“…Theorem 2. Consider the position dynamics ( 5) under Assumption 1-3, design the ET-ATPP capturing control strategy ( 59) and (29) with collision avoidance term (25), if 𝜅 ρ0 > max i, j (|𝜌 i, j (0)|), 𝜅 𝜂 0 > max i, j (|𝜂 i, j (0)|), and 𝜄 3 > 𝓁 Ξ ρ , where 𝓁 Ξ ρ ∶= max i (Ξ 𝜌,i ), the performance constraints (49) and (50) for ρi (t ) and 𝜂 i (t ) can always be guaranteed for t ≥ 0. More specifically, ρi, j (t ), 𝜂 i, j (t ) and ̇ρ i, j (t ) ( j = 1, 2, 3) will converge to the stability regions 𝕌 ρ,i j , 𝕌 𝜂,i j , and 𝕌 ̇ρ,i j before the predefined duration T c .…”