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In this paper, the consensus of fractional-order multiagent systems (FOMASs) is considered via sampled-data control over directed communication topology with the order 0 <; α <; 1. Two cases are considered. One is FOMASs without leader, and the other is FOMASs with a leader. For each case, by applying matrix theory and algebraic graph theory, some algebraic-type necessary and sufficient conditions based on the sampling period, the fractional-order, the coupling gain, and the structure of the network are established for achieving consensus of the system. Moreover, for the network with a dynamic leader, the sampling period, the coupling gain, and the spectrum of the Laplacian matrix are carefully devised, respectively. Finally, several simulation examples are employed to validate the effectiveness of the theoretical results.

In this paper, we study a two-person zero-sum linear-quadratic stochastic differential game problem. From a new viewpoint, we construct an optimal feedback control-strategy pair for the game in a closed-loop form based on the solution of a Riccati equation. A key part of our analysis involves proving the global solvability of this Riccati equation, which is interesting in its own right. Moreover, we demonstrate an indefinite phenomenon arising from the linear-quadratic game.

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This article considers the consensus of multi-agent systems (MASs) with external disturbances by using sliding mode control. First, by establishing a novel sliding mode surface and designing a sliding mode control protocol with constant gains, the consensus of MASs with unknown bounded disturbances is studied. Second, based on the barrier function, a new type of adaptive sliding mode switching protocol is proposed, in which the control gains can be chosen randomly and the upper bound of the disturbance does not need to be known in a prior. By using this protocol, the consensus error can converge to any given region of zero in finite time. Moreover, the leaderless consensus and leader-following tracking problem of MASs with general dynamics and external disturbances are also investigated via extending the proposed adaptive sliding mode protocol. Finally, some examples are presented to illustrate the effectiveness of the control strategies. K E Y W O R D Sadaptive sliding mode control, consensus, multi-agent systems, unknown disturbances INTRODUCTIONCooperation behaviors such as flocking of birds, schooling of fish, and swarming in insects, exist in the human society extensively. Inspired by these phenomena, the study on cooperative control of multi-agent systems (MASs) has drawn significant attention of diverse research community over the past decades. The main potential applications include unmanned air vehicles, robotic teams, sensor networks, formation control, and so on. [1][2][3][4] The consensus is a fundamental problem of MASs and the main task is to design some distributed protocols such that all agents converge to a common state. The basic framework of the consensus was constructed in Reference 5. Since then, many useful schemes have been used to design the consensus protocols and a lot of fruitful results have been obtained. For instance, feedback control, 6,7 intermittent control, 8,9 impulsive control, 10,11 sample-data control, 12,13 event-triggered control, [14][15][16] adaptive control [17][18][19] and so on. In these works, the MASs with homogeneous dynamics were considered. In References 20-22, the leaderless consensus and leader-following consensus problems were considered for MASs with heterogeneous dynamics. All these efforts [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] focused on the consensus of MASs in ideal environments. However, in practical MASs, the external disturbances are unavoidable and the system performance is always affected. Hence, the study on consensus of MASs with external disturbances is very important and necessary.In this article, we address the consensus of MASs with external disturbances. In existing works, the external disturbances can be roughly divided into two categories: the disturbance is generated by an external linear autonomous system [Correction added on 19 July 2021, after first online publication: the Funding information section has been corrected in this version.]

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