Advances in Nonlinear Dynamics and Control: A Report from Russia: A Report from RussiaThe purpose of this volume is to present a coherent collection of overviews of recent Russian research in Control Theory and Nonlinear Dynamics written by active investigators in these fields. It is needless to say that the contribution of the scientists of the former Soviet Union to the development of nonlinear dynamics and control was significant and that their scientific schools and research community have highly evolved points of view, accents and depth which complemented, enhanced and sometimes inspired research directions in the West. With scientific exchange strongly increasing, there is still a consider able number of Eastern publications unknown to the Western community. We have therefore encouraged the authors to produce extended bibliogra phies in their papers. The particular emphasis of this volume is on the treatment of uncer tain systems in a deterministic setting-a field highly developed in the former Soviet Union and actively investigated in the West. The topics are concentrated around the three main branches of un certain dynamics which are the theory of Differential Games, the set membership approach to Evolution, Estimation and Control and the the ory of Robust Stabilization. The application of these techniques to non linear systems as well as the global optimization of the latter are also among the issues treated in this volume. |
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 bounding function calculation Cauchy problem characteristic polynomial consider constraints construction continuous function control synthesis control systems control theory convex crossections defined denote differential equation differential games differential inclusion disturbance dynamic systems equality estimate evolution equation exists feedback control function R(t given Hamilton-Jacobi Hamilton-Jacobi equation inclusion 3.6 inequality instant interval plant Krotov V.F. Kurzhanski Lemma linear Lipschitz lower semicontinuous Math matrix method method of characteristics motion Nauka nonlinear obtain optimal control optimal trajectory p₁ parameter position predictor polynomial problem 7.1 proof properties proved Pu(q resp respect robust nominal system robust stability robustly nominal Russian satisfies the condition Section semicontinuous sequence set-valued solving functions stochastic stochastic programs strategy sufficient conditions switching curve t₁ Theorem tion trajectory tubes u(xo variational calculus vector viability viable trajectory viscosity solutions x(to x[ti x₁