621,791 research outputs found
On the Relation between Discrete and Continuous-time Refined Instrumental Variable Methods
The Refined Instrumental Variable method for discrete-time systems (RIV) and its variant for continuous-time systems (RIVC) are popular methods for the identification of linear systems in open-loop. The continuous-time equivalent of the transfer function estimate given by the RIV method is commonly used as an initialization point for the RIVC estimator. In this letter, we prove that these estimators share the same converging points for finite sample size when the continuous-time model has relative degree zero or one. This relation does not hold for higher relative degrees. Then, we propose a modification of the RIV method whose continuous-time equivalent is equal to the RIVC estimator for any non-negative relative degree. The implications of the theoretical results are illustrated via a simulation example.</p
Safe Q-learning for continuous-time linear systems
Q-learning is a promising method for solving optimal control problems for
uncertain systems without the explicit need for system identification. However,
approaches for continuous-time Q-learning have limited provable safety
guarantees, which restrict their applicability to real-time safety-critical
systems. This paper proposes a safe Q-learning algorithm for partially unknown
linear time-invariant systems to solve the linear quadratic regulator problem
with user-defined state constraints. We frame the safe Q-learning problem as a
constrained optimal control problem using reciprocal control barrier functions
and show that such an extension provides a safety-assured control policy. To
the best of our knowledge, Q-learning for continuous-time systems with state
constraints has not yet been reported in the literature
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Identification of nonlinear interconnected systems
This thesis was submitted for the degree of Master of Philosophy and awarded by Brunel University.In this work we address the problem of identifying a discrete-time nonlinear system composed of a linear dynamical system connected to a static nonlinear component. We use linear fractional representation to provide a united framework for the identification of two classes of such systems. The first class consists of discrete-time systems consists of a linear time invariant system connected to a continuous nonlinear static component. The identification problem of estimating the unknown parameters of the linear system and simultaneously fitting a math order spline to the nonlinear data is addressed. A simple and tractable algorithm based on the separable least squares method is proposed for estimating the parameters of the linear
and the nonlinear components. We also provide a sufficient condition on data for consistency of the identification algorithm. Numerical examples illustrate the performance of the algorithm. Further, we examine a second class of systems that may involve a nonlinear static element of a more complex structure. The nonlinearity may not be continuous and is approximated by piecewise a±ne maps defined on different convex polyhedra, which are defined by linear
combinations of lagged inputs and outputs. An iterative identification procedure is proposed, which alternates the estimation of the linear and the nonlinear subsystems. Standard identification techniques are applied to the linear subsystem, whereas recently developed piecewise affine system identification techniques are employed for the estimation of the nonlinear component. Numerical examples show that the proposed procedure is able to successfully profit
from the knowledge of the interconnection structure, in comparison with a direct black box identification of the piecewise a±ne system.Funding was obtained as a Marie Curie Early Stage Researcher Training fellowship, under the NET-ACE project (MEST-CT-2004-6724)
Parametric Continuous-Time Blind System Identification
In this paper, the blind system identification problem for continuous-time systems is considered. A direct continuous-time estimator is proposed by utilising a state-variable-filter least squares approach. In the proposed method, coupled terms between the numerator polynomial of the system and input parameters appear in the parameter vector which are subsequently separated using a rank-1 approximation. An algorithm is then provided for the direct identification of a single-input single-output linear time-invariant continuous-time system which is shown to satisfy the property of correctness under some mild conditions. Monte Carlo simulations demonstrate the performance of the algorithm and verify that a model and input signal can be estimated to a proportion of their true values
Evolutionary L∞ identification and model reduction for robust control
An evolutionary approach for modern robust control oriented system identification and model reduction in the frequency domain is proposed. The technique provides both an optimized nominal model and a 'worst-case' additive or multiplicative uncertainty bounding function which is compatible with robust control design methodologies. In addition, the evolutionary approach is applicable to both continuous- and discrete-time systems without the need for linear parametrization or a confined problem domain for deterministic convex optimization. The proposed method is validated against a laboratory multiple-input multiple-output (MIMO) test rig and benchmark problems, which show a higher fitting accuracy and provides a tighter L�¢���� error bound than existing methods in the literature do
Modelling and Fast Terminal Sliding Mode Control for Mirror-based Pointing Systems
In this paper, we present a new discrete-time Fast Terminal Sliding Mode
(FTSM) controller for mirror-based pointing systems. We first derive the
decoupled model of those systems and then estimate the parameters using a
nonlinear least-square identification method. Based on the derived model, we
design a FTSM sliding manifold in the continuous domain. We then exploit the
Euler discretization on the designed FTSM sliding surfaces to synthesize a
