caa a22 4500 606204814 CHVBK 20210128101004.0 cr unu---uuuuu 210128e20150101xx s 000 0 eng 10.1007/s00034-014-9850-1 doi (NATIONALLICENCE)springer-10.1007/s00034-014-9850-1 Consensus for First- and Second-Order Discrete-Time Multi-agent Systems with Delays Based on Model Predictive Control Schemes [Elektronische Daten] [Zhaozhun Zhong, Lining Sun, Jingcheng Wang, Penghong Lv, Hongjing Zheng] The problem of consensus for first- and second-order discrete-time multi-agent systems with delays is concerned in this paper. In particular, we apply the decentralized model predictive control schemes to multi-agent systems with bounded time delays, by which the input constraints can be taken into account. First, we establish the stability properties of time-delayed systems under the connectivity assumption and the strict convexity update rule based on the concept of enlarged system. Then, decentralized model predictive control schemes are proposed to solve the consensus problem based on time-varying prediction horizon length, which gives better performance than the existing method with time invariant prediction horizon length. Finally, simulation results illustrate the effectiveness of the proposed methods. Springer Science+Business Media New York, 2014 Consensus problems nationallicence Multi-agent systems nationallicence Time delays nationallicence Model predictive control nationallicence $${\mathbb {R}}$$ R : The set of real numbers nationallicence $${\mathbb {N}}$$ N : The set of natural numbers nationallicence $$\subset $$ ⊂ : Strict set inclusion nationallicence $$\subseteq $$ ⊆ : Nonstrict set inclusion nationallicence $$X$$ X : A finite-dimensional Euclidean space nationallicence $$K$$ K : A subset of a finite-dimensional Euclidean space nationallicence $${\mathcal {B}}(K,c)\,$$ B ( K , c ) : The set of points in $$X$$ X whose distance to $$K$$ K is strictly smaller than $$c$$ c nationallicence $$2^X$$ 2 X : The collection of all closed subsets of $$X$$ X nationallicence $${\mathcal {N}}$$ N : The set of multi-agent nodes nationallicence $${\mathcal {A}}$$ A : The set of edges nationallicence $$w$$ w : Weight of edge nationallicence $$( {m,l})\in {\mathcal {A}}$$ ( m , l ) ∈ A : A directed arc from node $$m$$ m to node $$l$$ l nationallicence $$G=( {{\mathcal {N}},{\mathcal {A}},w})$$ G = ( N , A , w ) : A weighted directed graph nationallicence $$N_i ( G)$$ N i ( G ) : The set of neighbors of the node $$i$$ i nationallicence $$N_{\mathcal {L}} ( G)$$ N L ( G ) : The set of these nodes $$m\in {\mathcal {N}}\backslash {\mathcal {L}}$$ m ∈ N \ L for which there is $$l\in {\mathcal {L}}$$ l ∈ L such that $$m\in N_l ( G)$$ m ∈ N l ( G ) nationallicence $$( {{\mathcal {N}},\cup _{k\in {\mathcal {I}}} {\mathcal {A}}(k)})$$ ( N , ∪ k ∈ I A ( k ) ) : The union of graphs nationallicence $$\overline{P_1 P_2 } $$ P 1 P 2 ¯ : The segment joining $$P_1 ,P_2 \in X$$ P 1 , P 2 ∈ X nationallicence $$\left| {\overline{P_1 P_2 } } \right| $$ P 1 P 2 ¯ : Segment length nationallicence $$r_{P_1 P_2 } $$ r P 1 P 2 : The straight line passing through $$P_1 ,P_2 \in X$$ P 1 , P 2 ∈ X nationallicence $$s_{P_1 P_2 } $$ s P 1 P 2 : The straight half-line starting from $$P_1 $$ P 1 and passing through $$P_2 $$ P 2 nationallicence $$T=\left\{ {P_1 ,\ldots ,P_M } \right\} $$ T = P 1 , ... , P M : An ordered sequence of $$M$$ M points nationallicence $$x_i (k)$$ x i ( k ) : State of agent $$i$$ i at time step $$k$$ k nationallicence $$x(k)$$ x ( k ) : State of the