Robust Optimal Control with a Worst Case Time Domain Performance Criterion

In this paper, a method is described to design controllers by optimizing a worst case time domain performance index. This method directly maximizes a finite time ratio of weighted exogenous input energy to weighted energy error for the worst possible combination of commanded inputs, disturbances, and sensor noise. Robust performance can also be achieved by including the worst possible degradation of the performance index due to parameter variations and uncertainty. Extensions to non-linear and timevarying problems are possible, and neither the plant or the controller is required to be stable or minimum phase. In addition, this method synthesizes the worst possible case to verify it is a real possibility, and not just an idiosyncrasy of the mathematical design model. To demonstrate, several controllers are designed, including one for a six degree of freedom terrain following/terrain avoidance AFTI/F-16. The method is shown to be computationally intensive, but within the capabilities of desk-top workstations or high end PC´s.