Optimal controls and their discontinuities in quadratic problems of delay systems

We construct and study quadratic optimal controls in delay systems of neutral type. In these systems we allow functional lags in the derivative, the state, the control, and in the cost index. We point out that, typically, optimal controls of time lag systems are discontinuous: discontinuities might occur as a consequence of delays in the control action and of the neutrality of the system. We exhibit computed examples of jumps in optimal controls whose origins are in each of the two types. Our techniques are based on the method of steps which we generalize to fit systems with functional lags. The work includes an analysis of controllability in time lag systems.