Output regulation of heterogeneous linear multi-agent systems with differential graphical game

Summary This paper considers optimal consensus control problem for unknown nonlinear multiagent systems (MASs) subjected to control constraints by utilizing event‐triggered adaptive dynamic programming (ETADP) technique. To deal with the control constraints, we introduce nonquadratic energy consumption functions into performance indices and formulate the Hamilton‐Jacobi‐Bellman (HJB) equations. Then, based on the Bellman's optimality principle, constrained optimal consensus control policies are designed from the HJB equations. In order to implement the ETADP algorithm, the critic networks and action networks are developed to approximate the value functions and consensus control policies respectively based on the measurable system data. Under the event‐triggered control framework, the weights of the critic networks and action networks are only updated at the triggering instants which are decided by the designed adaptive triggered conditions. The Lyapunov method is used to prove that the local neighbor consensus errors and the weight estimation errors of the critic networks and action networks are ultimately bounded. Finally, a numerical example is provided to show the effectiveness of the proposed ETADP method.

Section: Introductionmentioning

confidence: 99%

Data‐driven optimal event‐triggered consensus control for unknown nonlinear multiagent systems with control constraints

Zhang

Park

Yue

et al. 2019

“…In these cases, the dynamics of the reference trajectory and the disturbance model are usually combined into a single dynamic model named exo‐system in the literature . One possible solution to such output regulation problems is by the means of internal model principle (IMP) , where the idea is to incorporate an internal model of the exo‐system in the dynamic controller of each agent . If the agents are additionally subject to unmodeled disturbances , then the IMP alone cannot be used for disturbance rejection and H ∞ control methods are required.…”

Section: Introductionmentioning

confidence: 99%

“…(i) We define the novel concept of graphical games for heterogeneous agents as opposed to homogeneous agents considered in the works of Vamvoudakis et al and Jiao et al This allows us to achieve output regulation among heterogeneous agents. Graphical game for heterogeneous agents is also considered in the work of Adib Yaghmaie et al, however, the communication graph in the aforementioned work is required to be acyclic (ie, there is no‐loop in the graph). This restrictive assumption significantly simplifies the formulation and decouples the controller design of each agent from the others.…”

Section: Introductionmentioning

confidence: 99%

Differential graphical games for H_∞ control of linear heterogeneous multiagent systems

Yaghmaie

Movric

Lewis

et al. 2019

Self Cite

Summary Differential graphical games have been introduced in the literature to solve state synchronization problem for linear homogeneous agents. When the agents are heterogeneous, the previous notion of graphical games cannot be used anymore and a new definition is required. In this paper, we define a novel concept of differential graphical games for linear heterogeneous agents subject to external unmodeled disturbances, which contain the previously introduced graphical game for homogeneous agents as a special case. Using our new formulation, we can solve both the output regulation and H∞ output regulation problems. Our graphical game framework yields coupled Hamilton‐Jacobi‐Bellman equations, which are, in general, impossible to solve analytically. Therefore, we propose a new actor‐critic algorithm to solve these coupled equations numerically in real time. Moreover, we find an explicit upper bound for the overall scriptL2‐gain of the output synchronization error with respect to disturbance. We demonstrate our developments by a simulation example.

“…One can solve such output regulation problem for linear heterogeneous multiagent systems by using the Internal Model Principle (IMP) . One possible solution is to incorporate a p ‐copy of the internal model of the exosystem, where p is the dimension of the output, to achieve output synchronization to the exosystem's output . This idea is used in the works of Wang et al, Lunze, and Adib Yaghmaie et al to study output regulation of linear heterogeneous agents communicating over an acyclic graph.…”

Section: Introductionmentioning

confidence: 99%

“…One possible solution is to incorporate a p ‐copy of the internal model of the exosystem, where p is the dimension of the output, to achieve output synchronization to the exosystem's output . This idea is used in the works of Wang et al, Lunze, and Adib Yaghmaie et al to study output regulation of linear heterogeneous agents communicating over an acyclic graph. Furthermore, it is used in the work of Su et al to study output regulation of linear, yet homogeneous, agents over a general graph.…”

Section: Introductionmentioning

confidence: 99%

H_∞‐output regulation of linear heterogeneous multiagent systems over switching graphs

Yaghmaie

Movric

Lewis

et al. 2018

Self Cite

Summary In this paper, we analyze H∞‐output regulation of linear heterogeneous multiagent systems. The agents are subject to modeled and unmodeled disturbances and communicate over a switching graph. We derive a sufficient condition that guarantees H∞ output regulation for the mentioned setup. This sufficient condition places requirements on both the single‐agent systems and the switching graph. The requirement on the single‐agent systems is an H∞‐criterion that should be satisfied by a proper design of the controller. Meanwhile, the switching graph needs to be maximally connected. Moreover, we derive an upper bound for the overall L2‐gain of the output synchronization error with respect to the unmodeled disturbances over a fixed communication graph. We illustrate our technical developments by a simulation example.