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, 189, 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, 147 249

Purchased from American Mathematical Society for the exclusive use of nofirst nolast (email unknown) Copyright 2009 American Mathematical Society. Duplication prohibited. Please report unauthorized use to cust-serv@ams.org. Thank You! Your purchase supports the AMS' mission, programs, and services for the mathematical community.