## Topics in OptimizationMathematics in Science and Engineering, Volume 31: Topics in Optimization compiles contributions to the field of optimization of dynamical systems. This book is organized into two parts. Part 1 covers reported investigations that are based on variational techniques and constitute essentially extensions of the classical calculus of variations. The contributions to optimal control theory and its applications, where the arguments are primarily geometric in nature, are discussed in Part 2. This volume specifically discusses the inequalities in a variational problem, singular extremals, mathematical foundations of system optimization, and synthesis of optimal controls. This publication is recommended for both theoreticians and practitioners. |

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admissible control assume assumption B-subarc belongs bound vector boundary conditions calculus of variations comp cone conic neighborhood consider const constant constraints continuous function control function control variable convex sets corner condition Corollary corresponding curve defined definition denote derivatives determined differential equations Euclidean space Euler equations exists extremal extremaloid finite follows function f(x given grad gradient Halkin Hence implies inequality initial conditions integral interior point interval Lagrange multipliers Lemma limiting surface linear matrix maximum principle minimizing multiplier rule necessary condition neighborhood normal obtain open ball optimal control optimal control problem optimal trajectory optimum problems orbital parameter piecewise continuous plane Pontryagin's maximum principle positive number proof properties real numbers refraction region relation result satisfied scalar separating hyperplane singular subarc ſº space subset tangent Theorem thrust vector valued function zero