Distributed L2-gain output-feedback control of homogeneous and heterogeneous systems

Abstract

L 2 -gain synchronization LQR based optimal design Output-feedback control a b s t r a c tThe importance of static output feedback (OPFB) design for aircraft control, process control, and elsewhere has been well documented since the 1960s, since full state measurements are not usually available in practical systems. This problem is compounded in the case of multi-agent systems (MAS) where each agent has its own state variable and measured outputs. Therefore, this paper addresses the L 2 -gain OPFB synchronization of linear MAS subject to external disturbances. Both homogeneous and heterogeneous MAS are considered. For homogeneous MAS, it is shown that the L 2 -gain static OPFB synchronization problem of MAS can be cast into the L 2 -gain static OPFB problem for a set of decoupled systems that depend on the graph topology. A modified Riccati equation is introduced which gives the OPFB gain and the coupling gain of the proposed static OPFB control protocol. For heterogeneous MAS, it is shown that the L 2 -gain synchronization problem can be cast into the L 2 -gain static OPFB problem of a set of decoupled systems plus a coupling condition on their dynamic compensators that depends on the graph topology. A certain novel gain matrix is introduced in the dynamics of the control protocol to improve the performance.

A Markovian jump system approach to consensus of heterogeneous multiagent systems with partially unknown and uncertain attack strategies

“…The above systems and are the representative mathematical models for autonomous vehicles, where x 1 i , x 2 i , and x 3 i , are the position, the velocity, and the state of actuator, respectively, see References for the detailed discussion. In our system, each agent communicates with its neighboring agents periodically with the sampling period 0.1 second.…”

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

“…Indeed, one needs to obtain a condition to guarantee ‐stability. Comparing with few results on H ∞ output regulation of linear heterogeneous agents, the communication graph in the works of Adib Yaghmaie et al and Jiao et al is fixed and the switching graph in the work of Zhang et al can only change over a fixed set of topologies containing spanning trees.…”

“…Secondly, we allow the agents to communicate over a general class of switching graphs. In comparison, Adib Yaghmaie et al and Jiao et al do not consider switching graphs, and the switching graphs in the work of Zhang et al can change only over a set of topologies containing spanning trees. We do not need those assumptions in our paper.…”

Synchronization of linear systems via relative actuation

“…Within the boundary of this setup different approaches have yielded various interesting solutions to the synchronization problem, where the universal goal is to drive the agents' states x i (t) to a common trajectory. E.g., communication delays are considered in [15], L 2 -gain output-feedback is employed in [2], distributed containment problem is studied in [4]. Among many other works contributing to our wealth of knowledge are [5] on adaptive protocols, [8] on switching topologies, and [14] on optimal state feedback and observer design.…”

“…1 , the current source u 12 connects n (1) p and n (2) p . Since for these two current sources the indices (1 and p) of the nodes they are associated to are different, we cannot find a scalar a that satisfies B 12 = aB 32 .…”