Robust Sampling-Based Control for Elastic Lattices with Parameter Uncertainty

This work presents a sampling-based Quadratic Stability Control (QSC) framework for nonlinear mechanical systems with parametric uncertainty and compares it with a nominal Linear Quadratic Regulator (LQR). The proposed method synthesizes a single state-feedback gain by enforcing a common quadratic Lyapunov condition over a finite set of locally linearized models sampled in state and parameter space. A systematic numerical study evaluates the effects of the number of sampled models, state sampling radius, parameter uncertainty, and actuator configuration. Performance is assessed using trajectory mean-squared error, final position error, and offline controller-synthesis time. The results show that QSC has higher position error than nominal LQR at 5% uncertainty but lower error at 10% and 15% across five independently sampled designs, with greater force effort while maintaining comparable nominal performance. The common quadratic certificate covers the sampled models and their convex hull, not the full continuous nonlinear domain. These benefits are obtained at the cost of higher offline semidefinite-programming complexity.