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The philosophy of the extremal disturbance analysis for dynamical systems with uncertain inputs is described. This analysis involves solving optimal control problems in which the time histories of the inputs (external disturbances) are regarded as the control functions and a response measure of the system serves as the performance index. The performance index should be maximized or minimized over the disturbances within a prescribed class. Often this class is specified by lower and upper bounds (a corridor) between which the values of the disturbance must lie. The maximization and minimization problems are referred to as the worst disturbance and best disturbance problems, respectively. The solutions of these problems provide the extreme values between which the response measure lies for any disturbance from the specified class. The extremal disturbance analysis is important, in particular, when designing standards for testing devices for the protection of fragile objects from impact loads. This approach is illustrated for a single-degree-of-freedom system that can be regarded as a simplified model of the equipment for sled tests of automobile restraint systems

Extremal disturbance analysis for dynamical systems with uncertain input