Sampled Input Output Data Research Articles

Cloud-Based Computational Data-Enabled Predictive Control

This article considers the data-driven optimal control problem for unknown linear systems subject to system constraints from a computation efficiency improvement perspective. We propose a novel Computational Data-enabled Predictive Control (CDeePC) algorithm in a cloud environment, built on a recent work DeePC <xref ref-type="bibr" rid="ref1" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[1]</xref> . First, massive input–output data samples are precollected to describe the system input/output behavior through a behavioral systems theory approach, which might result in a large-scale online optimization problem with high dimensional decision variables. To solve it, in CDeePC, a multiblock alternating direction method of multipliers (ADMMs) algorithm is then employed, in which a solution to the original large problem can be calculated by solving iteratively a set of small subproblems. Next, to further improve the robustness of the algorithm, an online feedback CDeePC (OCDeePC) algorithm is proposed by utilizing real-time data samples to better capture the system characterization. Two analytic inversion formulas are derived for fast computation of time-varying controller parameters based on the result at the previous time. After that, we discuss the computational complexity and provide the convergence proof of proposed algorithms. Finally, after designing a cloud-based control architecture and formulating the iterative scheme to compute control actions as a workflow, we construct and deploy the proposed controllers as a service in the cloud. A case study of tracking control of wheeled mobile robots is provided to illustrate the efficacy of the proposed algorithms.

A simple robust method of fractional time-delay estimation for linear dynamic systems

This paper is concerned with estimating the parameters of single-input, continuous-time systems from sampled input–output data, where any input time delays may be a fraction of the sampling interval. The proposed method estimates the parameters by minimizing a cost function defined by the sum of squared errors between the predicted and measured outputs using the optimal Refined Instrumental Variable method for Continuous-time models (RIVC). Potential difficulties may be encountered when standard gradient-based optimization is used for solving this optimization problem directly. These arise because the cost function is normally multi-modal with respect to the fractional time delay and they can occur for several reasons, such as aliasing errors, the nature of the system dynamics, and the selection of the excitation signal. In order to avoid the problems caused by these local minima, a two-stage procedure is proposed combining RIVC estimation of the model parameters with a grid search for the fractional time delay. Although this algorithm is not quite as computationally efficient as standard gradient-based optimization, it is simple, robust, and more widely applicable, as illustrated by numerical examples.

Data-Driven Modeling of Wireless Power Transfer Systems With Multiple Transmitters

This article develops a new method of data-driven modeling for a class of multiple-transmitter single-receiver wireless power transfer (WPT) systems. A continuous-time multiple-input single-output (MISO) model with pure time delays is used to characterize the input–output behavior of the system, where the transfer functions associated with each input channel are not constrained to have the same denominator. Moreover, the time delays are allowed to be a fraction of the sampling interval in order to account for the delay effects that stem from circuit components and wireless communication, which are, by nature, often a fraction of the sampling interval. An optimal refined instrumental variable method is proposed to estimate the parameters and time delays of the MISO model based on sampled input–output data. In contrast to the conventional circuit-theory-based modeling methods that rely on circuit parameters and result in models which are often complex, the proposed data-based method yields parsimonious models, whose parameters are directly estimated from input–output data. Due to the easy availability of sampled data in control engineering applications, the proposed method is clearly more user-friendly, having a broad prospect for efficient operation of WPT systems, such as prediction, optimization, and control. Numerical and experimental results are presented to validate the effectiveness and merit of the proposed method.

Data-Driven Modeling of Wireless Power Transfer Systems With Slowly Time-Varying Parameters

This article considers the data-driven modeling of a class of phase-controlled wireless power transfer (WPT) systems, where the load may vary slowly with respect to time. The dominant mode analysis suggests that a model of the Hammerstein type, which consists of a static nonlinearity function, followed by a linear time-varying model with a pure time delay, is the best structure to describe the input–output relationship of the system. On this basis, we derive a small-signal model that is linear in the variables in order to aid control design and allow the associated model parameters to be estimated from sampled input–output data using the standard refined instrumental variable (RIV) method. In the presence of a time-varying load, however, the plant model parameters may not be correctly estimated if the load response is not removed. In order to address this problem, a new recursive RIV method is proposed, in which an effective technique is introduced to track the load response, so allowing the parameters and time delay of the time-varying model to be accurately estimated. The effectiveness of the proposed method is verified by applying it to both a simulation model and a laboratory system.

Continuous-Time Model Identification From Filtered Sampled Data: Error Analysis

In this article, an upper bound is established for the estimation error of a standard least squares (LS) algorithm used to identify a continuous-time model from filtered, sampled input–output data. It is found that the error has three constituent components due to the initial conditions, observation noise, and sample period. In particular, the initial condition bias is bounded by $O(1/[N\Delta t])$ , which requires sufficiently large $[N\Delta t]$ for accurate LS estimation. The theoretical results obtained are confirmed by simulation.

Optimization-Oriented RAW Modeling of IEEE 802.11ah Heterogeneous Networks

The new medium access method of IEEE 802.11ah, called restricted access window (RAW), divides stations into different groups, and only allows stations in the same group to access the channel simultaneously, in order to reduce collisions and thus achieve better performance (e.g., throughput). However, the existing station grouping strategies only support homogeneous scenarios where all stations use the same modulation and coding scheme (MCS) and packet size. A surrogate model is an efficient mathematical model that represents the behavior of a complex system, trained with a limited set of labeled input–output data samples. In this article, we present a surrogate model that can accurately predict RAW performance under a given RAW configuration in heterogeneous networks. Different from the homogeneous scenario, heterogeneous networks are defined by a large number of parameters, leading to an enormous design space, i.e., the order of 1017 possible data points. This is too big to achieve feasible training convergence. In this article, we present a novel training methodology that leads to a new design space with highly reduced size, i.e., the order of 105 data points. The surrogate model converges when less than 6000 labeled data points are used for training, which is only a tiny portion of the whole design space. The results show that, the relative error between model prediction and simulation results is less than 0.1 for 95% of the data points, in the areas of the design space studied. Its low complexity and high precision make the proposed model a valuable tool to develop real-time RAW optimization algorithms for heterogeneous IEEE 802.11ah networks.

