Robust Stability of Neural-Network Controlled Nonlinear Systems with Parametric Variability

• URL: http://arxiv.org/abs/2109.05710v1
• Date: Mon, 13 Sep 2021 05:09:30 GMT
• Title: Robust Stability of Neural-Network Controlled Nonlinear Systems with Parametric Variability
• Authors: Soumyabrata Talukder, Ratnesh Kumar
• Abstract summary: We develop a theory for stability and stabilizability of a class of neural-network controlled nonlinear systems. For computing such a robust stabilizing NN controller, a stability guaranteed training (SGT) is also proposed.
• Score: 2.0199917525888895
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Stability certification and identification of the stabilizable operating region of a system are two important concerns to ensure its operational safety/security and robustness. With the advent of machine-learning tools, these issues are specially important for systems with machine-learned components in the feedback loop. Here we develop a theory for stability and stabilizability of a class of neural-network controlled nonlinear systems, where the equilibria can drift when parametric changes occur. A Lyapunov based convex stability certificate is developed and is further used to devise an estimate for a local Lipschitz upper bound for a neural-network (NN) controller and a corresponding operating domain on the state space, containing an initialization set from where the closed-loop (CL) local asymptotic stability of each system in the class is guaranteed under the same controller, while the system trajectories remain confined to the operating domain. For computing such a robust stabilizing NN controller, a stability guaranteed training (SGT) algorithm is also proposed. The effectiveness of the proposed framework is demonstrated using illustrative examples.

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