This article considers the problem of bilinearization and optimal control a control-affine nonlinear system by projecting dynamics onto Koopman eigenspace. Although there are linearization techniques like Carleman for embedding finite-dimensional into an infinite-dimensional space, they depend on analytic property vector fields work only polynomial space. The proposed method utilizes canonical transform, specifically eigenfunctions drift field, to transform bilinear under certain...

Koopman-based lifted linear identification have been widely used for data-driven prediction and model predictive control (MPC) of nonlinear systems. It has found applications in flow-control, soft robotics, unmanned aerial vehicles (UAV). For autonomous systems, this system method works by embedding the a higher-dimensional space computing finite-dimensional approximation corresponding Koopman operator with Extended Dynamic Mode Decomposition (EDMD) algorithm. EDMD is algorithm that...

This paper considers the problem of global bilinearization drift and control vector fields a control-affine system. While there are linearization techniques like Carleman for embedding finite-dimensional nonlinear system into an infinite-dimensional space, they depend on analytic property work only polynomial space. The proposed method utilizes Koopman Canonical Transform to transform dynamics ensures bilinearity from projection operator associated with eigenspace operator. resulting...

Modeling of crowd and pedestrian dynamics has intrigued engineers, physicists, sociologists alike, even in recent times. Scientists have long sought to model the collective motion large groups individuals study mathematical basis what seems be apparently random behavior. A number macroscopic models been proposed that describe as a whole, much like partial differential equations fluid mechanics. This paper proposes Lagrangian approach modeling by taking into consideration various forces act...

A cooperative mapping and target-search algorithm is presented for detecting a single moving ground target in an urban environment that initially unknown to team of autonomous quadrotors equipped with noisy, range-limited sensors. The moves according biased random-walk model, search agents (quadrotors) build state graph encodes past present positions. track-before-detect assimilates measurements into the log-likelihood ratio anisotropic kriging interpolation predicts location occupancy nodes...

Dynamical systems described by ordinary and stochastic differential equations can be analyzed through the eigen-decomposition of Perron-Frobenius (PF) Koopman transfer operators. While operator may approximated data-driven techniques, e.g., extended dynamic mode decomposition (EDMD), approximation PF uses a single-pass Monte Carlo approach in Ulam's method, which requires sufficiently long time step. This letter proposes finitedimensional technique for that multi-pass data to pose solve...

This paper considers the problem of non-Gaussian estimation and dynamic output feedback in both linear nonlinear settings. Estimation with process noise, although important fields such as environmental sampling, is typically specific suboptimal. The approach described here uses Gaussian mixture model to approximate an unknown distribution employ Kalman filter its variants: extended unscented filters. error bounded analytically illustrated numerically for systems. estimate used control...

This paper considers the problem of data-driven estimation with sparse measurements for a complex nonlinear system. While model-based methods are well known, state from partial observations unmodeled dynamics is less understood. Here we use method model-free based on an echo-state network (ESN) where reasonably accurate set training data available during period and some obtained testing phase. The assimilated by ensemble Kalman filter (EnKF) to improve predictor's performance when compared...

Since the early modern age, development of various means transit has contributed to a dramatic improvement in quality life. However, past decades (particularly urban environments), simultaneous utilization mobility options resulted poor air quality, traffic congestion, and lack parking. To solve these problems without imposing severe restrictions on personal mobility, alternatives cars powered by internal combustion engines are necessary (see "Summary").

The recently developed Kinect sensor has opened a new horizon to Human-Computer Interface (HCI) and its native connection with Microsoft's product line of Xbox 360 One video game consoles makes completely hands-free control in next generation gaming. Games that requires lot degree freedoms, especially the driving car racing games is best suitable be driven by gestures, as use simple buttons does not scale increased number assistive, comfort, infotainment functions. In this paper, we propose...

This paper considers the problem of non-Gaussian estimation and observer-based feedback in linear nonlinear settings. Estimation systems with process noise statistics is important for applications atmospheric oceanic sampling. Non-Gaussian filtering is, however, largely specific mostly sub-optimal. manuscript uses a Gaussian Mixture Model (GMM) to characterize prior distribution, applies Kalman filter update estimate state uncertainty. The boundedness error both cases analytically justified...

Absence of sufficiently high-quality data often poses a key challenge in data-driven modeling high-dimensional spatio-temporal dynamical systems. Koopman Autoencoders (KAEs) harness the expressivity deep neural networks (DNNs), dimension reduction capabilities autoencoders, and spectral properties operator to learn reduced-order feature space with simpler, linear dynamics. However, effectiveness KAEs is hindered by limited noisy training datasets, leading poor generalizability. To address...

This paper proposes a novel and interpretable recurrent neural-network structure using the echo-state network (ESN) paradigm for time-series prediction. While traditional ESNs perform well dynamical systems prediction, it needs large dynamic reservoir with increased computational complexity. It also lacks interpretability to discern contributions from different input combinations output. Here, systematic architecture is developed smaller parallel reservoirs driven by combinations, known as...

Dynamic Mode Decomposition (DMD) is a widely used data-driven algorithm for estimating the Koopman Operator.This paper investigates how estimation process affected when data quantized. Specifically, we examine fundamental connection between estimates of operator obtained from unquantized and those quantized data. Furthermore, using law large numbers, demonstrate that, under regime, estimate can be considered regularized version estimate. This key theoretical finding paves way to accurately...

This letter presents a Koopman-theoretic lifted linear parameter-varying (LPV) system with countably infinite dimensions to model the nonlinear dynamics of quadrotor on SE(3) for facilitating control design. The LPV evolves in time space observables, called space. A primary challenge utilizing Koopman-based linearization is identifying set observables that can adequately span space, majority current methods using data learn these observables. In this study, we analytically derive formulate...

Extended Dynamic Mode Decomposition (EDMD) is a widely used data-driven algorithm for estimating the Koopman Operator. EDMD extends (DMD) by lifting snapshot data using nonlinear dictionary functions before performing estimation. This letter investigates how estimation process affected when quantized. Specifically, we examine fundamental connection between estimates of operator obtained from unquantized and those quantized via EDMD. Furthermore, law large numbers, demonstrate that, under...

Principle of Swarm Intelligence has recently found widespread application in formation control and automated tracking by the multi-agent system. This article proposes an elegant effective method inspired foraging dynamics to produce geometric-patterns search agents. Starting from a random initial orientation, it is investigated how can be modified achieve convergence agents on desired pattern with almost uniform density. Guided through proposed dynamics, also track moving point continuously...

This paper considers the problem of data-driven prediction partially observed systems using a recurrent neural network. While network based dynamic predictors perform well with full-state training data, partial observation during phase poses significant challenge. Here predictor for observations is developed an echo-state (ESN) and time delay embedding state. The proposed method theoretically justified Taken's theorem strong observability nonlinear system. efficacy demonstrated on three...

The study of collective decision making system has become the central part Swarm- Intelligence Related research in recent years. most challenging task modelling a collec- tive is to develop macroscopic stochastic equation from its microscopic model. In this report we have investigated behaviour with specified rules that resemble chemical reaction and used different group size. Then ventured derive generalized analytical model collective-decision using hyper-geometric distribution. Index...