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

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