No abstract

Abstract-This brief investigates the control problem for a number of cooperative spacecraft with communication constraints. It is assumed that a set of cooperative local controllers corresponding to the individual spacecraft is given which satisfies the desired objectives of the formation. It is to be noted that due to the information exchange between the local controllers, the overall control structure can be considered centralized in general. However, communication in flight formation is expensive. Thus, it is desired to have some form of decentralization in control structure, which has a lower communication requirement. This decentralized controller consists of local estimators inherently, so that each local controller estimates the state of the whole formation. Necessary and sufficient conditions for the stability of the formation under the proposed decentralized controller are obtained. It is shown that the decentralized control system, if stable, behaves almost the same as its centralized counterpart. Moreover, robustness of the decentralized controller is studied and compared to that of the corresponding centralized controller. It is finally shown that the proposed decentralized controller comprises most of the features of its centralized counterpart. The efficacy of the proposed method is demonstrated through simulations.

This paper is concerned with the convergence of a class of continuous-time nonlinear consensus algorithms for single integrator agents. In the consensus algorithms studied here, the control input of each agent is assumed to be a state-dependent combination of the relative positions of its neighbors in the information flow graph. Using a novel approach based on the smallest order of the nonzero derivative, it is shown that under some mild conditions the convex hull of the agents has a contracting property. A set-valued LaSalle-like approach is subsequently employed to show the convergence of the agents to a common point. The results are shown to be more general than the ones reported in the literature in some cases. An illustrative example demonstrates how the proposed convergence conditions can be verified.

No abstract

This paper investigates the stabilization problem for a linear time-invariant (LTI) time-delay system by means of a decentralized finite-dimensional LTI output feedback controller. Both commensurate and incommensurate delays are considered. It is assumed that delay can appear in the state, inputs, and outputs of the system. In this case, using the definition of µ-decentralized fixed modes (µ-DFM) introduced in a recent work necessary and sufficient conditions for the decentralized stabilizability of LTI time-delay systems is obtained. Some algebraic conditions are also provided to determine if a mode of a time-delay system is a µ-DFM. A numerical algorithm is proposed to obtain the set of µ-DFMs of the system, and the notion of µ-approximate decentralized fixed modes (µ-ADFM) is also presented. Finally, three numerical examples are given to illustrate various applications of the results.