Active mode observation of switching systems based on set‐valued estimation of the continuous state

Abstract

SUMMARYMode observability is addressed for a class of discrete-time linear systems that may switch in an unknown and unpredictable way among different modes taken from a finite set. The possible a priori knowledge on the continuous state of the system and the presence of unknown but bounded noises affecting both the system and the measurement equations are explicitly taken into account. The mode observation is performed 'actively': control sequences (discerning control sequences) are searched, which allow to identify the switching sequence on the basis of the observations. Conditions that characterize discerning controls in a finite-horizon setting are obtained. Moreover, a procedure is proposed in order to derive 'persistently discerning' control sequences (over an infinite horizon). A numerical example is reported to clarify the approach.

Fault‐tolerant control of an air heating fan using set‐valued observers: An experimental evaluation

“…In [43], an approach to the synthesis problem of SVOs for linear time-varying plants with nonlinear equality constraints is described. A method for active mode observation of switching systems, based on SVOs, has been recently proposed in [44]. Another solution, applicable to LPV systems, is presented in [45].…”

“…In particular, in [56], a method is proposed that formulates the distinguishability problem as a concave optimization program, in order to obtain bounds on the intensity of the disturbances that guarantee the distinguishability of two dynamic systems. An alternative solution is proposed in [44], by deriving control input signals that lead to the identifiability of the system at hand.…”

Trade-offs between control and mode-observability properties for switching linear systems

“…Due to its practical importance, in recent years, the problem of identifying the active mode of the plant from observations has therefore attracted significant research efforts (e.g. see [2], [3], [6]). In this respect, while several results have been reported for autonomous systems, little is known for configurations such as the one depicted in Fig.…”

“…From a theoretical viewpoint, the main contributions to the study of switching systems have been basically of a two-fold nature: on one side several studies have focused on state/mode observability, viz. on the possibility of reconstructing from measured data the continuous state, the discrete mode, or both [2]- [6]; on the other side, the main interest has been devoted to stability and stabilization problems [7]- [9]. Within this latter source of contribution, however, the major emphasis has been on basic issues, namely the characterization of the control laws which can ensure stability to the switching system under the assumption that an exact knowledge of the active process mode is available in real-time or with delay.…”

On the distinguishability of discrete linear time-invariant dynamic systems

“…For the sake of completeness, we recall that there are also results in the literature providing sufficient conditions for absolute distinguishability. For instance, the authors of [21] show that, ifJ has full column rank and the sets X 0 and W are compact, then the systems can be distinguished for sufficiently large input control signals, regardless of their direction.…”