83,402 research outputs found
Identification of continuous-time models for nonlinear dynamic systems from discrete data
A new iOFR-MF (iterative orthogonal forward regression--modulating function) algorithm is proposed to identify continuous-time models from noisy data by combining the MF method and the iOFR algorithm. In the new method, a set of candidate terms, which describe different dynamic relationships among the system states or between the input and output, are first constructed. These terms are then modulated using the MF method to generate the data matrix. The iOFR algorithm is next applied to build the relationships between these modulated terms, which include detecting the model structure and estimating the associated parameters. The relationships between the original variables are finally recovered from the model of the modulated terms. Both nonlinear state-space models and a class of higher order nonlinear input–output models are considered. The new direct method is compared with the traditional finite difference method and results show that the new method performs much better than the finite difference method. The new method works well even when the measurements are severely corrupted by noise. The selection of appropriate MFs is also discussed
A Class of Logistic Functions for Approximating State-Inclusive Koopman Operators
An outstanding challenge in nonlinear systems theory is identification or
learning of a given nonlinear system's Koopman operator directly from data or
models. Advances in extended dynamic mode decomposition approaches and machine
learning methods have enabled data-driven discovery of Koopman operators, for
both continuous and discrete-time systems. Since Koopman operators are often
infinite-dimensional, they are approximated in practice using
finite-dimensional systems. The fidelity and convergence of a given
finite-dimensional Koopman approximation is a subject of ongoing research. In
this paper we introduce a class of Koopman observable functions that confer an
approximate closure property on their corresponding finite-dimensional
approximations of the Koopman operator. We derive error bounds for the fidelity
of this class of observable functions, as well as identify two key learning
parameters which can be used to tune performance. We illustrate our approach on
two classical nonlinear system models: the Van Der Pol oscillator and the
bistable toggle switch.Comment: 8 page
System identification, time series analysis and forecasting:The Captain Toolbox handbook.
CAPTAIN is a MATLAB compatible toolbox for non stationary time series analysis, system identification, signal processing and forecasting, using unobserved components models, time variable parameter models, state dependent parameter models and multiple input transfer function models. CAPTAIN also includes functions for true digital control
Multi-Robot Transfer Learning: A Dynamical System Perspective
Multi-robot transfer learning allows a robot to use data generated by a
second, similar robot to improve its own behavior. The potential advantages are
reducing the time of training and the unavoidable risks that exist during the
training phase. Transfer learning algorithms aim to find an optimal transfer
map between different robots. In this paper, we investigate, through a
theoretical study of single-input single-output (SISO) systems, the properties
of such optimal transfer maps. We first show that the optimal transfer learning
map is, in general, a dynamic system. The main contribution of the paper is to
provide an algorithm for determining the properties of this optimal dynamic map
including its order and regressors (i.e., the variables it depends on). The
proposed algorithm does not require detailed knowledge of the robots' dynamics,
but relies on basic system properties easily obtainable through simple
experimental tests. We validate the proposed algorithm experimentally through
an example of transfer learning between two different quadrotor platforms.
Experimental results show that an optimal dynamic map, with correct properties
obtained from our proposed algorithm, achieves 60-70% reduction of transfer
learning error compared to the cases when the data is directly transferred or
transferred using an optimal static map.Comment: 7 pages, 6 figures, accepted at the 2017 IEEE/RSJ International
Conference on Intelligent Robots and System
Model estimation of cerebral hemodynamics between blood flow and volume changes: a data-based modeling approach
It is well known that there is a dynamic relationship between cerebral blood flow (CBF) and cerebral blood volume (CBV). With increasing applications of functional MRI, where the blood oxygen-level-dependent signals are recorded, the understanding and accurate modeling of the hemodynamic relationship between CBF and CBV becomes increasingly important. This study presents an empirical and data-based modeling framework for model identification from CBF and CBV experimental data. It is shown that the relationship between the changes in CBF and CBV can be described using a parsimonious autoregressive with exogenous input model structure. It is observed that neither the ordinary least-squares (LS) method nor the classical total least-squares (TLS) method can produce accurate estimates from the original noisy CBF and CBV data. A regularized total least-squares (RTLS) method is thus introduced and extended to solve such an error-in-the-variables problem. Quantitative results show that the RTLS method works very well on the noisy CBF and CBV data. Finally, a combination of RTLS with a filtering method can lead to a parsimonious but very effective model that can characterize the relationship between the changes in CBF and CBV
Hierarchical Decomposition of Nonlinear Dynamics and Control for System Identification and Policy Distillation
The control of nonlinear dynamical systems remains a major challenge for
autonomous agents. Current trends in reinforcement learning (RL) focus on
complex representations of dynamics and policies, which have yielded impressive
results in solving a variety of hard control tasks. However, this new
sophistication and extremely over-parameterized models have come with the cost
of an overall reduction in our ability to interpret the resulting policies. In
this paper, we take inspiration from the control community and apply the
principles of hybrid switching systems in order to break down complex dynamics
into simpler components. We exploit the rich representational power of
probabilistic graphical models and derive an expectation-maximization (EM)
algorithm for learning a sequence model to capture the temporal structure of
the data and automatically decompose nonlinear dynamics into stochastic
switching linear dynamical systems. Moreover, we show how this framework of
switching models enables extracting hierarchies of Markovian and
auto-regressive locally linear controllers from nonlinear experts in an
imitation learning scenario.Comment: 2nd Annual Conference on Learning for Dynamics and Contro
On Reduced Input-Output Dynamic Mode Decomposition
The identification of reduced-order models from high-dimensional data is a
challenging task, and even more so if the identified system should not only be
suitable for a certain data set, but generally approximate the input-output
behavior of the data source. In this work, we consider the input-output dynamic
mode decomposition method for system identification. We compare excitation
approaches for the data-driven identification process and describe an
optimization-based stabilization strategy for the identified systems
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