Abstract
This paper proposes a new notion of robust invertibility for nonlinear dynamical systems, and introduces constructive parameterizations of recurrent neural network which are robustly invertible by design. We define robust invertibility as the existence of a causal inverse system such that both the forward and inverse systems are contracting and have bounded incremental input-output gains (the system is bi-Lipschitz), implying that both forward prediction and input reconstruction are robust to signal perturbations and initial-state mismatch. We construct robustly invertible recurrent models via series composition of static orthogonal layers and dynamic layers satisfying a strong input-output monotonicity property, and provide a differentiable neural network parameterizations in the form of the bi-Lipschitz recurrent equilibrium network (BiLipREN). Additionally, composition with dynamic orthogonal layers yields a nonlinear minimum-phase/all-pass (a.k.a. inner--outer) factorization. We illustrate the utility of the framework through a series of application examples in data-driven internal model control, dynamic surrogate loss learning, and signal-space normalizing flows, illustrating its utility for robust control, trajectory optimization, and generative modeling of complex trajectory distributions.
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Aug 5, 2026eess.SY
In this paper, we address the certification of datadriven feedforward control for periodic tracking of unknown nonlinear systems under partial state measurements. To this end, we adopt an invertible neural network (INN) as a surrogate for the unknown system. This choice allows us to bypass solving a nonconvex inversion problem, eliminating the associated inversion errors and reducing tracking error certification to a surrogate modeling problem. We then apply conformal prediction to provide finite-sample probabilistic guarantees on the surrogate modeling error which, through the derived tracking error bound, yield marginal certificates on feedforward tracking error. Finally, we demonstrate the approach on a DC-motor-driven mechanical load with nonlinear friction.
Berk Altiner, Rajasree Sarkar, Arunava Banerjee +2
Jul 15, 2026cs.LG
We investigate conditional invertible neural networks (cINNs) as probabilistic inverse-dynamics models for multirotor control. For a planar X8 coaxial multicopter, we learn
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Christian Wittke, Stephan Myschik, Oliver Niggemann
Aug 2, 2024cs.LG
We propose a framework for training neural network controllers with certified robust forward invariant polytopes. First, we parameterize a family of lifted control systems in a higher dimensional space, where the original neural controlled system evolves on an invariant subspace of each lifted system. We use interval analysis and neural network verifiers to further construct a family of lifted embedding systems, carefully capturing the knowledge of this invariant subspace. If the vector field of any lifted embedding system satisfies a sign constraint at a single point, then a certain convex polytope of the original system is robustly forward invariant. Treating the neural network controller and the lifted system parameters as variables, we propose an algorithm to train controllers with certified forward invariant polytopes in the closed-loop control system. Through two examples, we demonstrate how the simplicity of the sign constraint allows our approach to scale with system dimension to over
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