Related papers: Stability-Certified Koopman Observer Design for No…
We propose a provably stabilizing and tractable approach for control of constrained linear systems under intermittent observations and unreliable transmissions of control commands. A smart sensor equipped with a Kalman filter is employed…
Koopman operator theory has emerged as a leading data-driven approach that relies on a judicious choice of observable functions to realize global linear representations of nonlinear systems in the lifted observable space. However,…
Koopman operator theory enables a global linear representation of a given nonlinear dynamical system by transforming the nonlinear dynamics into a higher dimensional observable function space where the evolution of observable functions is…
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…
The modeling of nonlinear dynamics based on Koopman operator theory, which is originally applicable only to autonomous systems with no control, is extended to non-autonomous control system without approximation to input matrix B. Prevailing…
In this paper, we study how the Koopman operator framework can be combined with kernel methods to effectively control nonlinear dynamical systems. While kernel methods have typically large computational requirements, we show how random…
We study the problem of designing interval-valued observers that simultaneously estimate the system state and learn an unknown dynamic model for partially unknown nonlinear systems with dynamic unknown inputs and bounded noise signals.…
Koopman operators provide tractable means of learning linear approximations of non-linear dynamics. Many approaches have been proposed to find these operators, typically based upon approximations using an a-priori fixed class of models.…
Koopman-based methods leverage a nonlinear lifting to enable linear regression techniques. Consequently, data generation, learning and prediction is performed through the lens of this lifting, giving rise to a nonlinear manifold that is…
Learning tractable linear representations of nonlinear dynamical systems via Koopman operator theory is often hindered by dictionary selection, temporal memory encoding, and numerical ill-conditioning. Inspired by Reservoir Computing (RC)…
Ordinary Differential Equations are a simple but powerful framework for modeling complex systems. Parameter estimation from times series can be done by Nonlinear Least Squares (or other classical approaches), but this can give…
We introduce two novel generalizations of the Koopman operator method of nonlinear dynamic modeling. Each of these generalizations leads to greatly improved predictive performance without sacrificing a unique trait of Koopman methods: the…
In the theory of quantum dynamical filtering, one of the biggest issues is that the underlying system dynamics represented by a quantum stochastic differential equation must be known exactly in order that the corresponding filter provides…
Nonlinear model predictive control has become a popular approach to deal with highly nonlinear and unsteady state systems, the performance of which can however deteriorate due to unaccounted uncertainties. Model predictive control is…
Koopman operator, as a fully linear representation of nonlinear dynamical systems, if well-defined on a reproducing kernel Hilbert space (RKHS), can be efficiently learned from data. For stability analysis and control-related problems, it…
Real-world time series are characterized by intrinsic non-stationarity that poses a principal challenge for deep forecasting models. While previous models suffer from complicated series variations induced by changing temporal distribution,…
The problem of finite/fixed-time cooperative state estimation is considered for a class of quasilinear systems with nonlinearities satisfying a H\"older condition. A strongly connected nonlinear distributed observer is designed under the…
This paper studies the problem of output regulation for a class of nonlinear systems experiencing matched input disturbances. It is assumed that the disturbance signal is generated by an external autonomous dynamical system. First, we show…
Nonlinear coupled systems are ubiquitous in science and engineering. The analysis and modeling of such systems is challenging due to their high dimensionality and complex interactions among subsystems. In recent years, operator-theoretic…
This paper addresses the synthesis of an optimal fixed-gain distributed observer for discrete-time linear systems over wireless sensor networks. The proposed approach targets the steady-state estimation regime and computes fixed observer…