Investigation of worst-case errors when inputs and their rate of change are bounded

The worst-case error analysis is extended to include the problem of bounded input
r(t)
and its rate of change
dr/dt
for a a dynamical system described by a set of differential equations with separable forcing function. The problem is reformulated as a bounded-input, bounded-state variable problem, and Pontryagin's Maximum Principle is applied to maximize a given error function. For a wide class of systems, the time derivative of the worst forcing function is shown to be "bang-bang" for the open region defined by the constraint of
r(t)
and zero on its boundary. A computational algorithm is developed to solve the resulting two-point boundary value problem.