Worst case analysis of nonlinear systems

The authors work out a framework for evaluating the performance of a continuous-time nonlinear system when this is quantified as the maximal value at an output port under bounded disturbances-the disturbance problem. This is useful in computing gain functions and L _∞-induced norms, which are often used to characterize performance and robustness of feedback systems. The approach is variational and relies on the theory of viscosity solutions of Hamilton-Jacobi equations. Convergence of Euler approximation schemes via discrete dynamic programming is established. The authors also provide an algorithm to compute upper bounds for value functions. Differences between the disturbance problem and the optimal control problem are noted, and a proof of convergence of approximation schemes for the control problem is given. Case studies are presented which assess the robustness of a feedback system and the quality of trajectory tracking in the presence of structured uncertainty