Robust optimal control: low-error operation for the longest time

The problem of maximizing the time during which an open loop system can operate without exceeding a specified error bound is considered for linear systems that are subject to uncertainties about their parameters and their initial conditions, and whose operation is hampered by disturbance signals. The objective is to characterize an optimal input signal that keeps performance errors within specified bounds for the longest time. It is shown that such an input signal exists, and that it can be approximated by a bang-bang input signal without significantly affecting performance. Revised September 2009 1Department of Electrical Engineering, Indian Institute of Technology, Bombay Powai, Mumbai 400076, India 2Department of Electrical and Computer Engineering, University of Florida, Gainesville, FL 32611-6130, USA