Control of dynamics of systems with space and time integral models (Q1407163)

The dependence of outputs on actions distributed in a domain and concentrated on its boundaries is studied. The basic domain \(S\) is given in the space-time coordinate system and contains a finite set of subdomains \(\{S_n \}\) bounded by the contours \(\{\gamma_n\}\). The dependence of the output vector function \(y(s)\) is imposed on the control input \(n(s)\) in the domain \(S_* =S \setminus\cup^N_{n=1}S_n\) and on some boundary conditions \(Y^n_r(s^n_r)\), \(s^n_r \in \gamma_n\), \(r=1,\dots,R_n\), using a linear integral operator and correspondingly a linear first-order differential operator. The construction of \(y(s)\) for given \(n(s)\) and \(Y_r^n(s^n_r)\) was considered by the first author in a previous paper. Here, the analysis is focussed on the inverse problem: find the inputs \(n(s)\) and \(Y^n_r(s^n_r)\) such that the values of the output vector function \(y(s)\), \(s\in S_*\), are approached in the best way according to some associated minimization problem.