SINGULAR CHARACTERISTICS OF THE HJBI EQUATION IN STATE CONSTRAINT OPTIMAL CONTROL PROBLEMS

摘要

For a state constraint optimal control problem the equations of motion along the constraint surface are derived in the form of singular characteristics which are given by an ODE system in closed form (no uncertain multipliers). A sufficient condition is found for the Bellman function's gradient to be a continuous adjoint vector in maximum principle. It is shown that the solution of the original problem can be composed from the solutions of two dynamic programming problems which provides an interpretation and new proof of the jump condition for the adjoint vector. An illustrative example is considered.