multi-agent system nationallicence $${\mathcal {X}}\subseteq {\mathbb {R}}^q$$ X ⊆ R q : State space of each agent nationallicence $${\mathcal {X}}^n\subseteq {\mathbb {R}}^{qn}$$ X n ⊆ R q n : State space of the multi-agent system nationallicence $$h$$ h : The bound of delays nationallicence $$x_{i+\tau n} (k)=x_i (k-\tau )$$ x i + τ n ( k ) = x i ( k - τ ) : Noncomputing agent $$i+\tau n$$ i + τ n nationallicence $${{\tilde{\mathcal {N}}}}$$ N ~ : All the nodes of enlarged multi-agent system nationallicence $${\tilde{x}}(k)$$ x ~ ( k ) : State of the enlarged multi-agent system nationallicence $${\mathcal {X}}^{hn}\subseteq {\mathbb {R}}^{qhn}$$ X h n ⊆ R q h n : State space of enlarged multi-agent system nationallicence $$\Phi $$ Φ : The set of equilibrium points nationallicence $$\phi \in \Phi $$ ϕ ∈ Φ : Equilibrium point nationallicence $${\varvec{V}}:{\mathcal {X}}^n\mapsto ( {2^{\mathcal {X}}})^n$$ V : X n ↦ ( 2 X ) n : Set-valued function nationallicence $$\hbox {Co}( {\cup _{j\in {\tilde{\mathcal {N}}}} \left\{ {x_j (k)} \right\} })$$ Co ( ∪ j ∈ N ~ x j ( k ) ) : The convex hull of states $$\left\{ {x_1 ,\ldots ,x_n ,\ldots ,x_{hn} } \right\} $$ x 1 , ... , x n , ... , x h n nationallicence $$\hbox {card}( {a_i (k)})$$ card ( a i ( k ) ) : The cardinal number of the set $$a_i (k)$$ a i ( k ) nationallicence $$\hbox {Ci}( {\left\{ {y_1 ,y_2 } \right\} })$$ Ci ( y 1 , y 2 ) : The relative interior of $$\hbox {Co}( {\left\{ {y_1 ,y_2 } \right\} })$$ Co ( y 1 , y 2 ) nationallicence $$N$$ N : Prediction horizon length nationallicence Zhong Zhaozhun School of Computer Science and Technology, Soochow University, 215006, Suzhou, Jiangsu, People's Republic of China aut Sun Lining School of Mechanical and Electric Engineering, Soochow University, 215006, Suzhou, Jiangsu, People's Republic of China aut Wang Jingcheng Department of Automation, Shanghai Jiaotong University, 200240, Shanghai, People's Republic of China aut Lv Penghong Department of Industry Development, Zhejiang Province Development Planning and Research Institute, 310012, Hangzhou, Zhejiang, People's Republic of China aut Zheng Hongjing School of Computer Engineering, Suzhou Vocational University, 215104, Suzhou, Jiangsu, People's Republic of China aut Circuits, Systems, and Signal Processing Springer US; http://www.springer-ny.com 34/1(2015-01-01), 127-152 0278-081X 34:1<127 2015 34 34 https://doi.org/10.1007/s00034-014-9850-1 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00034-014-9850-1 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Zhong Zhaozhun School of Computer Science and Technology, Soochow University, 215006, Suzhou, Jiangsu, People's Republic of China aut NATIONALLICENCE 700 1- Sun Lining School of Mechanical and Electric Engineering, Soochow University, 215006, Suzhou, Jiangsu, People's Republic of China aut NATIONALLICENCE 700 1- Wang Jingcheng Department of Automation, Shanghai Jiaotong University, 200240, Shanghai, People's Republic of China aut NATIONALLICENCE 700 1- Lv Penghong Department of Industry Development, Zhejiang Province Development Planning and Research Institute, 310012, Hangzhou, Zhejiang, People's Republic of China aut NATIONALLICENCE 700 1- Zheng Hongjing School of Computer Engineering, Suzhou Vocational University, 215104, Suzhou, Jiangsu, People's Republic of China aut NATIONALLICENCE 773 0- Circuits, Systems, and Signal Processing Springer US; http://www.springer-ny.com 34/1(2015-01-01), 127-152 0278-081X 34:1<127 2015 34 34