Quadratic BSDEs with random terminal time and elliptic PDEs in infinite dimension.
Motivated by digital communication channel, we consider the distributed output regulation problem for linear multi-agent systems with quantized state measurements. Quantizers take finitely many values and have an adjustable "zoom" parameter. Quantized distributed output regulation concerns designing distributed feedback by employing quantized technique for multi-agent systems such that all agents can track an active leader, and/or distributed disturbance rejection. With the solvability conditions...
We consider the Cauchy problem for nonlinear parabolic equations with functional dependence represented by the Hale functional acting on the unknown function and its gradient. We prove convergence theorems for a general quasilinearization method in natural subclasses of unbounded solutions.