Sampled-data based consensus for multiple harmonic oscillators with directed switching topology

Abstract

This paper investigates the distributed consensus problem for a group of harmonic oscillators under directed switching topology. First, under the assumption that the union of the directed interaction graphs has a spanning tree, a class of sampleddata based consensus protocols are designed by using motion planning approaches and Pontryagin's principle. The proposed protocols only require that the union of communication topologies switched at the sampled instants has a spanning tree, without requiring information exchanges over the sampled interval and the connectivity of communication topology at each sampling instant. Then, the distributed consensus problem can be solved under directed switching topology by using stability principle and the properties of stochastic matrixes. Compared with the existing sampled-data based consensus algorithms, in this article, a remarkable advantage is that, for the proposed sampled-data based protocols, the sampled periods, communication topologies and control gains are decoupling and can be separately designed, which relaxes many restrictions in controller designs. Finally, as an extension of the leaderless consensus protocols, a leader-following consensus algorithm is further proposed in this paper. Some numerical examples are also given to illustrate the effectiveness of the analytical results.

A specified‐time control framework for control‐affine systems and rigid bodies: A time‐rescaling approach

“…Remark From above analysis, one can conclude that the specified‐time control law derived from the finite‐time control law has faster convergence performance than specified‐time control law derived from the exponential control law in the sense of , while the convergence performance of specified‐time control law is faster than specified‐time control law derived from the asymptotical control law . This shows that our specified‐time control framework can distinguish the convergence performance among different specified‐time control laws, which is an extra benefit over existing approaches …”

“…There are few works considering the specified‐time control problem. By using the Pontryagin's maximum principle, the specified‐time control law is derived from an optimal control problem in the work of Liu et al Since then, a variety of specified‐time control laws have been studied to solve other different scenarios, such as sampled data control, switching graphs control, and so forth . The specified‐time control problem for multiagent systems is proposed in the works of Song et al, wherein the convergence rate is analyzed by the Lyapunov function method.…”

“…First of all, simplifying the design procedure of specified‐time control laws is a significant issue. It is difficult to obtain the specified‐time control laws from the existing asymptotical, exponential, or finite‐time control laws in previous approaches . Secondly, when adopting the optimal control design procedure from Pontryagin's maximum principle, the convergence rate analysis for existing specified‐time control laws is complex.…”

“…Thereby, finding a simple proof method is a key point. Thirdly, a comparative result on convergence performance among different specified‐time control laws cannot be obtained from existing approaches . Designing and distinguishing the different convergence performance of various specified‐time control laws become an even more challenging issue.…”

“…There are few works [26][27][28][29][30][31][32] considering the specified-time control problem. By using the Pontryagin's maximum principle, the specified-time control law is derived from an optimal control problem in the work of Liu et al 26 Since then, a variety of specified-time control laws have been studied to solve other different scenarios, such as sampled data control, switching graphs control, and so forth.…”