control
  Systems Applications to RBF Networks."
• P. Singla, K. Subbarao, J. Junkins, "A Novel
  Multiresolution Modeling Technique Using Radial
  Basis Functions and Sequential Learning."

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Plans for Year Two

• The Experiments for SJA wing control
• Complete implementation (MATLAB SIMULINK
  dSPACE)
• SJA Wing design architecture needs to be extended
• Soft large a restraints!, Controllability at
  small a, power supply issues
• Extend configuration to permit Plunge Motion
  Control.
• Multiple SJAs Distributed actuation
  Distributed Sensing Reconfigurability Smart
  Wing
• Refine the RBF Network Approximation Theory and
  Algorithms gt enhanced methods to localize
  learning and manage dimensionality
• Improve the algorithms for localization and
  controlling the input/output model dimension gt
  investigate weighting function technique.
• Investigate methods to characterize the
  confidence/uncertainty of local approximation.
• Refine the Adaptive Control Theory and Algorithms
  
• gt improve handshake with RBFN approximation
  theory/computation
• Collaborate with Lagoudas, Rediniotis, et al
• gt more connections to multifunctional systems
  research, especially
• gt incorporate additional embedded sensing and
  actuation to extend analysis and experiments to a
  wider class of physical systems.
• Outreach Continue to involve students at all
  levels, post-docs, and visiting scientists,
  integrate research with academic programs.

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Thanks You