This paper proposes a directional bounded-confidence variant of the discrete-time Vicsek multiagent model, in which pairwise heading alignment is modulated by a state-dependent, positive semidefinite matrix that independently gates orthogonal radial and tangential components in the instantaneous line-of-sight frame. We analyze the normalized, matrix-weighted system dynamics, proving a uniform non-vanishing bound on proposal vectors that guarantees global well-posedness across arbitrary network states. For local small-spread states under complete metric interaction, we prove linear geometric contraction of the heading diameter and establish an offline-verifiable spatial bootstrap condition that guarantees metric contact preservation and coincidence avoidance a priori. A counterexample demonstrates invariant polarized states on connected matrix graphs, delineating systemic structural limits. Numerical experiments against unfiltered Vicsek averaging, scalar tied confidence, trace-matched scalar baselines, and restricted-angle rules demonstrate component-selective filtering without rejected-channel leakage, along with improved fixed-bound alignment on multi-seed benchmarks across varying population densities.
This paper introduces a directional bounded-confidence extension of the Cucker--Smale (CS) flocking model that decomposes pairwise relative velocities into independent radial and tangential channels within the instantaneous line-of-sight frame. Gating these components via compactly supported kernels creates a time-varying, state-dependent, matrix-weighted interaction that strictly generalizes classical scalar CS alignment. We establish an exact energy-dissipation identity with conserved mean velocity and prove exponential velocity consensus under a sliding-window persistent excitation (PE) condition formulated directly on the disagreement subspace. Furthermore, we derive a CS bounded-diameter criterion separating metric decay from aggregate directional coercivity, along with a cluster convergence guarantee. Simulations validate the exact dissipation balance and demonstrate that directional gating successfully restores global alignment in scenarios where traditional isotropic tied-confidence laws remain polarized.