Formation control of a multi-agent system subject to Coulomb friction

The Interconnection of Quadratic Droop Voltage Controllers Is a Lotka-Volterra System: Implications for Stability Analysis

“…Notice that although variations of θ i,j depend on voltage magnitudes based on the physical laws, the results of this section are independent of these effects. In fact, the variations of the relative angles will cause variations in ∆ c 1,2 and ∆ s 1,2 , which are both bounded and take a value in the set [−1, +1], in Ψ(θ(t)) (16). Thus, without making any specific assumption on the dynamics of θ i,j , we can mathematically model the variations of θ i,j as a time varying variable which takes a value in [−1, +1].…”

“…where σ ∈ R is treated as a constant parameter. The approach in [11] discusses the stability of homogeneous time-varying systems of a positive order (see Definition 4) as well as a class of non-homogeneous time-varying systems which possesses a homogeneous approximation when the system state (e.g., ||V ||) is sufficiently large, i.e., system (16). First let us write Ψ(θ(σ)) in (14) We now prove the asymptotic stability ofV = diag(V )Ψ(θ(σ))V .…”

“…First let us write Ψ(θ(σ)) in (14) We now prove the asymptotic stability ofV = diag(V )Ψ(θ(σ))V . This result is required in the proof of boundedness of the time-varying network (16).…”

Robust consensus of unicycles using ternary and hybrid controllers

“…In fact, the real‐world constraints, that is, communication and information constrains, in implementation of coordination algorithms have motivated the use of a specific class of nonsmooth controllers that are based on quantized and coarse information, for example, binary and ternary controllers. For instance, papers have studied binary information and control in consensus and formation‐keeping problems for a group of continuous‐time dynamical systems including single/double integrators and strictly passive systems. A rendezvous problem for Dubins cars based on a ternary feedback has been studied in .…”

“…Our design, which is motivated by real‐world constraints in coordination problems, is based on simple control commands. Recent literature in this line of research (e.g., ) has mainly introduced binary controllers for the position coordination of other classes of dynamic agents and shown exact convergence to the desired formations. This paper uses ternary controllers for unicycles.…”