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Content-Transfer-Encoding: quoted-printable Content-Type: text/xml; charset="utf-8" ------=_NextPart_01C60EF8.AFC15880 Content-Location: file:///C:/A51BD64C/CellMapping4NonlinControl_files/slide0002.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Cell Mapping for Nonlinear Control
Control of Deterministic & Stochasti= c = Nonlinear Systems
with the Cell Mapping Methods
Jian-Qiao Sun
Ph.D., P.E., Professor
Department of Mechanical Engineering
University of Delaware
Newark, DE 19716, USA
------=_NextPart_01C60EF8.AFC15880 Content-Location: file:///C:/A51BD64C/CellMapping4NonlinControl_files/slide0101.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Cell Mapping for Nonlinear Control
Outline
§Deterministic Opt= imal Control
  Introductory Concepts
Fixed Final State Problem
Tracking Control and Extensions
§Stochastic Optimal Control
  Introductory Concepts
Solution Approach
Evaluation of the Control Solution
Applications
Extensions
§Conclusions
------=_NextPart_01C60EF8.AFC15880 Content-Location: file:///C:/A51BD64C/CellMapping4NonlinControl_files/slide0057.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Cell Mapping for Nonlinear Control
Non-linear dynamics
Simple cell mapping
Global control solution
Optimal control
Outline
§Deterministic Opt= imal Control
  Introductory Concepts
Fixed Final State Problem
Tracking Control and Extensions
§Stochastic Optimal Control
  Introductory Concepts
Solution Approach
Evaluation of the Control Solution
Applications
Extensions
§Conclusions
§ =
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The Simple Cell Mapping Method
•The Concept:
Consequences:=
   Advantages: Numerical efficiency for global analysis
   Drawbacks: Loss of accuracy=
Cumulative error after several mappings
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x1<= /span>
x2<= /span>
zi<= /span>
zj<= /span>
zk<= /span>
•Description:=  
R= 26; = Since a cell dynamics is represented by its center, a mapping= closest to the center of an image can be found.
•
R= 26; This leads to non-uniform mapping time steps.
•
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Global Control Solution
Control
Velocity
Position
Intuitive Example:
<= span style=3D'color:#00279F'>Ø We will look for global solutions = u =3D f(x)
<= span style=3D'color:#00279F'>Ø Optimal (x*,u*) and bang-bang solutions
A
B
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file:///C:/A51BD64C/CellMapping4NonlinControl_files/slide0055.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Cell Mapping for Nonlinear Control
Optimal Control
Formulation:=
Me= thods of Solution:
Ø= Minimum Principle (MP)
Ø= Bellman’s Principle of Optimality (BPO) =
Ø= Hamilton-Jacobi-Bellman Equation (HJB)
Given
, find
such that
is minimized
while
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