Output synchronization of linear parameter-varying systems via dynamic couplings

Abstract

We address the output synchronization problem for groups of linear parameter-varying (LPV) agents. The agents are assumed to have identical LPV structure depending on different local parameters which make the group heterogeneous. First, we show that homogeneous groups of LPV systems with static diffusive couplings synchronize over uniformly connected graphs. Then, based thereon, we propose a constructive and scalable solution to the output synchronization problem for groups of LPV systems with heterogeneous parameters. The results are illustrated in a numerical example.

Cooperative Output Regulation of Multiagent Linear Parameter‐Varying Systems

“…The main contribution of this paper is in the design of an LPV controller that can guarantee the output regulation problem for multiagent LPV systems. A relevant problem to the output regulation problem has been studied from the synchronization point of view in [12][13][14]. Furthermore, the output regulation problem has been addressed in [15] for systems, in which the state-space matrices are affinely dependent on the scheduling variables.…”

“…First, we describe few assumptions imposed on the agents. It is noted that the following assumptions are standard ones that have also been considered in previous relevant studies [5,14,15,[22][23][24]. (2) is not asymptotically stable for any ∈ N and ∈ P .…”

“…In these studies, the controllers are designed based on the dissipativity theory, while it is assumed that each agent has access to the varying parameters of all other agents. The output synchronization problem has been investigated for heterogenous multiagent LPV systems [14]. The full state feedback controller was considered to solve a consensus problem for homogeneous and heterogenous multiagent LPV systems with affine dependency on LPV parameters, a.k.a.…”

Gain‐scheduled leader‐follower tracking control for interconnected parameter varying systems

“…Thanks to this and many other potential applications, the theory of cooperative control for parameter varying systems has been gaining attention in recent years [21,22].The main contribution of this paper concerns the leader-follower control of parameter varying interconnected systems. A related problem, from the synchronization viewpoint, has been studied in [23,24]. In the first reference, the synchronization problem is solved for heterogeneous systems, which depend on the parameters in an affine fashion, under the assumption that the network of LPV agents allows for an internal model for synchronization while the agents are decoupled from each other.…”

“…One way to enforce such an information constraint is to employ a block diagonal Lyapunov function. This is the solution approach undertaken in this paper and is its main difference from solutions that could be obtained in a centralized setup.Different from many papers that study synchronization of decoupled systems (including the aforementioned references [23,24], also see [2,3]), in the case of coupled systems, it is essential to distinguish the network representing the existing interactions between the subsystems (including interactions with the leader) from the network that realizes communication and control. This leads us to consider a two-network structure in this paper.…”