discrete-time controller. Furthermore, we improve the transient dynamics of the
sliding surface by adding a linear term. Finally, we prove the stability of the
proposed controller based on the Sarpturk reaching condition. Extensive
simulations, followed by comparisons with the Terminal Sliding Mode (TSM) and
Model Predictive Control (MPC) have been carried out to evaluate the
effectiveness of the proposed approach. A comparative study with data obtained
from a real-time experiment was also conducted. The results indicate the
advantage of the proposed method over the other techniques.Comment: In Proceedings of the 15th International Conference on Control,
Automation, Robotics and Vision (ICARCV 2018
A harmonic framework for the identification of linear time-periodic systems
This paper presents a novel approach for the identification of linear
time-periodic (LTP) systems in continuous time. This method is based on
harmonic modeling and consists in converting any LTP system into an equivalent
LTI system with infinite dimension. Leveraging specific harmonic properties, we
demonstrate that solving this infinite-dimensional identification problem can
be reduced to solving a finitedimensional linear least-squares problem. The
result is an approximation of the original solution with an arbitrarily small
error. Our approach offers several significant advantages. The first one is
closely tied to the harmonic system's inherent LTI characteristic, along with
the Toeplitz structure exhibited by its elements. The second advantage is
related to the regularization property achieved through the integral action
when computing the phasors from input and state trajectories. Finally, our
method avoids the computation of signals' derivative. This sets our approach
apart from existing methods that rely on such computations, which can be a
notable drawback, especially in continuous-time settings. We provide numerical
simulations that convincingly demonstrate the effectiveness of the proposed
method, even in scenarios where signals are corrupted by noise
Discrete-time linear and nonlinear aerodynamic impulse responses for efficient CFD analyses
This dissertation discusses the mathematical existence and the numerical identification of linear and nonlinear aerodynamic impulse response functions. Differences between continuous-time and discrete-time system theories, which permit the identification and efficient use of these functions, will be detailed. Important input/output definitions and the concept of linear and nonlinear systems with memory will also be discussed. It will be shown that indicial (step or steady) responses (such as Wagner\u27s function), forced harmonic responses (such as Theodorsen\u27s function or those from doublet lattice theory), and responses to random inputs (such as gusts) can all be obtained from an aerodynamic impulse response function. This will establish the aerodynamic discrete-time impulse response function as the most fundamental and computationally efficient aerodynamic function that can be extracted from any given discrete-time, aerodynamic system. The results presented in this dissertation help to unify the understanding of classical two-dimensional continuous-time theories with modern three-dimensional, discrete-time theories.;Nonlinear aerodynamic impulse responses are identified using the Volterra theory of nonlinear systems. The theory is described and a discrete-time kernel identification technique is presented. The kernel identification technique is applied to a simple nonlinear circuit for illustrative purposes. The method is then applied to the nonlinear viscous Burger\u27s equation as an example of an application to a simple CFD model. Finally, the method is applied to a three-dimensional aeroelastic model using the CAP-TSD (Computational Aeroelasticity Program - Transonic Small Disturbance) code and then to a two-dimensional model using the CFL3D Navier-Stokes code.;Comparisons of accuracy and computational cost savings are presented. Because of its mathematical generality, an important attribute of this methodology is that it is applicable to a wide range of nonlinear, discrete-time systems
System Identification for Continuous-time Linear Dynamical Systems
The problem of system identification for the Kalman filter, relying on the
expectation-maximization (EM) procedure to learn the underlying parameters of a
dynamical system, has largely been studied assuming that observations are
sampled at equally-spaced time points. However, in many applications this is a
restrictive and unrealistic assumption. This paper addresses system
identification for the continuous-discrete filter, with the aim of generalizing
learning for the Kalman filter by relying on a solution to a continuous-time
It\^o stochastic differential equation (SDE) for the latent state and
covariance dynamics. We introduce a novel two-filter, analytical form for the
posterior with a Bayesian derivation, which yields analytical updates which do
not require the forward-pass to be pre-computed. Using this analytical and
efficient computation of the posterior, we provide an EM procedure which
estimates the parameters of the SDE, naturally incorporating irregularly
sampled measurements. Generalizing the learning of latent linear dynamical
systems (LDS) to continuous-time may extend the use of the hybrid Kalman filter
to data which is not regularly sampled or has intermittent missing values, and
can extend the power of non-linear system identification methods such as
switching LDS (SLDS), which rely on EM for the linear discrete-time Kalman
filter as a sub-unit for learning locally linearized behavior of a non-linear
system. We apply the method by learning the parameters of a latent,
multivariate Fokker-Planck SDE representing a toggle-switch genetic circuit
using biologically realistic parameters, and compare the efficacy of learning
relative to the discrete-time Kalman filter as the step-size irregularity and
spectral-radius of the dynamics-matrix increases.Comment: 31 pages, 3 figures. Only light changes and restructuring to previous
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