Formation and Containment Control for High-order Linear by Xiwang Dong

By Xiwang Dong

This publication makes a speciality of research and layout difficulties for high-order linear time-invariant (LTI) swarm structures (multi-agent structures) to accomplish consensus, formation, containment and formation-containment. As a primary step, the thoughts of useful consensus and formation-containment are brought. not like earlier study, the formation during this publication could be time-varying. A basic framework for consensus, consensus monitoring, formation, containment and country formation-containment is gifted for the 1st time.

Sufficient/necessary and adequate stipulations, and ways to designing the protocols for swarm platforms to accomplish those regulate ambitions, are respectively proposed. independent time-varying formation experiments utilizing 5 quadrotor unmanned aerial automobiles (UAVs) are carried out in an outside surroundings to illustrate the theoretical results.

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1) is called controllable or (A, B) is controllable. 5 ([6]) If rank B, AB, . . , An−1 B = n, then (A, B) is controllable. 6 (Popov-Belevitch-Hautus (PBH) test for controllability [6]) If rank [s I − A, B] = n (∀s ∈ C), then (A, B) is controllable. 1) is called observable or (C, A) is observable. 7 ([6]) If rank C T , A T C T , . . , (An−1 ) C T observable. 8 (PBH test for observability [6]) If rank C T , s I − A T then (C, A) is observable. 1) is asymptotically stable. 1) is asymptotically stable; (ii) For any given positive matrix R, the Lyapunov function A T P + PA + R = 0 has positive definite solution P; (iii) There exists a positive definite matrix R such that the Lyapunov function A T P + PA + R = 0 has unique positive definite solution P; and (iv) There exists a positive definite matrix P such that A T P + PA < 0.

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