Adaptive RBFNN Control of Uncertain Bilateral Teleoperation Systems with Delay-Dependent LMI Stability Conditions
arXiv:2608.20182
2026
Dynamics
2 ideas extracted · analyzed Sep 1, 2026
What the math gives to ML
The paper provides a transferable mechanism for delayed neural dynamical systems: a Lyapunov–Krasovskii functional combines current-state energy, adaptive-estimation error, and integrals over delayed states, while free-weighting-matrix LMIs certify delay-dependent ultimate boundedness. Its second useful construction is dimensionality-independent robust adaptation: two scalar sigma-modified estimates bound aggregate neural approximation and disturbance errors instead of adapting one parameter per RBF basis function. The strongest neural-network applications are delayed RNNs, state-space models, and learned controllers, where delay margins and robust residual gains can be tested quantitatively.
Ideas from this paper
✗ Failed on benchmark
2026
Treat hidden-state communication, stale activation caches, or asynchronous distributed updates as bounded delays and impose a delay-dependent Lyapunov–Krasovskii certificate on the recurrent Jacobian. The network is accepted only when an LMI is feasible for the measured or conservatively bounded delay, producing an explicit maximum-delay prediction rather than relying only on empirical stability.
Useful7/10
Difficulty7/10
Novelty7/10
Unverified
2026
Add two scalar adaptive gains to a neural controller or learned dynamical model: one estimates the unknown norm of the ideal neural approximation weights, and the other estimates the combined approximation, friction, and disturbance envelope. Sigma modification prevents unbounded gain growth, while the robust residual correction uses only these scalar estimates, independent of the number of neural features.
Useful6/10
Difficulty5/10
Novelty6/10