Distributed multi-agent consensus under constraints
Date of Issue2017-06-12
School of Electrical and Electronic Engineering
As a basic problem in the cooperative control of multi-agent systems (MASs), distributed multi- agent consensus aims to achieve an agreement of certain interested variables among a group of agents by exchanging information between neighbors. It has found a variety of engineering applications in different areas, e.g. coordination, rendezvous, ﬂocking and formation control. To implement consensus in practice, we need to consider different kinds of constraints. On the one hand, practical MASs bear their own physical limits, such as limited communication bandwidth and kinematic constraints; on the other hand, the ﬁnal consensus value needs to satisfy further requirements in some specific tasks. This thesis is dedicated to the study of two specific consensus problems under constraints: quantized consensus under data rate constraint, and optimal consensus under set or kinematic constraints. The ﬁrst part of the thesis considers the quantized consensus problem under data rate constraint. In a multi-agent network, any communication channel has limited capacity and only ﬁnite bits of error-free information can be transmitted per unit time. As a result, the consensus protocol is designed in the presence of quantized signals and limited data rate. Although the result on using ﬁnite bits of data exchange to achieve quantized consensus for MASs with some general linear dynamics has been established, it is still an open problem about how many bits of data suffice to achieve consensus for systems with high-order dynamics and a partially measured state, and it is not clear what determines the sufficient data rate for consensus In this work, we focus on the quantized consensus for two kinds of critical high-order dynamics: n-th order integrators (n ≥ 3), and 2m-th order oscillators (m ≥ 1) with m identical pairs of conjugate poles on the unit circle. Besides, in either case only the ﬁrst state variable is measurable. We design an observer-based dynamic encoding-decoding scheme to estimate the unmeasurable state variables, and devise a control protocol based on the encoder/decoder outputs. By employing perturbation techniques, we are able to explicitly design the control gains and provide a sufficient data rate for quantized consensus. Under a ﬁxed and connected network, for MASs with integrator dynamics it only needs n bits of information exchange to achieve exponentially fast consensus, while for oscillator dynamics the number of required bits is an integer between m and 2m, which is dependent on the location of poles, or the oscillation frequency. These results not only achieve the lowest data rate among existing works, but also indicate that the sufficient data rate is independent of the network topology, and closely related with the system structure. The second part of the thesis considers the optimal consensus problem under set or kinematic constraints. The optimal consensus aims to achieve an agreement of state that minimizes the aggregate cost, which is the sum of individual costs assigned to each agent. A typical example is the shortest-distance rendezvous, which may be further required to be achieved within a given constraint set. Continuous-time MASs with single integrator dynamics are ﬁrst studied. To achieve the constrained optimum, we combine three diﬀerent terms into the control protocol: local averaging, local projection, and local subgradient descent with a decaying gain α(t). Under a balanced network with uniformly joint spanning trees, we employ non-smooth analysis to show that the convergence to the constrained optimum set can be guaranteed if α(t) is non-integrable. Provided that the aggregate cost is strongly convex, we further analyze the convergence rate for diﬀerent types of α(t). In a similar vein, we establish corresponding results for discrete-time systems, and further discuss the necessary conditions and the issue of communication delay when the balanced network is ﬁxed. We also explore the optimal consensus under kinematic constraints, speciﬁcally for MASs with hererogeneous EL dynamics under bounded input and velocity. Assuming an exact knowledge of nonlinearity and a priori estimate of the optimum, we show that an exponentially fast convergence is guaranteed while satisfying the bounded kinematic constraints, if the ﬁxed and undirected topology is connected.
DRNTU::Engineering::Electrical and electronic engineering::Control and instrumentation::Control engineering