Switching control laws in the presence of measurement noise

摘要

In this paper we study a class of systems governed by piecewise continuous control laws, subject to measurement noise and such that more than one state configuration could be a desired point for the system to be stabilized. Such a problem is common in many practical situations, including, for example, vehicle attitude control, robotic manipulator positioning, deployment of multistable structures, etc. Our aim is to characterize, both for continuous and discrete-time models, control properties and switching policies ensuring that any possible state trajectory of the closed-loop system is robustly asymptotically convergent to one of the desired "target points". First we will show that in the discrete-time case, conditions guaranteeing the asymptotic stability to a set of points can be derived by exploiting the intrinsic "holding" nature of the discrete-time framework. Such results can be extended to continuous time by means of standard sample-and-hold techniques. However, this kind of solution is revealed to be very conservative and then not realistically employable in many contexts. For such a reason further less restrictive policies will be introduced and investigated; these are mostly based on the concept of "strategy holding" in time (by providing a slower switching policy sampling time) and space (by using hysteresis regions). Those strategies will be characterized both in terms of global stabilizability and in terms of switching flexibility, i.e., the capability to react in a convenient way to sudden state changes. Driven by the above analysis an "opportunistic switching" strategy combining all the advantages of the strategies considered will be proposed and analyzed. Synthesis results are presented, providing a constructive procedure to design the proposed control laws. The paper is concluded with an application example based on the attitude control of a Ducted-Fan Aerial Vehicle, showing the effectiveness of the proposed approach in a practical application.