\documentstyle[11pt]{article} \textheight 24cm \textwidth 16cm \newcommand{\vt}{\vartheta} \newcommand{\cd}{\cdot} \begin{document} \title{Some Stable Algorithm for Solving Problems of Feedback Control and Reconstruction for Distributed Parameter Systems} \author{\it V.~I.~Maksimov} \date{ } \vbox{ \rule[-1.9cm]{0pt}{0pt} \maketitle } \thispagestyle{empty} The problems of control and reconstruction of disturbances for systems with distributed parameters are considered. The theory of these problems has been much studied. The approach based on the method of feedback control with a model developed by Ekaterinburg's school is discussed. This approach is characterized by the following two features: firstly, directedness to the work with nonlinear dynamical systems and, secondly, orientation to construction of such solving algorithms that are stable with respect to informational noises and computational errors. These algorithms are required to be dynamical. It means that they should work in real time'' and take into account only previous history of the process. Solving algorithms for two types of problems are constructed for new classes of nonlinear systems according to the approach mentioned above. Briefly, the essence of the problems under consideration may be formulated by the following way. A motion of dynamical system $\Sigma$ proceeds on a given time interval $T=[t_0,\vt]$. This system is described by a parabolic inclusion. Its trajectory $x(t)=x(t;u(\cd),v(\cd))$, $t \in T$ depends on a time-varying unknown input $v=v(t) \in Q \subset U_c$ and a control $u=u(t) \in P \subset U_c$. $P$ and $Q$ are given sets from space of controls $U_c$. One takes a uniform partition $\Delta = \{ \tau_i \}_{i=0}^m$ with diameter $\dl$. Phase states $x(\tau_i)$ are measured inaccurately at the moments $\tau_i$. The results of inaccurate measurements $\xi_i$ satisfy inequalities $\chi(\xi_i,x(\tau_i)) \le h$, $i \in [0:m-1]$, where $h$ is the value of level of informational noise, $\chi(\cd,\cd)$ is the criterion for accuracy of measurements. It is required to organize such process of control of system $\Sigma$ by feedback principle that allows to preserve given properties of its trajectory under the action of any admissible input $v=v(\cd)$. This is qualitative formulation of the control problems considered. However, sometimes a system may be uncontrollable. Its trajectory depends only on an unknown input $v=v(\cd)$. In this case we consider the problem of reconstruction of the input. \end{document} 