On “discontinuous” continuity equation and impulsive ensemble control

Impulsive control of nonlocal transport equations

“…Together with [36], this article presents a "gentleman's set" of very basic results for optimal impulsive control of distributed multi-agent systems.…”

“…control theory, first adapted to the framework of transport equations in [36]. Such a reparameterization reduces system (S), driven by an "unbounded" vector field v, to an auxiliary PDE, actuated by another control-affine vector field w with geometrically constrained inputs.…”

“…The following definition, extending [36], is an infinite-dimensional version of the notion [29] of generalized solution to a control system:…”

“…The forthcoming construction of a desired relaxation relies on the discontinuous time reparameterization technique [29], which is a standard workhorse of the finite-dimensional impulsive control theory, first adapted to the framework of transport equations in [36]. Such a reparameterization reduces system (S), driven by an "unbounded" vector field v, to an auxiliary PDE, actuated by another control-affine vector field w with geometrically constrained inputs.…”

On Nonlinear Forced Impulsive Differential Equations under Canonical and Non-Canonical Conditions

“…In general, it is well-known that several natural phenomena are driven by impulsive differential equations. Examples of the aforementioned phenomena are related to population dynamics, biological and mechanical systems, pharmacokinetics, biotechnological processes, theoretical physics, chemistry, control theory [5,6] and engineering. Another interesting application is in some vibrational problems [1].…”