Nonlinear Discrete-Time Observers with Physics-Informed Neural Networks

In modern feedback control systems theory and practice, reliable access to the dynamically evolving system states is needed at both the implementation stage of advanced control algorithms and for process/system condition and performance monitoring purposes [16, 8, 39, 13, 47]. Traditionally, an explicit use of an available dynamic model complemented by sensor measurements, involving measurable physical and chemical variables of the system of interest, represented a first option to respond to the above need. However, in practice, key critical state variables are often not available for direct on-line measurement, due to inherent physical as well as practically insurmountable technical and economic limitations associated with the current state of sensor technology as it is invariably deployed in cases of considerable system complexity [47, 16, 8, 39]. In light of the above remarks, a better, scientifically sound and practically insightful option is the design of a state estimator (an observer). This is itself an appropriately structured dynamical system itself that utilizes all information provided by a system model as well as available sensor measurements to accurately reconstruct the dynamic profiles of all other unmeasurable state variables [47, 16, 8, 13].