A disturbance observer based practical coordinated tracking controller for uncertain heterogeneous multi‐agent systems

This paper presents a coordinated tracking controller for multi‐agent systems. We assume that agents are uncertain, nonidentical, and affected by external disturbances. The information available to the tracking controller is a weighted sum of relative measurements. A coordinated tracking controller based on the disturbance observer, which is known as a robust output feedback controller, is designed so that the disturbances acting on agents are attenuated and at the same time the weighted sum of relative measurements approximately satisfies a differential equation defined by the leader's dynamics, which results in practical coordinated tracking. Systematic design procedures of the controller as well as numerical simulations are provided. Copyright © 2014 John Wiley & Sons, Ltd.     

An adaptive algorithm applied to a design of robust observer

Primary goal of adaptive observers would be to estimate the true states of a plant. Identification of unknown parameters is of secondary interest and is achieved frequently with the persistent excitation condition of some regressors. Nevertheless, two problems are linked to each other in the classical approaches to adaptive observers; as a result, we get a good state estimate once after a good parameter estimate is obtained. This paper focuses on the state estimation without parameter identification so that the state is estimated regardless of persistent excitation. In this direction of research, Besancon (2000) recently summarized that most of adaptive observers in the literature share one common canonical form, in which unknown parameters do not affect the unmeasured states. We enlarge the class of linear systems from the canonical form of (Besancon. 2000) by proposing an adaptive observer (with additional dynamics) that allows unknown parameters to affect those unmeasured states. A recursive algorithm is presented to design the proposed dynamic observer systematically. An example confirms the design procedure with a simulation result.     

A Disturbance Observer-based Robust Tracking Controller for Uncertain Robot Manipulators

This paper considers the trajectory tracking problem for uncertain robot manipulators subject to external disturbance torques. The external disturbance torques are assumed to be unknown and time-varying. We present a disturbance observer-based controller which estimates the lumped disturbance (the external disturbance torque combined with the effect of plant uncertainties), and compensates it so that the overall closed-loop system behaves like the nominal closed-loop system that is composed of the nominal model of robot manipulator and the feedback linearization-based tracking controller. A simplified implementation of the proposed controller is also introduced. Simulation results on a robot manipulator are given to validate the performance of the proposed controller.     

Consensus of high-order linear systems using dynamic output feedback compensator: Low gain approach

In this paper, we study the consensus (and synchronization) problem for multi-agent linear dynamic systems. All the agents have identical MIMO linear dynamics which can be of any order, and only the output information of each agents is delivered throughout the communication network. It is shown that consensus is reached if there exists a stable compensator which simultaneously stabilizes N−1 systems in a special form, where N is the number of agents. We show that there exists such a compensator under a very general condition. Finally, the consensus value is characterized as a function of initial conditions with stable compensators in place.     

Dynamic observer error linearization

In this paper, a new framework of observer error linearization problem is proposed. The main idea of our approach is twofold. The one is to introduce an auxiliary dynamics whose input is the system output, and the other is to transform the augmented system into an observable linear system with an injection term which contains the system output as well as the state of the auxiliary dynamics. It is a natural extension of the recently developed dynamic observer error linearization where the injection term contains only newly defined output. It is also shown that whenever an n dimensional system is immersible into an n+d dimensional linear system up to an output injection, then it can be also dynamically observer error linearizable in our sense with a d dimensional auxiliary dynamics. Moreover, we show that the converse is not true by providing a counterexample, which implies that our approach is applicable to a strictly wider class of systems than that of the system immersion method.     

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.     

Immersion of Non-Linear Systems into Linear Systems up to Output Injection: Characteristic Equation Approach

There exists a class of non-linear systems which cannot be transformed into non-linear observer form via diffeomorphism, but can be immersed into higher dimensional non-linear observer form. This paper investigates when n dimensional non-linear systems can be immersed into (n + m)-dimensional non-linear systems in non-linear observer form, and provides a necessary and sufficient condition. We also present an algorithm to check the immersibility. In general, at the first step of the algorithm, one should solve a differential equation with m + 1 unknowns rather than solving one with n + m unknowns simultaneously. When a solution to the differential equation can be obtained, the immersibility can be checked by a recursive algorithm. Moreover, when 2m ≤ n, a straightforward algorithm is provided to check the immersibility.     

New Internal Model Average Consensus Estimators with Light Communication Load

The dynamic average consensus problem for a group of agents is considered. Each agent in the group is supposed to estimate the average of inputs applied to all agents and the estimation should be done in a distributed way. By reinterpreting the proportional integral type estimator, a new structure for the average estimator which can embed the internal model of inputs is proposed and conditions which result in the zero estimation error in the steady state are derived. We present constructive design procedures for the cases of constant inputs and time-varying inputs employing the root locus for the former and LQR-based design for the latter. The theory is validated through numerical simulations.     

An algorithm for system immersion into nonlinear observer form: SISO case

The class of nonlinear systems that can be put into nonlinear observer form (linear system with output injection) can be broadened if we employ the system immersion. We provide an immersion algorithm for SISO nonlinear systems with relative degree r. The proposed algorithm is an extension of the previous results and does not require the relative degree 1 assumption. In addition, it is seen that the immersion can always be computed via algebraic computations and simple integrations except in a very special case in which the relative degree equals the system dimension (in this case, only one first order differential equation appears in the algorithm).