Semi‐global containment control for linear systems in the presence of actuator position and rate saturation

Abstract

Summary This paper studies the semi‐global containment control problem for a group of general linear systems in the presence of actuator position and rate saturation. Both a state feedback containment control algorithm and an output feedback containment algorithm are constructed for each follower agent in the system by using low gain approach. We show that the states of all follower agents will converge to the convex hull formed by the leader agents asymptotically under these control algorithms when the communication topology among follower agents is a connected undirected graph and each leader agent is a neighbor of at least one follower agent. Simulation results illustrate the theoretical results.

Exponential bipartite synchronization of random signed networks with Markovian switching via impulsive control

“…The dotted lines divide signed digraphs into two structurally balanced parts. And the corresponding weights are given as follows state 1 d (1) 2,1 = d (1) 8,7 = d (1) 11,4 = 0.02; d (1) 3,2 = d (1) 7,6 = d (1) 11,10 = 0.0109; d (1) 8,1 = d (1) 12,11 = −0.0201; d (1) 4,3 = d (1) 6,5 = d (1) 9,8 = d (1) 12,9 = 0.021; d (1) 4,5 = −0.02; d (1) 10,9 = −0.0109; state 2 d (2) 1,10 = d (2) 4,3 = 0.044; d (2) 2,1 = 0.079; d (2) 3,11 = 0.077; d (2) 5,12 = d (2) 8,7 = d (2) 10,2 = 0.07; d (2) 6,5 = 0.033; d (2) 6,12 = 0.045; d (2) 9,7 = 0.049; d (2) 11,9 = −0.077; d (2) 12,10 = −0.072; and other weights are 0. It is clear that the signed digraph ( u , (d qp ) 12×12 ), where d qp = max i∈S {c (i) |d (i) qp |}, is strongly connected.…”

“…By simple calculation, we can obtain that M = 0.61. Choose c (1) = 1, c (2) = 0.99, and one can obtain that (1) 1 = (1) 5 = 0; (1) 2 = 4.519; (1) 3 = (1) 7 = (1) 10 = 4.500; (1) 4 = 4.561, (1) 6 = (1) 9 = 4.521;…”

“…(1) 8 = (1) 11 = (1) 12 = 4.559; (2) 1 = (2) 4 = 4.552; (2) 2 = 4.622, (2) 3 = 4.618; (2) 6 = 4.620;…”

“…and (1) = 0.09, (2) = 0.1. Therefore, we get = max i∈S,q∈ { (i) q } = 4.622 and = max i∈S { (i) } = 0.1.…”

Parametric Lyapunov equation based event‐triggered and self‐triggered control of input constrained linear systems

“…Most physical actuators of practical systems are subject to saturations. Therefore, the study of saturated control problem has important significance and many achievements have been proposed (see References 30‐35 and the reference therein). In the past decades, numerous results have been published for linear systems with actuator saturation (see References 32,36‐39 and the references cited there).…”