Feedback control of linear distributed parameter systems via adaptive model reduction in the presence of device network communication constraints

Abstract

We focus on model-based networked control of general linear dissipative distributed parameter systems, the infinite dimensional representation of which can be decomposed to finite-dimensional slow and infinite-dimensional fast and stable subsystems. The controller synthesis of such systems is addressed using adaptive proper orthogonal decomposition (APOD). Specifically, APOD is used to recursively construct locally accurate low dimensional reduced order models (ROMs). The ROM is included in the control structure to reduce the frequency of spatially distributed sensor measurements over the network by suspending communication. The main objective of the current work is to identify a criterion for minimizing communication bandwidth (snapshots transfer rate) from the distributed sensors to the control structure considering closedloop stability. The proposed approach is successfully used to regulate the thermal dynamics in a tubular chemical reactor.

Control of spatially distributed processes with unknown transport‐reaction parameters via two layer system adaptations

“…27 An APOD-based geometric observer/controller pair was also synthesized to track the desired output of nonlinear dissipative distributed parameter systems. 28,29 Even though adaptation laws have been previously used to revise POD techniques online in the literature, 21,23,[30][31][32][33][34][35] to the best knowledge of the authors, the combination of data-driven model reduction and adaptive controller synthesis have not been previously applied to address the control problem of DPS with unknown parameters. The numerous control structures that are based on APOD and other PODlike methods that can be found in the literature, cannot be used directly to address such problems because the controllers cannot be constructed in the presence of unknown parameters in the system.…”

Design of APOD-based switching dynamic observers and output feedback control for a class of nonlinear distributed parameter systems

“…APOD-based geometric observers and controllers was designed to track the output of nonlinear dissipative DPSs [10,11]. A criterion was identified to reduce the computational and measuring costs by minimizing the frequency of ROM revisions [9,12].…”

Dynamic shaping of transport–reaction processes with a combined sliding mode controller and Luenberger-type dynamic observer design

“…Statistical approaches can be employed as an alternative solution to compute the empirical basis functions of a general class of DPSs from an ensemble of solution profiles. Proper orthogonal decomposition is one of the commonly used statistical techniques to find the optimal set of empirical basis functions for a representative set of solution data which has been widely applied in model reduction, optimization and control of DPSs [2,5,6,36,55] where geometric and Lyapunov based approaches have been used.…”