Application of a Parameter Robust Game Theoretic Controller to the Benchmark Problem

A new control algorithm based upon worst case design in which the uncertain parameters are explicitly included as adversaries is tested on the benchmark problem. The system matrices are assumed to be a function of the uncertain parameters. Both the uncertain parameters and the initial states are assumed to lie in sets defined by ellipsoids. The time-invariant, infinite-time version of this control with partial informaton is used. The algorithm for determining the control gains requires an iterative process between the solution of an algebraic Riccati equation, an algebraic Lyapunov equation and the saddle point initial state. Global necessary and sufficient conditions indicate the precise set of initial states and uncertain parameters for which the saddle point inequality will hold. This region guarentees performance robustness and is included in a larger set that guarentees stability robustness. The three parameter uncertainties for the benchmark problem are the two masses and the spring constant. For large enough ellipsoid uncertainty bounds, there appears two saddle point solutions. The saddle that is choosen produces the largest regions of performance and stability robustness.