Adaptive consensus estimation of multi-agent systems

Abstract

Abstract-This paper considers the effects of a penalty term in both the state and parameter estimates for multi-agent systems. It is assumed that the plant parameters are desired to be identified on-line and N agents are available to implement adaptive observers. Using an additive term which takes the form of a penalty on the mismatch between the state and parameter estimates, the proposed adaptive consensus estimation scheme ensures that both state and parameter estimates reach consensus. While the proposed adaptive consensus identifiers assume an all-to-all connectivity, the abstract framework that the adaptive identifiers are examined under, allows for any form of agent connectivity to be examined. As a measure of agreement of the estimates that is independent of the network topology, the deviation from the mean estimate for both the state and parameter estimates is defined and shown to converge to zero. Simulation studies of a second order system provide a verification of the proposed theoretical predictions.

Adaptive estimation of external fields in reproducing kernel Hilbert spaces

“…Problems of this type are studied in the family of papers. [9][10][11] These formulations are quite general and are formulated for systems where the evolution laws for the agents are defined in terms of Gelfand triples, with the constituent operators satisfying some standard boundedness and coercivity properties for common DPS. In these papers the agent states evolve in an infinite dimensional state space, in contrast to the situation here.…”

“…This argument employs a definition of PE in the weak topology on the RKHS and is the first of its kind for this class of evolution problems in an RKHS. It is possible to view this strategy as an adaptation of the weak PE analyses that have been used in the study of DPS associated with some types of partial differential equations (PDEs) as in References 9‐11. For the DPS in Equation () we exploit the uniform embedding of the RKHS space and the proof of output convergence to simplify some of the arguments of convergence in the weak topology in this case.…”

“…In addition to the discrete time formulation of adaptive estimation summarized above, there also is a body of work that studies infinite dimensional consensus estimation problems for various classes of DPSs generated by families of PDEs. Problems of this type are studied in the family of papers 9‐11 . These formulations are quite general and are formulated for systems where the evolution laws for the agents are defined in terms of Gelfand triples, with the constituent operators satisfying some standard boundedness and coercivity properties for common DPS.…”

“…In contrast to prior work, in this article we explore weak PE conditions that are stated in terms of the weak topology on for adaptive estimation of an external scalar field. The strategy based on the weak topology is qualitatively similar to that in Reference 33 for the study of certain classes of PDEs as in References 9‐11, but the details of the proofs must be modified to exploit properties of the RKHS and the RKHS embedding formulation. This characterization of convergence is made precise by defining a weak norm $$$ {\left|\cdotp \right|}_w $$$ on and defining a linear subspace that consists of functions that, in some sense, “fail to be weakly persistently excited.” It is later shown that any solution $$$ \tilde{g}(t) $$$ of the governing ideal error equation () is contained in $$$ \overline{B_r(0)} $$$, the closed ball in of radius $$$ r $$$ centered at the origin, for a suitably large $$$ r>0 $$$.…”

Adaptive Estimation Using Multiagent Network Identifiers With Undirected and Directed Graph Topologies

“…[8] for the very restrictive case of all-to-all graph connectivity. In particular, the proposed framework allows one to decouple the graph connectivity (i.e., the graph Laplacian) from the stability analysis of the parameter errors by simply replacing a nonnegative damping-like matrix representing the connectivity of the graph topology with another matrix representing a more general interagent connectivity.…”