Consensus Tracking Control of Multi-agent Systems with A Time-varying Reference State under Binary-valued Communication

TL;DR

This work advances consensus tracking in discrete-time multi-agent systems where inter-agent communication is binary-valued and the leader reference state varies over time. It introduces an identification-based approach in which neighbor states are estimated via recursive projection, and control actions are computed from these estimates, analyzed through two Lyapunov functions that couple estimation and control. For an asymptotically convergent reference, a CRS algorithm with decaying estimation step and decaying control gain yields mean-square convergence of both the estimation and tracking errors, with rate tied to the reference change. For a bounded reference, a BRS algorithm with constant gains ensures the followers track the leader to a neighborhood, with the neighborhood size depending on the leader dynamics. Simulations corroborate the theory, demonstrating asymptotic tracking under decaying gains and exponential convergence to a neighborhood under constant gains, illustrating practical viability with binary communication.

Abstract

This paper investigates the problem of consensus tracking control of discrete time multi-agent systems under binary-valued communication. Different from most existing studies on consensus tracking, the transmitted information between agents is the binary-valued. Parameter identification with binary-valued observations is applied to the estimation of neighbors'states and the tracking control is designed based on the estimation. Two Lyapunov functions are constructed to deal with the strong coupling of estimation and control. Compared with consensus problems under binary-valued communication, a reference state is required for consensus tracking control. Two scenarios of the time-varying reference state are studied respectively. (1) The reference state is asymptotically convergent. An online algorithm that performs estimation and control simultaneously is proposed, in which the estimation step size and the control gain are decreasing with time. By this algorithm, the multi-agent system is proved to achieve consensus tracking with convergence rate O(1/k^ε ) under certain conditions. (2) The reference state is bounded, which is less conservative than that in the first case. In this case, the estimation step size and control gain are designed to be constant. By this algorithm, all the followers can reach to a neighborhood of the leader with an exponential rate. Finally, simulations are given to demonstrate theoretical results.

Figures (3)

• Figure 1: Network topology of three multi-agents.
• Figure 2: Algorithm of CRS with $\beta =150$.
• Figure 3: Algorithm of BRS with $\beta =3$.

Theorems & Definitions (24)

• Remark 1
• Remark 2
• Remark 3
• Lemma 1
• proof
• Remark 4
• Proposition 1: ref18, Proposition 1
• Remark 5
• Lemma 2
• Lemma 3