Event-triggered sparse anchor-assisted residual-cancellation neurodynamics for moving KKT-path tracking in time-varying second-order cone optimization

Xu Wu; Juhe Sun; Li Wang; Yunlai Zhong; Xu Wu; Juhe Sun; Li Wang; Yunlai Zhong

doi:10.3934/math.20261368

AIMS Mathematics

2026, Volume 11, Issue 10: 35200-35237. doi: 10.3934/math.20261368

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Research article

Event-triggered sparse anchor-assisted residual-cancellation neurodynamics for moving KKT-path tracking in time-varying second-order cone optimization

1.
College of Artificial Intelligence, Shenyang Aerospace University, Shenyang 110136, China
2.
College of Science, Shenyang Aerospace University, Shenyang 110136, China

Received: 30 July 2026 Revised: 11 September 2026 Accepted: 23 September 2026 Published: 27 October 2026
MSC : 34D06, 65K05, 90C25, 90C30

This work developed an event-triggered sparse anchor-assisted residual-cancellation neurodynamic method for tracking the moving Karush–Kuhn–Tucker (KKT) path of time-varying strongly convex optimization problems with product second-order cone (SOC) constraints. The resulting continuous-time architecture is a zeroing neural network (ZNN)-type computational-intelligence framework for online conic optimization in time-varying engineering environments. The model was motivated by three-finger contact-force allocation, where quasi-static wrench balance and exact Coulomb friction constraints yield a strongly convex SOC program. A smoothed natural-residual (NR) KKT system was constructed to regularize cone complementarity and define a differentiable moving primal–dual path. A feedforward residual-cancellation law compensates for explicit temporal variation. An anchor tracks the residual-zero path, while replicated solver units exchange delayed state information and receive event-triggered Top-$ p $ sparse corrections. The Top-$ p $ rule gives an explicit coverage ratio without an additional sparse-coverage assumption. Under uniform residual regularity on a forward-invariant domain, bounded communication delays and implementation disturbances, and a computable impulsive-delay condition, local exponential anchor tracking and disturbance-dependent synchronization were established. The complete estimate separates delay-induced mismatch, implementation disturbance, anchor residual error, and smoothing bias. Experiments on three-finger grasping and four-contact force allocation demonstrated accurate moving-path tracking, a lower aggregate squared correction magnitude relative to matched periodic updates, and finite-horizon recovery across multiple solver-fault amplitudes, directions, and disturbance scenarios.
Citation: Xu Wu, Juhe Sun, Li Wang, Yunlai Zhong. Event-triggered sparse anchor-assisted residual-cancellation neurodynamics for moving KKT-path tracking in time-varying second-order cone optimization[J]. AIMS Mathematics, 2026, 11(10): 35200-35237. doi: 10.3934/math.20261368

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Abstract

This work developed an event-triggered sparse anchor-assisted residual-cancellation neurodynamic method for tracking the moving Karush–Kuhn–Tucker (KKT) path of time-varying strongly convex optimization problems with product second-order cone (SOC) constraints. The resulting continuous-time architecture is a zeroing neural network (ZNN)-type computational-intelligence framework for online conic optimization in time-varying engineering environments. The model was motivated by three-finger contact-force allocation, where quasi-static wrench balance and exact Coulomb friction constraints yield a strongly convex SOC program. A smoothed natural-residual (NR) KKT system was constructed to regularize cone complementarity and define a differentiable moving primal–dual path. A feedforward residual-cancellation law compensates for explicit temporal variation. An anchor tracks the residual-zero path, while replicated solver units exchange delayed state information and receive event-triggered Top-$ p $ sparse corrections. The Top-$ p $ rule gives an explicit coverage ratio without an additional sparse-coverage assumption. Under uniform residual regularity on a forward-invariant domain, bounded communication delays and implementation disturbances, and a computable impulsive-delay condition, local exponential anchor tracking and disturbance-dependent synchronization were established. The complete estimate separates delay-induced mismatch, implementation disturbance, anchor residual error, and smoothing bias. Experiments on three-finger grasping and four-contact force allocation demonstrated accurate moving-path tracking, a lower aggregate squared correction magnitude relative to matched periodic updates, and finite-horizon recovery across multiple solver-fault amplitudes, directions, and disturbance scenarios.

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