## Advances in Nonlinear Dynamics and Control: A Report from Russia: A Report from RussiaThis work presents overviews of Soviet research on nonlinear dynamics, particularly as applied to uncertain systems in a deterministic setting. The book concentrates on the three main branches of uncertain dynamics: differential games; evolution, estimation and control; and robust stabilization. |

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### Contents

The Decomposition of Controlled Dynamic Systems | 1 |

A Differential Game for the Minimax of a Positional Functional | 41 |

Global Methods in Optimal Control Theory | 74 |

On the Theory of Trajectory Tubes A Mathematical Formalism for Uncertain Dynamics Viability and Control | 122 |

A Theory of Generalized Solutions to FirstOrder PDEs with an Emphasis on Differential Games | 189 |

Adaptivity and Robustness in Automatic Control Systems | 230 |

### Other editions - View all

Advances in Nonlinear Dynamics and Control: A Report from Russia Alexander B. Kurzhanski Limited preview - 2012 |

Advances in Nonlinear Dynamics and Control: A Report from Russia Alexander B. Kurzhanski No preview available - 2012 |

### Common terms and phrases

adaptive systems algorithms assume assumptions Avtomat bounding function calculation Cauchy problem characteristic polynomial consider constraints construction continuous function control synthesis control systems control theory convex convex hull crossections defined denote differential equation differential games differential inclusion disturbance dynamic systems equality estimate evolution equation exists feedback control formulation given global Hamilton-Jacobi equation Hamiltonian inclusion 3.6 inequality instant interval plant Krasovskii Krotov V.F. Kurzhanski Lemma linear Lipschitz lower minimax solution lower semicontinuous Math matrix method method of characteristics motion multivalued function Nauka nonlinear obtain optimal trajectory parameter polynomial G(q predictor polynomial problem 7.1 proof properties proved Pu(q resp respect robust nominal system robust stability Russian satisfies the condition Section semicontinuous sequence set-valued solving functions stochastic stochastic programs strategy Subbotin sufficient conditions Suppose switching curve Theorem tion trajectory tubes u-stability upper minimax solution variable variational calculus vector viability viable trajectory viscosity solutions