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The Koopman operator has become an essential tool for data-driven analysis, prediction and control of complex systems. The main reason is the enormous potential of identifying linear function space representations of nonlinear dynamics from…
Credible forecasting and representation learning of dynamical systems are of ever-increasing importance for reliable decision-making. To that end, we propose a family of Gaussian processes (GP) for dynamical systems with linear…
Linear partial differential equations (PDEs) are an important, widely applied class of mechanistic models, describing physical processes such as heat transfer, electromagnetism, and wave propagation. In practice, specialized numerical…
This paper investigates the state estimation problem for a class of complex networks, in which the dynamics of each node is subject to Gaussian noise, system uncertainties and nonlinearities. Based on a regularized least-squares approach,…
Natural gas transmission pipelines are complex systems whose flow characteristics are governed by challenging non-linear physical behavior. These pipelines extend over hundreds and even thousands of miles. Gas is typically injected into the…
This paper is concerned with the leader-following output consensus problem in the framework of distributed nonlinear observers. In stead of certain hypotheses on the leader system, a group of geometric conditions is put forward to develop a…
This paper presents a class of linear predictors for nonlinear controlled dynamical systems. The basic idea is to lift the nonlinear dynamics into a higher dimensional space where its evolution is approximately linear. In an uncontrolled…
Improving distribution grid reliability is a major challenge for planning and operation of distribution systems having a high share of distributed generators (DGs). The rise of DGs share can lead to unplanned contingencies while on the…
Data-driven approximations of the Koopman operator are promising for predicting the time evolution of systems characterized by complex dynamics. Among these methods, the approach known as extended dynamic mode decomposition with dictionary…
The design of grid-connected distributed energy systems (DES) has been investigated extensively as an optimisation problem in the past, but most studies do not include nonlinear constraints associated with unbalanced alternating current…
We consider the problem of optimal power allocation in a sensor network where the sensors observe a dynamic parameter in noise and coherently amplify and forward their observations to a fusion center (FC). The FC uses the observations in a…
We derive a data-driven method for the approximation of the Koopman generator called gEDMD, which can be regarded as a straightforward extension of EDMD (extended dynamic mode decomposition). This approach is applicable to deterministic and…
Differential equations (DE) constrained optimization plays a critical role in numerous scientific and engineering fields, including energy systems, aerospace engineering, ecology, and finance, where optimal configurations or control…
We analyze a system of nonlinear stochastic partial differential equations (SPDEs) of mixed elliptic-parabolic type that models the propagation of electric signals and their effect on the deformation of cardiac tissue. The system governs…
We are concerned with the simulation and optimization of large-scale gas pipeline systems in an error-controlled environment. The gas flow dynamics is locally approximated by sufficiently accurate physical models taken from a hierarchy of…
This paper describes a method for learning low-dimensional approximations of nonlinear dynamical systems, based on neural-network approximations of the underlying Koopman operator. Extended Dynamic Mode Decomposition (EDMD) provides a…
The co-optimization of behind-the-meter distributed energy resources is considered for prosumers under the net energy metering tariff. The distributed energy resources considered include renewable generations, flexible demands, and battery…
Power losses in electrical power systems especially, distribution systems, occur due to several environmental and technical factors. Transmission & Distribution line losses are normally 17% and 50% respectively. These losses are due to the…
When complex systems with nonlinear dynamics achieve an output performance objective, only a fraction of the state dynamics significantly impacts that output. Those minimal state dynamics can be identified using the differential geometric…
We present a framework for distributed Pose Graph Optimization (PGO) by formulating the problem as a second-order continuous-time dynamical system evolving on Lie groups. By modeling pose variables as massive particles subject to damping,…