Learning formation control for fractional‐order multiagent systems

Luo, Dahui; Wang, JinRong; Shen, Dong

doi:10.1002/mma.4948

Cited by 47 publications

(24 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Fractional differential operators describe mechanical and physical processes with historical memory and spatial global correlation and for the basic theory-see [1][2][3]. Results on existence, stability and controllability for differential equations with Caputo, Riemann-Liouville and Hilfer type fractional derivatives can be found, for example, in [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. Caputo and Fabrizio [20] introduced a new nonlocal derivative without a singular kernel and Atangana and Nieto [21] studied the numerical approximation of this new fractional derivative and established a modified resistance loop capacitance (RLC) circuit model.…”

Section: Introductionmentioning

confidence: 99%

Hyers–Ulam Stability and Existence of Solutions for Differential Equations with Caputo–Fabrizio Fractional Derivative

et al. 2019

Self Cite

View full text Add to dashboard Cite

In this paper, the Hyers-Ulam stability of linear Caputo-Fabrizio fractional differential equation is established using the Laplace transform method. We also derive a generalized Hyers-Ulam stability result via the Gronwall inequality. In addition, we establish existence and uniqueness of solutions for nonlinear Caputo-Fabrizio fractional differential equations using the generalized Banach fixed point theorem and Schaefer's fixed point theorem. Finally, two examples are given to illustrate our main results.

show abstract

Section: Introductionmentioning

confidence: 99%

Hyers–Ulam Stability and Existence of Solutions for Differential Equations with Caputo–Fabrizio Fractional Derivative

et al. 2019

Self Cite

View full text Add to dashboard Cite

show abstract

“…Relative controllability and its related problems of linear systems represented by different type delay systems have been studied in literature . In particular, rank and Kalman criteria for relative controllability are studied extensively.…”

Section: Introductionmentioning

confidence: 99%

Finite time stability and relative controllability of Riemann‐Liouville fractional delay differential equations

Wang

2019

Math Methods in App Sciences

Self Cite

View full text Add to dashboard Cite

This paper firstly deals with finite time stability (FTS) of Riemann-Liouville fractional delay differential equations via giving a series of properties of delayed matrix function of Mittag-Leffler. We secondly study relative controllability of such type-controlled system. With the help of the representation of solution, both Gram-like type matrix and rank criterion are derived, which extend the corresponding results for linear systems. KEYWORDSdelayed matrix function of Mittag-Leffler, finite time stability, fractional delay differential equations, relative controllability INTRODUCTIONRecently, some authors apply delayed exponential matrix function to find the explicit solution formula of linear delay equations. 1-3 Further, there are some continued work on finding the representation of solutions to delay continuous and discrete systems; see, for example, previous studies. [4][5][6][7][8][9][10][11] Fractional differential equations have been used in solving the practical problems in the fields of natural science. 12,13 In particular, FTS of linear fractional delay differential equations with controls was offered in Lazarević, 14 and an inequality of Gronwall type is used to derive the results. For other related contribution, one can refer to previous works. [15][16][17][18][19][20][21][22][23][24][25] However, an initial singular condition for the Riemann-Liouville fractional differential equations is much different from the standard initial condition for a Caputo fractional differential equations. The main results of the standard initial condition for a Caputo fractional delay differential equation were obtained in Li and Wang. 11 Relative controllability and its related problems of linear systems represented by different type delay systems have been studied in literature. [26][27][28][29][30][31][32][33] In particular, rank and Kalman criteria for relative controllability are studied extensively.Very recently, Li and Wang 12 studiedHere, D − + x denotes Riemann-Liouville fractional derivative, I 1− − + x denotes Riemann-Liouville fractional integral, T = k * < ∞ for a fixed k * ∈ {1, 2, … }, is a constant, ∈ C([− , T], R n ), and (D − + )( ) exists. We consider the Riemann-Liouville fractional derivative D − + , where the lower limit is − + (− is a singular point). To keep the "consistence" with the lower limit in Riemann-Liouville derivative, we keep the initial condition at − + .

show abstract

“…However, very few results have been noted for addressing the repetitive MASs of fractional‐order agents except Luo et al In this paper, we consider the distributed learning schemes for the formation control of linear fractional‐order MASs. In particular, both P ‐type and PI ‐type distributed learning schemes were investigated to fully use the available information from previous iterations so that an asymptotical consensus of the whole system was achieved.…”

Section: Introductionmentioning

confidence: 99%

PD^α‐type distributed learning control for nonlinear fractional‐order multiagent systems

Luo

Wang

Shen

2019

Math Methods in App Sciences

Self Cite

View full text Add to dashboard Cite

This paper considers the consensus tacking problem for nonlinear fractional-order multiagent systems by presenting a PD -type iterative learning control update law with initial learning mechanisms. The asymptotical convergence of the proposed distributed learning algorithm is strictly proved by using the properties of fractional calculus. A sufficient condition is derived to guarantee the whole multiagent system achieving an asymptotic output consensus.An illustrative example is given to verify the theoretical results. KEYWORDS asymptotical convergence, nonlinear fractional-order multiagent systems, PD -type iterative learning control Math Meth Appl Sci. 2019;42:4543-4553.wileyonlinelibrary.com/journal/mma

show abstract

Learning formation control for fractional‐order multiagent systems

Cited by 47 publications

References 29 publications

Hyers–Ulam Stability and Existence of Solutions for Differential Equations with Caputo–Fabrizio Fractional Derivative

Hyers–Ulam Stability and Existence of Solutions for Differential Equations with Caputo–Fabrizio Fractional Derivative

Finite time stability and relative controllability of Riemann‐Liouville fractional delay differential equations

PD^α‐type distributed learning control for nonlinear fractional‐order multiagent systems

Contact Info

Product

Resources

About

Learning formation control for fractional‐order multiagent systems

Cited by 47 publications

References 29 publications

Hyers–Ulam Stability and Existence of Solutions for Differential Equations with Caputo–Fabrizio Fractional Derivative

Hyers–Ulam Stability and Existence of Solutions for Differential Equations with Caputo–Fabrizio Fractional Derivative

Finite time stability and relative controllability of Riemann‐Liouville fractional delay differential equations

PDα‐type distributed learning control for nonlinear fractional‐order multiagent systems

Contact Info

Product

Resources

About

PD^α‐type distributed learning control for nonlinear fractional‐order multiagent systems