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E-raamat: Iterative Dynamic Programming [Taylor & Francis e-raamat]

(University of Toronto, Toronto, Ontario, Canada)
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Iterative Dynamic ProgrammingSuurem pilt
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Raamatu kodulehekülg: https://www.taylorfrancis.com/books/9780429123641
Brings together results of work carried out by the author and others, previously available only in scattered journal articles, along with insights that led to the development of iterative dynamic programming (IDP). Provides necessary background, then examines the effects of the parameters involved and illustrates IDP's advantages. Contains chapters on allowable values for control, piecewise linear control, time-delay systems, and state constraints. Appendices offer computer code. Of interest to applied mathematicians and theoretical physicists, as well as computer science engineers. Luus is professor of chemical engineering at the University of Toronto, Canada. Annotation c. Book News, Inc., Portland, OR (booknews.com)

Dynamic programming is a powerful method for solving optimization problems, but has a number of drawbacks that limit its use to solving problems of very low dimension. To overcome these limitations, author Rein Luus suggested using it in an iterative fashion. Although this method required vast computer resources, modifications to his original scheme have made the computational procedure feasible.
With iteration, dynamic programming becomes an effective optimization procedure for very high-dimensional optimal control problems and has demonstrated applicability to singular control problems. Recently, iterative dynamic programming (IDP) has been refined to handle inequality state constraints and noncontinuous functions.
Iterative Dynamic Programming offers a comprehensive presentation of this powerful tool. It brings together the results of work carried out by the author and others - previously available only in scattered journal articles - along with the insight that led to its development. The author provides the necessary background, examines the effects of the parameters involved, and clearly illustrates IDP's advantages.
Fundamental concepts
1(35)
Introduction
1(1)
Fundamental definitions and notation
2(5)
Operator
2(1)
Vectors and matrices
3(2)
Differentiation of a vector
5(1)
Taylor series expansion
5(1)
Norm of a vector
6(1)
Sign definite
6(1)
Stationary and maxima (minima) points
7(1)
Steady-state system model
7(1)
Continuous-time system model
7(1)
Discrete-time system model
8(2)
The performance index
10(1)
Interpretation of results
11(1)
Examples of systems for optimal control
11(6)
Linear gas absorber
11(2)
Nonlinear continuous stirred tank reactor
13(2)
Photochemical reaction in CSTR
15(1)
Production of secreted protein in a fed-batch reactor
16(1)
Solving algebraic equations
17(15)
Separation of the equations into two groups
18(1)
Numerical examples
19(12)
Application to multicomponent distillation
31(1)
Solving ordinary differential equations
32(1)
References
32(3)
Steady-state optimization
35(32)
Introduction
35(1)
Linear programming
35(9)
Example -- diet problem with 5 foods
38(4)
Interpretation of shadow prices
42(2)
LJ optimization procedure
44(20)
Determination of region size
46(2)
Simple example -- 5 food diet problem
48(1)
Model reduction example
48(6)
Parameter estimation
54(4)
Handling equality constraints
58(6)
References
64(3)
Dynamic programming
67(14)
Introduction
67(1)
Examples
67(13)
A simple optimal path problem
68(1)
Job allocation problem
69(3)
The stone problem
72(1)
Simple optimal control problem
73(2)
Linear optimal control problem
75(1)
Cross-current extraction system
76(4)
Limitations of dynamic programming
80(1)
References
80(1)
Iterative dynamic programming
81(10)
Introduction
81(1)
Construction of time stages
82(1)
Construction of grid for x
