Fault-tolerant cooperative control of multiagent systems has attracted ever-increasing attention in recent years due to the fact that multiple agents can provide much more redundancy than a single agent system, thereby making the fault tolerant cooperative control design more flexible. However, multiagent systems may bring severe challenges that do not exist in single-agent systems. This article aims at presenting a survey of trends and methodologies of fault tolerant cooperative control in multiagent systems. Depending on the countermeasure against the faults, the existing fault-tolerant cooperative control methodologies are first classified into four categories: Individual methodologies, cooperative methodologies, topology reconfiguration-based methodologies, and composition reconfiguration-based methodologies. Then the characteristics and implementation schemes of four categories of methodologies are discussed in detail. Furthermore, the applicability of fault tolerant cooperative control in smart grids is outlined. Finally, several challenging issues are envisioned for future research.

This paper investigates the multi-player pursuit-evasion differential games in the presence of malicious pursuers. Firstly, three types of malicious pursuers, namely greedy, lazy, and traitorous pursuers are formulated by using two subjectively malicious factors in the performance index. Then, an N-player nonzero-sum game framework is established to study the relationships among healthy pursuers, malicious pursuers and evaders. The capturability and Nash equilibrium of such a new multi-player pursuit-evasion differential game are rigorously analyzed. Finally, the effects of malicious pursuers on the capture time are explicitly quantified by the minimal pursuit coefficient, whose explicit form is obtained by the solutions from coupled Riccati differential equations.

This paper addresses the distributed optimal fault estimation (FE) and fault-tolerant control (FTC) issues under the bidirectional interaction between a possibly faulty interconnected system and its associated diagnostic interconnected observer. The proposed methodology is based on a framework, named Stackelberg differential graphical game, in which the interconnected observer and its corresponding interconnected system are formulated as two graphical games, and they respectively play the role of the follower and leader to make sequential decisions of the FE and the FTC. Such a framework allows to fully reveal the property of the bidirectional interaction, based on which a distributed optimal FE and FTC scheme is developed. Moreover, a new concept named interactive Stackelberg equilibrium is proposed, where to reach this equilibrium, an auxiliary controller is suitably designed for each sub-observer. In this way, this auxiliary controller can cooperate with other auxiliary controllers of sub-observers, and non-cooperate with controllers of subsystems, which helps to achieve the distributed optimal FE and FTC goals.

This article addresses the distributed optimal fault-tolerant control (FTC) issue by using the two-level game approach for a class of nonlinear interconnected systems, in which each subsystem couples with its neighbors through not only the states but also the inputs. At the first level, the FTC problem for each subsystem is formulated as a zero-sum differential game, in which the controller and the fault are regarded as two players with opposite interests. At the second level, the whole interconnected system is formulated as a graphical game, in which each subsystem is a player to achieve the global Nash equilibrium for the overall system. The rigorous proof of the stability of the interconnected system is given by means of the cyclic-small-gain theorem, and the relationship between the local optimality and the global optimality is analyzed. Moreover, based on the adaptive dynamic programming (ADP) technology, a distributed optimal FTC learning scheme is proposed, in which a group of critic neural networks (NNs) are established to approximate the cost functions. Finally, an example is taken to illustrate the efficiency and applicability of the obtained theoretical results.

This paper proposes a fault-tolerant game control methodology that facilitates the simultaneous inner-loop attitude tracking and outer-loop formation control of quadrotor helicopters subject to actuator faults. The quadrotor helicopters are modelled as fully actuated systems (FAS), based on which, an incentive Stackelberg differential graphical (ISDG) game is established for studying the bidirectional interactions between the inner and outer loops. In such a game, the rotational subsystems act as follower players responsible for achieving inner-loop fault-tolerant attitude tracking, whereas the translational subsystems act as leader players responsible for achieving outer-loop fault-tolerant formation control. In addition, an adaptive fault estimation law is proposed for fault compensation, facilitating controller reconfiguration not only for the inner loop but also for the outer loop. Rigorous analysis shows that the proposed fault-tolerant game control ensures the boundedness of fault estimation errors, attitude tracking errors and formation errors. Moreover, an interactive Stackelberg equilibrium is achieved under the designed fault-tolerant game controllers. Finally, simulations are presented to illustrate the effectiveness of the proposed approach.

This paper proposes a game theoretic framework for dealing with the integration design problem of task allocation, path planning and formation control for multi-agent systems. In this framework, an anonymous hedonic game (AHG) is established for allocating tasks according to agents' preferences, while a Stackelberg differential graphical game (SDGG) is nested within the AHG for path planning and controlling agents' formation. In order to capture the characteristics and interactions of the three phases, a group of coupled performance indexes are designed, based on which, a backward strategy-design mechanism is proposed, i.e., following the sequence of formation control → path planning → task allocation to obtain the optimal strategy of each phase. The proposed framework makes the strategies to be designed in a closed-loop form, and the performance of each phase to be bi-directionally adjustable. It is rigorously proved that the designed strategies can achieve the desired performance of each phase as well as the Gestalt Nash equilibrium of the integrated game. Finally, an integrated game algorithm is further developed to optimize the parameters of the strategies