Sufficient conditions for the controllability of nonlinear distributed systems

For nonlinear distributed systems representable as a Volterra functional operator equation in a Lebesgue space, sufficient conditions for pointwise controllability with respect to a vector of non-linear functionals are proved. The controls are assumed to be piecewise constant vector functions. The reduction of controlled distributed systems to the functional operator equation under study is illustrated by two examples: a Dirichlet boundary value problem for the diffusion equation and a mixed problem for the transport equation.