Research On Methods Of Containment Control For Nonlinear Multi-agent Networks

At present, with the rapid development of science and technology, the coordinationcontrol of multi-agent networks is the favour of the researchers, being the research hotspot incomplex systems and complexity science and the frontier topic in the field of control. As thetypical case of multi-leader coordination control, containment control has a large number ofpotential applications in military and civilian. And in the practical applications, due to theexistence of inherent nonlinearity, uncertainty and external disturbance and so on, thenetworks reflect the nonlinear characteristics. Therefore, research on methods of thecontainment control for nonlinear multi-agent networks has extremely important theorysignificance and practical value.Based on algebraic graph theory, matrix theory, Lyapunov stability principle, the slidingmode variable structure control theory and finite-time stability analysis method, it is focusedon the containment control problems for nonlinear second-order multi-agent networks in thispaper.At first, the asymptotic containment control problem is researched for the second-ordermulti-agent networks with inherent nonlinearity. Two conditions are considered withstationary leaders and dynamic ones. The distributed control protocol is designed based onrelative positions and relative velocities. Applying Lyapunov stability analysis principle, thesufficient condition is gained that followers asymptotically converge to the desired position inthe convex hull formed by leaders, meanwhile, the lower limits of control coefficients areobtained. Simulation examples are given to verify the rationality of theoretical analysis.Then the finite time containment control problem is considered for the second-ordermulti-agent networks with nonlinear perturbations with bounded norm. When topologybetween the followers are connected, the control protocols with switching part is designed onthe basid of variable structure control idea, moreover, the sufficient conditions to achieve thefinite time containment control based in matrix theory and finite-time stability principle.When topology between the followers are strong connected, the nonsingular terminal slidingmode surface and nonsingular fast terminal sliding mode surface are defined according tonetwork errors, correspongding nonsingular discontinuous control protocols are designed andthe appropriate value range of control parameters are given as to achieve finite timecontainment control. Simulation examples of two kinds of network topologies are given toverify the correctness and effectiveness of theoretical schemes.Finally, the practical finite time containment control problem is considered for themulti-agent networks with norm-bounded nonlinear perturbations. On the basis of definingthe nonsingular fast terminal sliding mode surface according to network errors, thecorresponding distributed control protocols are investigated with fast power reaching law anddouble power reaching law, so as to make the followers converge to the small neighborhoodof the desired location within finite time and keep staying within the dynamic convex hull formed by the multiple leaders to achieve practical finite time containment control.Simulation examples are given to verify the correctness theoretical results.