| Popis: |
This chapter applies interval reachability analysis to the problem of evaluating the robustness of a system against the effects of uncertain parameters. Specifically, we consider the volume of an interval reachable set as a continuous performance measure to gauge the robustness of a system, which can be used to guide the design of a robust controller. The volume of the interval over-approximation measures the effect of the parameter uncertainty on system trajectories starting in a given initial set: a smaller volume implies a smaller effect, and therefore, greater robustness. We illustrate this approach to robustness analysis on a medical exoskeleton model which has 6 states and 12 uncertain parameters. The dynamics of this system are too complicated to derive detailed system information such as bounds on the Jacobian matrix or growth bound functions, which precludes the use of the more efficient methods introduced in this book. Instead, we rely on the computationally expensive but widely applicable sampling-based methods on sampled-data mixed monotonicity and the Monte Carlo approach. |
