We consider a projection-based model reduction approach to computing the maximal impact, one agent or a group of agents has on the cooperative system. As a criterion for measuring the agent-team impact on multi-agent systems, we use the $H_{\infty }$ norm, and output synchronization is taken as the underlying cooperative control scheme. We investigate a projection-based model reduction approach that allows efficient $H_{\infty }$ norm calculation. The convergence of this approach depends on initial interpolation points,...

Let $\left(z_{\nu }\right)$ be a sequence in the upper half plane. If $1\<p\le \infty$ and if$$y_{\nu }^{1/p}f(z_{\nu })=a_{\nu },\nu =1,2,...(*)$$has solution $f\left(z\right)$ in the class of Poisson integrals of $L^p$ functions for any sequence $(a_{\nu })\in {\ell }^p$, then we show that $\left(z_{\nu }\right)$ is an interpolating sequence for $H^{\infty }$. If $f(z_{\nu })=a_{\nu }$, $\nu =1,2,...$ has solution in the class of Poisson integrals of BMO functions whenever $(a_{\nu })\in {\ell }^{\infty }$, then $\left(z_{\nu }\right)$ is again an interpolating sequence for $H^{\infty }$. A somewhat more general theorem is also proved and a counterexample for the case $p\le 1$ is described.

Given information about a harmonic function in two variables, consisting of a finite number of values of its Radon projections, i.e., integrals along some chords of the unit circle, we study the problem of interpolating these data by a harmonic polynomial. With the help of symbolic summation techniques we show that this interpolation problem has a unique solution in the case when the chords form a regular polygon. Numerical experiments for this and more general cases are presented.

Se considera la interpolación de Hermite de funciones de una variable mediante polinomios generalizados. Se pretende mostrar que técnicas computacionales conocidas para interpolación polinómica se pueden aplicar también a interpolación mediante polinomios generalizados. Como aplicación se estudia con cierto detalle la interpolación mediante funciones racionales con polos prefijados. La interpolación polinómica corresponde al caso particular en que todos los polos prefijados están en el infinito.