82(1)
Allowable values for control
82(1)
First iteration
82(2)
Stage P
83(1)
Stage P -- 1
83(1)
Continuation in backward direction
83(1)
Iterations with systematic reduction in region size
84(1)
Example
85(1)
Use of accessible states as grid points
85(1)
Algorithm for IDP
86(3)
Early applications of IDP
89(1)
References
90(1)
Allowable values for control
91(8)
Introduction
91(1)
Comparison of uniform distribution to random choice
92(6)
Uniform distribution
93(1)
Random choice
94(4)
References
98(1)
Evaluation of parameters in IDP
99(20)
Introduction
99(1)
Number of grid points
100(6)
Bifunctional catalyst blend optimization problem
100(4)
Photochemical CSTR
104(2)
Multi-pass approach
106(3)
Nonlinear two-stage CSTR system
107(2)
Further example
109(8)
Effect of region restoration factor η
111(1)
Effect of the region contraction factor γ
112(1)
Effect of the number of time stages
112(5)
References
117(2)
Piecewise linear control
119(20)
Introduction
119(1)
Problem formulation
119(1)
Algorithm for IDP for piecewise linear control
120(2)
Numerical examples
122(16)
Nonlinear CSTR
122(2)
Nondifferentiable system
124(2)
Linear system with quadratic performance index
126(10)
Gas absorber with a large number of plates
136(2)
References
138(1)
Time-delay systems
139(10)
Introduction
139(1)
Problem formulation
140(1)
Examples
140(8)
Example 1
140(2)
Example 2
142(1)
Example 3 -- Nonlinear two-stage CSTR system
143(5)
References
148(1)
Variable stage lengths
149(28)
Introduction
149(6)
Variable stage-lengths when final time is free
155(2)
IDP algorithm
156(1)
Problems where final time is not specified
157(8)
Oil shale pyrolysis problem
158(3)
Modified Denbigh reaction scheme
161(4)
Systems with specified final time
165(10)
Fed-batch reactor
168(7)
References
175(2)
Singular control problems
177(22)
Introduction
177(1)
Four simple-looking examples
178(13)
Example 1
178(3)
Example 2
181(6)
Example 3
187(1)
Example 4
188(3)
Yeo's singular control problem
191(2)
Nonlinear two-stage CSTR problem
193(4)
References
197(2)
State constraints
199(38)
Introduction
199(1)
Final state constraints
199(25)
Problem formulation
199(1)
Quadratic penalty function with shifting terms
200(18)
Absolute value penalty function
218(5)
Remarks on the choice of penalty functions
223(1)
State inequality constraints
224(10)
Problem formulation
224(1)
State constraint variables
225(9)
References
234(3)
Time optimal control
237(18)
Introduction
237(1)
Time optimal control problem
237(1)
Direct approach to time optimal control
238(1)
Examples
239(12)
Example 1: Bridge crane system
239(2)
Example 2: Two-link robotic arm
241(2)
Example 3: Drug displacement problem
243(3)
Example 4: Two-stage CSTR system
246(3)
Example 5
249(2)
High dimensional systems
251(2)
References
253(2)
Nonseparable problems
255(10)
Introduction
255(1)
Problem formulation
255(1)
Examples
256(8)
Example 1 -- Luus-Tassone problem
256(8)
Example 2 -- Li-Haimes problem
264(1)
References
264(1)
Sensitivity considerations
265(8)
Introduction
265(2)
Example: Lee-Ramirez bioreactor
267(5)
Solution by IDP
268(4)
References
272(1)
Toward practical optimal control
273(10)
Introduction
273(1)
Optimal control of oil shale pyrolysis
274(4)
Future directions
278(4)
References
282(1)
A Nonlinear algebraic equation solver 283(4)
Program listing
283(2)
Output of the program
285(2)
B Listing of linear programming program 287(4)
Main program for the diet problem
287(1)
Input subroutine
288(1)
Subroutine for maximization
289(1)
Output subroutine
290(1)
C LJ optimization programs 291(6)
Five food diet problem
291(2)
Model reduction problem
293(2)
Geometric problem
295(2)
D Iterative dynamic programming programs 297(18)
CSTR with piecewise constant control
297(6)
IDP program for piecewise linear control
303(5)
IDP program for variable stage lengths
308(7)
E Listing of DVERK 315(6)
DVERK
315(6)
Index 321
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