## Computation of optimal controls within a class of piecewise continuous functions |

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### Contents

First Variational Analysis | 6 |

Second Order Algorithms | 36 |

Analytic Example | 53 |

17 other sections not shown

### Common terms and phrases

admissibility condition admissible 6u admissible extremal admissible perturbations Algorithm arithmetic was approximately assumed auxillary behavior class of piecewise CM CM complete reachability constraint multipliers continuous functions control constraints control inequality constraints Control trajectories control vector iteration costate equation dead zone defined differential equations double precision Dyer and McReynolds dynamic programming effective constraints evaluated exists feedback control laws Figure fixed time base given in Table imposed incremental state equation iteration methods Lagrange multiplier Legendre transformation linear matrix Maximum Principle nonsingular null space obtained optimal control performance index performance Lagrangian piecewise constant control piecewise continuous functions precision arithmetic quadratic rH CM rH rH rH satisfied second variation space of piecewise stationarity straint strengthened Legendre condition strictly positive subinterval sufficiency conditions switching locations switching sequence terminal constraints terminal error terminal tangent space tion Tk+1 trajectories for trial trial 2b weak relative minimum