Maximum principle for implicit control systems (Q1292207)

The paper studies the problem of minimizing a functional \(l(x(T))\) over the pairs of absolutely continuous functions \(x(t)\) and measurable controls \(u(t)\) that satisfy for almost all \(t \in [0,T]\) the constraints \(\varphi (\dot{x}(t), x(t), u(t)) \leq 0\), \(\psi (x(t), u(t)) \leq 0\), \(u(t) \in U\) and the initial condition \(x(0)=x_0.\) The optimal control problem is reduced to an equivalent nonsmooth variational problem.