Index
C1, 8
C2, 8
D1, 8
abnormal case, 172, 177
acceleration
due to gravity, 2, 27, 34
accessory equation, 59
action integral, 26
admissible, 8, 127, 136
admissible control, see control
admissible extremal, see extremal
admissible variation, see variation
augmented state, 142, 168–176
bang-bang control, see control
beaver population, 218
Bernoulli, John, 1
biotechnical productivity, 206, 211,
216
brachistochrone problem, 1, 25,
30–32, 56, 109
branch cut, 105
broken extremal, see extremal
calculus of variations, 1, 9, 127,
131, 134, 146
cancer chemotherapy, 163–166
carrying capacity, 129, 204
catchability, 129, 204
catenary, 221
Chaplygin’s problem, 190–193
circle, 87, 123
co-state
equations, 140, 142, 160
variable, 140
vector, 142
adjusted, 176
modified, 175
cone of attainability, 172
conjugate point, 59–65, 115
constrained optimization, 124–126
control
admissible, 136, 146, 154, 164
bang-bang, 131, 144, 155
feedback, 146, 152, 166, 187, 18
209
open-loop, 146
optimal, 136–142, 146, 152, 154
existence of, 216, 219
synthesis of, 146, 151–157
piecewise-continuous, 167
singular, 144, 159–162, 208–215
time-optimal, 149–151, 183–189
controllability, 154–155
convex
combination, 167
subset, 167
corner, 8, 23, 36, 41
condition
first, 38, 45, 47, 147
24
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