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VIDEO LIBRARY |
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Control of diffeomorphisms and densities A. A. Agrachevab a International School for Advanced Studies (SISSA) b Steklov Mathematical Institute of Russian Academy of Sciences, Moscow |
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Abstract: Consider a classical control system as it was deŻned by Pontryagin: \begin{equation} \dot x=f(x,u), \qquad x\in M, \quad u\in U, \tag{1} \end{equation} Assume that the state space We call controls the mappings \begin{equation} \dot x=f(x,\mathbf u(t,x)), \tag{2} \end{equation} which generates a family of diffeomorphisms Given an integral cost functional $$ J(u(\,\cdot\,))=\int_0^T\varphi(x(t),u(t))\,dt $$ and a probability measure $$ \mathbf J_\mu(\mathbf u)=\int_0^T\int_M\varphi(P_t(x),\mathbf u(t,x))\,d\mu\,dt $$ a functional on the space of controls In my talk, I am going to discuss the controllabilty and optimal control issues for the defined in this way systems on the group of diffeomorphisms. Language: English |