Amir Modares

Amir Modares, Bahare Kiumarsi, Hamidreza Modares

This paper develops a data-driven safe control framework for nonlinear discrete-time systems with parametric uncertainty and additive disturbances. The proposed approach constructs a data-consistent closed-loop representation that enables controller synthesis and safety certification directly from data. Unlike existing methods that treat unmodeled nonlinearities as global worst-case uncertainties using Lipschitz bounds, the proposed approach embeds nonlinear terms directly into the invariance conditions via a geometry-aware difference-of-convex formulation. This enables facet- and direction-specific convexification, avoiding both nonlinearity cancellation and the excessive conservatism induced by uniform global bounds. We further propose a vertex-dependent controller construction that enforces convexity and contractivity conditions locally on the active facets associated with each vertex, thereby enlarging the class of certifiable invariant sets. For systems subject to additive disturbances, disturbance effects are embedded directly into the verification conditions through optimized, geometry-dependent bounds, rather than via uniform margin inflation, yielding less conservative robust safety guarantees. As a result, the proposed methods can certify substantially larger safe sets, naturally accommodate joint state and input constraints, and provide data-driven safety guarantees. The simulation results show a significant improvement in both nonlinearity tolerance and the size of the certified safe set.

Amir Modares, Zhen Zhang, Themistoklis Charalambous et al.

This paper develops a data-driven reachability framework for linear systems whose disturbances are modeled by probabilistic zonotopes (PZs), combining bounded deterministic and Gaussian stochastic components. In contrast to methods that require a precisely known disturbance model (either purely deterministic or purely stochastic), we assume only a conservative prior PZ and refine it from data. The framework separates two uncertainty sources: realized disturbances, which act along the collected trajectory and govern the size of the data-consistent model set, and aleatory disturbances, which enter as future additive uncertainty during reachable-set propagation; both shape the reachable sets, but through different mechanisms. Refinement exploits prior system knowledge together with trajectory-consistency constraints induced by the data, which impose affine couplings between deterministic and Gaussian latent variables. We accordingly develop a constrained-PZ calculus that absorbs the stochastic part of these constraints into an equivalent representation, removes infeasible latent directions, and reduces stochastic covariance, together with identification-aware fusion rules for combining heterogeneous constrained-PZ descriptions. The refined realized-disturbance proxies then serve as scenarios in a linear program that learns the smallest translated and scaled copy of the prior disturbance set that contains all proxy confidence sets while remaining nested in the prior. The resulting deterministic, high-probability reachable sets carry formal containment guarantees with substantially reduced conservatism, and numerical examples confirm that the pipeline tightens both the data-consistent model set and the propagated reachable sets.