Advances in Reachability Analysis and Control of Nonlinear Systems

The field of nonlinear systems is moving towards the development of more efficient and accurate methods for reachability analysis and control. Researchers are exploring the use of neural networks, polyhedral enclosures, and constrained zonotopes to improve the analysis and control of these systems. Notably, innovative approaches such as certified approximate reachability and exact multiplication methods are being proposed to address the challenges of non-convex reachable sets. Furthermore, the integration of neural networks with advanced control techniques, such as model predictive control, is showing promising results. Noteworthy papers include:

  • Certified Approximate Reachability (CARe), which provides soundness guarantees on learned reachable sets of continuous dynamical systems.
  • Verifying Nonlinear Neural Feedback Systems using Polyhedral Enclosures, which proposes a novel algorithm for forward reachability analysis of nonlinear neural feedback systems.
  • Data-Driven Nonconvex Reachability Analysis using Exact Multiplication, which develops an exact multiplication method that preserves the non-convex geometry of reachable sets.

Sources

Algorithmic analysis of systems with affine input and polynomial state

Verifying Nonlinear Neural Feedback Systems using Polyhedral Enclosures

Certified Approximate Reachability (CARe): Formal Error Bounds on Deep Learning of Reachable Sets

An ANN-Enhanced Approach for Flatness-Based Constrained Control of Nonlinear Systems

Set-based state estimation of nonlinear discrete-time systems using constrained zonotopes and polyhedral relaxations

Data-Driven Nonconvex Reachability Analysis using Exact Multiplication

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