Hongkeun Kim

Output Consensus of Heterogeneous Uncertain Linear Multi-Agent Systems

This technical note studies the output consensus problem for a class of heterogeneous uncertain linear multi-agent systems. All the agents can be of any order (which might widely differ among the agents) and possess parametric uncertainties that range over an arbitrarily large compact set. The controller uses only the output information of the plant; moreover, the delivered information throughout the communication network is also restricted to the output of each agent. Based on the output regulation theory, it is shown that the output consensus is reached if the (state) consensus is achieved within the internal models among the agents controllers (even though the plants outputs, rather than the internal models outputs, are communicated). The internal models can be designed and embedded into the controller, which provides considerable flexibility to designers in terms of the type of signals that are agreed on among the agents.

Cucker-Smale Flocking With Inter-Particle Bonding Forces

The Cucker-Smale (CS) flocking model is an interacting particle system, in which each particle updates its velocity by adding to it a weighted average of the differences of its velocity with those of other particles. It has been shown that by using the C-S model, the velocities of particles converge to a common value despite the absence of a central command. In this note, we make an extension of the C-S model by introducing additional interaction terms between agents which we refer to as the inter-particle bonding force, in order to incorporate collision avoidance between agents, and at the same time achieve tighter spatial configurations. The proposed inter-particle bonding force makes use of position and velocity information of other agents in order to achieve such separation and cohesion. With the inter-particle bonding forces and the velocity-alignment term of the original C-S model, we show the emergent behavior of asymptotic flocking to spatial equilibrium configurations.

Consensus of output-coupled linear multi-agent systems under fast switching network: Averaging approach

This study addresses the problem of consensus of multi-agent systems, consisting of a set of identical MIMO LTI systems, under a time-varying network that has a well-defined average (with uniform convergence to the average). The information delivered through the communication network is the output of each system. First, it is shown that consensus is reached asymptotically by using a group of compensators if the network switches sufficiently fast and the compensators are designed such that the multi-agent system asymptotically achieves consensus for the average of the network. Further, we find a relation between the two agreements, one obtained from considering the switching network and the other obtained from replacing the network with its average. Then, for a class of minimum phase systems, we remove the fast switching condition by redesigning the compensators. Finally, the formation stabilization of unicycle-type mobile robots is dealt with as an application of the problem, and it is demonstrated via a computer simulation.

Consensus of output-coupled linear multi-agent systems under frequently connected network

This paper studies the problem of consensus for linear multi-agent systems under a frequently connected communication network. All the agents, which have identical MIMO linear dynamics, can be of any order and only the output information of each agent is delivered through the communication network. To tackle the problem we first present a necessary and sufficient condition for achieving the consensus under the fixed network topology. After that, a sufficient condition for the problem is provided under the circumstances of frequently connected network topology. The key idea is the average dwell-time and its use in stability theory.

Consensus of Multi-Agent Systems Under Periodic Time-Varying Network *

Abstract In this paper, we address the consensus problem for a class of feedback linearizable nonlinear multi-agent systems under a dynamically changing and periodic network communication. The information delivered throughout the communication network is the output of each identical MIMO autonomous agent which can be of any order. First of all, with a local-level control strategy, we show that the consensus is reached by only using a linear time-invariant compensator if the network changes sufficiently fast in time and the compensator is designed so that the multi-agent system achieves the consensus for the average of the communication network. In this case, it is also shown that the state trajectories are close to those of average system if one of the agents is. Finally, in the case of integrator chains, we relax the fast switching condition of the network and give an example that verifies the result.

Locally optimal and globally inverse optimal controller for multi-input nonlinear systems

The Hinfin-optimal control for nonlinear systems is hard to obtain because one must solve the Hamilton-Jacobi-Isaacs (HJI) equation. To overcome this problem, a nonlinear controller is proposed by Ezal, Pan, and Kokotovic. The controller guarantees local optimality and global inverse optimality, that is, it behaves as a linear optimal controller in the region where the linearized dynamics dominates, and is inverse optimal in the global sense. However, the system class under their consideration is single-input strict-feedback nonlinear systems which is somewhat restrictive. In this paper, we propose a nonlinear optimal controller for a class of multi-input nonlinear systems. Moreover, under the proposed controller, the closed-loop system is globally exponentially stable, whereas the controller proposed by Ezal et al. just guarantees global asymptotic stability.

Technical communique: A note on the differential regulator equation for non-minimum phase linear systems with time-varying exosystems

Some control problems in practice are often formulated as a linear output regulation problem with time-varying exosystems. Although this problem has been studied recently, an explicit and constructive solution has been given only for minimum phase systems. This paper presents a solution for non-minimum phase systems whose zero dynamics is hyperbolic (or has an exponentially dichotomic split in the case of time-varying zero dynamics). The idea is inspired by the non-causal stable inversion.

A simple noise reduction disturbance observer and Q-filter design for internal stability

The noise reduction disturbance observer is an unconventional construction of disturbance observer which has the ability of attenuating the high frequency measurement noise as well as the low frequency input disturbance. While retaining the same capabilities, this paper explores a more concise and prevailing version of the noise reduction disturbance observer with a more relaxed almost necessary and sufficient condition for the closed-loop system to be internally stable without requiring the stability of the nominal plant. Moreover, the proposed version is reduced-order compared with the classical disturbance observers in the sense that the two low-pass filters, commonly set to be identical, are now distinct and, as a result, one of them can have order less than the relative degree of the nominal plant. All of which are the direct consequence of a simplified configuration, we additionally present a design method for the two distinct low-pass filters to guarantee the internal stability of the system.

Design of output feedback controller for consensus of linear systems having non-uniform ranks With switching topology

This paper studies the design problem of a controller to achieve a consensus of a group of N identical and high-order linear systems that possibly have non-uniform ranks but do not have finite zeros. The local interactions among the N systems are modeled by a switching graph that ranges over a finite set of connected and undirected graphs and has a non-vanishing dwell time. Under these conditions, we propose a controller for the consensus of the N systems which uses only relative output measurements from the neighboring systems for the purpose of feedback.