A tracking problem is considered in the context of a class $𝒮$ of multi-input, multi-output, nonlinear systems modelled by controlled functional differential equations. The class contains, as a prototype, all finite-dimensional, linear, -input, -output, minimum-phase systems with sign-definite “high-frequency gain". The first control objective is tracking of reference signals by the output of any system in $𝒮$: given $\lambda \ge 0$, construct a feedback strategy which ensures that, for every (assumed...

We study existence and approximation of non-negative solutions of partial differential equations of the type 
 $${\partial }_{t}u-div\left(A(\nabla \left(f\left(u\right)\right)+u\nabla V)\right)=0\text{in}(0,+\infty )\times {ℝ}^n,(0.1)$$ where is a symmetric matrix-valued function of the spatial variable satisfying a uniform ellipticity condition, $f:[0,+\infty )\to [0,+\infty )$ is a suitable non decreasing function, $V:{ℝ}^n\to ℝ$ is a convex function. Introducing the energy functional $\phi \left(u\right)={\int }_{{ℝ}^n}F\left(u\left(x\right)\right)\mathrm{d}x+{\int }_{{ℝ}^n}V\left(x\right)u\left(x\right)\mathrm{d}x$, where is a convex function linked to by $f\left(u\right)=u{F}^{\text{'}}\left(u\right)-F\left(u\right)$, we show that is the “gradient flow” of with respect to the 2-Wasserstein distance between probability measures on the...