Optimal control problems for singular systems

Abstract

Singular systems of the form E[xdot] = ƒ(x,u,t) are considered, where E is a square matrix and may be singular. It is assumed that for any ‘admissible’ initial state x(t 0), any control u(t) ∊ U yields one and only one continuous state x(t), and there is one and only one continuous adjoint state λ(t). The formulae for functional variation are derived; the necessary condition for optimality—the maximum principle—is obtained; the boundary conditions for the adjoint equations of the singular systems are given; and the necessary and sufficient condition for optimality of linear singular systems is derived.