Control of asynchronous dynamical systems with rate constraints on events

Abstract

Abstract-In this paper we consider dynamical systems which are driven by "events" that occur asynchronously. It is assumed that the event rates are fixed, or at least they can be bounded on any time period of length T . Such systems are becoming increasingly important in control due to the very rapid advances in digital systems, communication systems, and data networks. Examples of such systems include, control systems in which signals are transmitted over an asynchronous network; distributed control systems in which each subsystem has its own objective, sensors, resources and level of decision making; parallelized numerical algorithms in which the algorithm is separated into several local algorithms operating concurrently at different processors; and queuing networks. We present a Lyapunov-based theory for asynchronous dynamical systems and show how Lyapunov functions and controllers can be constructed for such systems by solving linear matrix inequality (LMI) and bilinear matrix inequality (BMI) problems. Examples are also presented to demonstrate the effectiveness of the approach.

Switching Stabilizability for Continuous-Time Uncertain Switched Linear Systems

“…In the following, we will show that the existence of such conic partition based stabilizing switching law implies conditions (13) and (14).…”

“…From Corollary 1, we obtain that the rank condition (13) implies that the intersection of , namely the set , is a polyhedral C-set. Therefore, we may partition the state space into finite cones which are induced by the facets of , and relabel these cones as .…”

“…For feedback stabilization, the switching signals are assumed to be given or restricted, while the continuous-variable control laws, in the form of state or output feedback, are designed to stabilize the switched systems under these given switching signals. Several classes of switching signals are considered in the literature, for example arbitrary switching [7], [11], slow switching [4], [13], restricted switching induced by partitions of the state space [6], [17], [29], [30] etc. The focus of this paper is on a typical switching stabilizability problem, where the switching signals are assumed to be free design variable, while no continuous-variable inputs are considered.…”

Decentralized event-triggered control with asynchronous updates

“…Some results are already available along this lines for the case of weakly coupled systems [12], linear systems [13], or requiring synchronized measurements [14]. There are also other results in the literature, in most cases restricted to linear systems, addressing the topic of asynchronous control [15], [16] and applications requiring this kind of control [17].…”

Robust stability conditions for remote SISO DMC controller in networked control systems

“…Hassibi et al [2] modeled NCSs with data dropouts as Asynchronous Dynamical Systems (ADSs). Branicky et al [3] discussed in detail the problem of how to guarantee the stability of NCSs when various transmission delays or data packet dropouts occur.…”