Formation Control of Multiagent System Based on Higher Order Partial Differential Equations

We propose a method of controlling the formation in a multiagent system using partial differential equations (PDEs). In this method, the behavior of the entire multiagent system is modeled by second-order or higher order PDEs. We also propose a boundary controller that exponentially stabilizes the PDE model. By discretizing the PDE model under the proposed controller, the follower agents’ control laws can be derived. Moreover, the boundary controller corresponds to the leader agents’ control laws. The use of higher order PDEs leads to the generation of various formations that cannot be generated by using lower order PDEs. Finally, we conduct numerical simulations and experiments to validate the proposed method

Non-collocated boundary control for contact-force control of a one-link flexible arm

This paper deals with contact-force control of a one-link flexible arm whose tip is constrained to a rigid environment. To realize the contact-force control, a boundary controller is proposed based on a dynamic model represented by an infinite dimensional model. In particular, the proposed controller does not need the physical parameters in its implementation, and this results in the non-collocated boundary controller. The closed-loop system is analyzed in an appropriate Hilbert space, and it is shown that the exponential stability of the closed-loop system is obtained by setting the feedback gains to locate the eigenvalues of the closed-loop system on the complex left half-plane. In addition, in an attempt to realize the better control performance, another controller which is a modified version of our controller is proposed. Finally, the stability, robustness to the uncertainty in physical parameters, and disturbance response of the closed-loop system are investigated by numerical simulations