One of the “practical” problems of control theory motivated primarily by environmental studies consists, loosely speaking, in the following.
x.=f(t,x,ω),τ⩽t⩽θ

with “input variables” x (τ) = x 0; ω(•) = ω(θ + σ), τ - θ ≤ σ ≤ 0. These are restricted by inequalities
hj(x0)⩽μj,j=1,...,p

gs(ω(∙))⩽βs,s=1,...,q

. Also given are the constraints on system trajectories — the “outputs” x(•) = x(θ + σ), τ - θ ≤ σ ≤ 0, i.e.
φi(x(∙))⩽υi,i=1,...,k