Hyers-Ulam stability for nonlocal fractional partial integro-differential equation with uncertainty

et al. 2022

IEEE Access

This paper studies leaderless consensus of semi-linear parabolic partial integro-differential equations based multi-agent systems (PIDEMASs) with time delays. Making use of the information interaction and coordination among the neighboring agents, consensus control of the leaderless PIDEMAS is constructed. Consensus of the leaderless PIDEMAS is analyzed by using a Lyapunov approach. Dealing with time-invariant delays and time-varying delays, two sufficient conditions for consensus of the leaderless PIDEMAS are respectively obtained in terms of LMIs. Two examples illustrate the effectiveness of developed theoretical results.INDEX TERMS consensus, multi-agent systems, LMIs, Lyapunov, partial integro-differential equations.

Section: Consensus Of the Pidemas With Time-varying Delaysmentioning

confidence: 99%

Leaderless Consensus Control of Nonlinear PIDE-Type Multi-Agent Systems With Time Delays

Dai

et al. 2022

IEEE Access

“…Remark 3. Different from the control design for synchronization of parabolic PDEs-based CSTNs [44,45], this paper deals with the synchronization of hyperbolic PDEs-based CSTNs.…”

Section: Synchronization Of Hpdecstns With Multi-weightsmentioning

confidence: 99%

Exponential Synchronization of Hyperbolic Complex Spatio-Temporal Networks with Multi-Weights

2022

Mathematics

This paper deals with the leader-following synchronization of first-order, semi-linear, complex spatio-temporal networks. Firstly, two sorts of complex spatio-temporal networks based on hyperbolic partial differential equations (CSTNHPDEs) are built: one with a single weight and the other with multi-weights. Then, a new distributed controller is designed to address CSTNHPDE with a single weight. Sufficient conditions for the synchronization and exponential synchronization of CSTNHPDE are presented by showing the gain ranges. Thirdly, the proposed distributed controller addresses of CSTNHPDE with multi-weights, and gain ranges are obtained for synchronization and exponential synchronization, respectively. Finally, two examples show the effectiveness and good performance of the control methods.

“…□ Remark 2. Di erent from the control design for consensus of parabolic PDEMASs in [41,42], this paper deals with the consensus of a class of HPDEMASs.…”

Section: Consensus Of Hpdemass With the Symmetric Semipositive Defini...mentioning

confidence: 99%

Leaderless Consensus of Semilinear Hyperbolic Multiagent Systems with Semipositive or Seminegative Definite Convection

Dai

Discrete Dynamics in Nature and Society

et al. 2022

This paper deals with a leaderless consensus of semilinear first-order hyperbolic partial differential equation-based multiagent systems (HPDEMASs). A consensus controller under an undirected graph is designed. Dealing with different convection assumptions, two different boundary conditions are presented, one right endpoint and the other left endpoint. Two sufficient conditions for leaderless consensus of HPDEMAS are presented by giving the gain range in the case of the symmetric seminegative definite convection coefficient and the semipositive definite convection coefficient, respectively. Two examples are presented to show the effectiveness of the control methods.