## Optimal Control of Mechanical OscillationsThis book explores two important aspects of the optimal control of oscillatory systems: the initiation of optimal oscillatory regimes and control possibilities for random disturbances. The main content of the book is based upon assertions of the optimal control theory and the disturbance theory. All theoretical propositions are illustrated by examples with exact mechanical context. An appendix covers the necessary mathematical prerequisites. |

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

introduction | 1 |

Change Periodic Green Function of the Second Kind | 20 |

Periodic Control for Vibroimpact Systems | 65 |

Copyright | |

6 other sections not shown

### Other editions - View all

### Common terms and phrases

admissible controls analogous asymptotic asymptotically stable averaged system averaging method boundary conditions characteristics coefficients components conditions of Theorem considered constraints continuous with respect control u(t converges coordinates degree of freedom depend determined by Eq deterministic discontinuity conditions disturbed system domain dynamic programming estimate exists expected value finite follows formulated Fourier series holds true impact conditions impact impulse initial conditions integral equations interval Ito's Lagrange multiplier Let us construct linear system Markov process matrix minimizing the functional Moscow motion equations movement non-linear one-impact one-sided limiter optimal control optimal control problem periodic Green's function periodic regime periodic solution phase program control random disturbances random process reduced resonant satisfy conditions satisfy the conditions Section small parameter solution of Eq spectral densities standard form stationary solution stochastic differential equations striking element Substituting Suppose symmetric T-periodic tion trajectories uniformly with respect variables vector velocity vibroimpact systems white noise Wiener process