A parabolic approach to the control of opinion spreading

We analyze the problem of controlling to consensus a nonlinear system modeling opinion spreading. We derive explicit exponential estimates on the cost of approximately controlling these systems to consensus, as a function of the number of agents N and the control time-horizon T. Our strategy makes use of known results on the controllability of spatially discretized semilinear parabolic equations. Both systems can be linked through time-rescalin

Minimal set of generators of controllability space for singular linear dynamical systems

Due to the significant role played by singular systems in the form E ¿ x ( t ) = Ax ( t ) , on mathematical modeling of science and engineering problems; in the last years recent years its interest in the descriptive analysis of its structural and dynamic properties. However, much less effort has been devoted to studying the exact con- trollability by measuring the minimum set of controls needed to direct the entire system E ¿ x ( t ) = Ax ( t ) to any desired state. In this work, we focus the study on obtaining the set of all matrices B with a minimal number of columns, by making the singular system E ¿ x ( t ) = Ax ( t ) + Bu ( t ) controllable.Postprint (author's final draft

Proximal Analysis and the Minimal Time Function of a Class of Semilinear Control Systems

The minimal time function of a class of semilinear control systems is considered in Banach spaces, with the target set being a closed ball. It is shown that the minimal time functions of the Yosida approximation equations converge to the minimal time function of the semilinear control system. Complete characterization is established for the subdifferential of the minimal time function satisfying the Hamilton–Jacobi–Bellman equation. These results extend the theory of finite dimensional linear control systems to infinite dimensional semilinear control systems

Transmutation operators as a solvability concept of abstract singular equations

One of the methods of studying differential equations is the transmutation operators method. Detailed study of the theory of transmutation operators with applications may be found in the literature. Application of transmutation operators establishes many important results for different classes of differential equations including singular equations with Bessel operato