Sampling Strategies for Data-Driven Inference of Input–Output System Properties

Due to their relevance in controller design, we consider the problem of determining the $\mathcal{L}^2$-gain, passivity properties and conic relations of an input-output system. While, in practice, the input-output relation is often undisclosed, input-output data tuples can be sampled by performing (numerical) experiments. Hence, we present sampling strategies for discrete time and continuous time linear time-invariant systems to iteratively determine the $\mathcal{L}^2$-gain, the shortage of passivity and the cone with minimal radius that the input-output relation is confined to. These sampling strategies are based on gradient dynamical systems and saddle point flows to solve the reformulated optimization problems, where the gradients can be evaluated from only input-output data samples. This leads us to evolution equations, whose convergence properties are then discussed in continuous time and discrete time.

Control-Oriented Modeling of Wireless Power Transfer Systems With Phase-Shift Control

This paper is concerned with control-oriented modeling of a class of wireless power transfer systems with a phase-shift-controlled inverter. Two methods are investigated: the analytical modeling method, which is based on physical laws, and the refined instrumental variable method, which is based on sampled data. It shows that the former provides physical insights into the system, and that the resulting models will be accurate if the true circuit component parameters are a priori known. Otherwise, the model accuracy may decline. By contrast, the latter provides a cheap solution for accurate modeling, based only on a set of sampled input–output data, and the resulting model can capture very well the dynamic behavior of the system within a defined operating range. In real applications, it is always hard to know the actual circuit component parameters, since they may drift from the nominal values, due to some reasons such as the aging of circuit components and the variation of coil placement, making the analytical modeling method not very accurate. Therefore, to preserve the virtues of both methods, it is suggested to use them as a combination, that is, using the analytical modeling method to determine the model structure while using the data-driven modeling method to estimate the model parameters. All results derived in this paper are verified by means of both numerical simulation and experimental validation.

Identification of discrete Hammerstein systems by using adaptive finite rational orthogonal basis functions

In this paper, an adaptive identification method is presented, it is developed for discrete Hammerstein systems. We adopt a frequency-domain technique by using sampled input–output data. The excitation signals are chosen to be the fundamental harmonics, by which one could get approximating estimate of frequency responses to linear subsystem. By using adaptive rational orthogonal basis functions, we obtain approximations of linear subsystem, it is carried out through selecting poles of the basis functions under some criterion. Meanwhile, efficient estimates of both the nonlinear part and linear part could be obtained in the presence of noise.

Recursive IV Identification of Continuous-Time Models With Time Delay From Sampled Data

This brief investigates recursive instrumental variable (IV) identification of time-delayed continuous-time (CT) models from the sampled input–output data. The refined IV method is extended for the first time to identify recursively both the parameters and time delay of a CT transfer function model. It is shown that the proposed method is able to yield consistent parameter estimation. Due to the nonlinear nature of the loss function to be optimized, time-delay estimation suffers from local minima. Thus, the global convergence performance relies on the quality of initial parameters. To increase the chance of converging to the global optimum, several guidelines are suggested to help the choice of starting values. The main results derived in this brief are confirmed by numerical examples and an experimental application.

Design of delayed fractional state variable filter for parameter estimation of fractional nonlinear models

This paper presents a novel direct parameter estimation method for continuous-time fractional nonlinear models. This is achieved by adapting a filter-based approach that uses the delayed fractional state variable filter for estimating the nonlinear model parameters directly from the measured sampled input–output data. A class of fractional nonlinear ordinary differential equation models is considered, where the nonlinear terms are linear with respect to the parameters. The nonlinear model equations are reformulated such that it allows a linear estimator to be used for estimating the model parameters. The required fractional time derivatives of measured input–output data are computed by a proposed delayed fractional state variable filter. The filter comprises of a cascade of all-pass filters and a fractional Butterworth filter, which forms the core part of the proposed parameter estimation method. The presented approaches for designing the fractional Butterworth filter are the so-called, square root base and compartmental fractional Butterworth design. According to the results, the parameters of the fractional-order nonlinear ordinary differential model converge to the true values and the estimator performs efficiently for the output error noise structure.

A recursive algorithm for estimating multiple models continuous transfer function with non-uniform sampling

ABSTRACTA multiple model recursive least squares algorithm combined with a first-order low-pass filter transformation method, named λ-transform, is proposed for the simultaneous identification of multiple model orders continuous transfer functions from non-uniformly sampled input–output data. The λ-transformation is shown to be equivalent to a canonical transformation between discrete z-domain and δ-domain using the negative value of the λ-transform filter time-constant instead of the sampling interval parameter. The proposed algorithm deals with oversampling, sampling jitter or non-uniform sample intervals without the need for extra digital anti-aliasing pre-filtering, downsampling or interpolation algorithms, producing multiple models with a cost function that facilitates automatic selection of best-fitted models. Besides, measurement noise is noted as beneficial, bringing up an inherent bias toward low-order models. Simulated examples and a drum-boiler level experimental result exhibiting non-minimum phase behaviour illustrate the application of the proposed method.

Type-2 Fuzzy Modeling and Control for Bilateral Teleoperation System With Dynamic Uncertainties and Time-Varying Delays

This paper develops data-driven Type-2 Takagi–Sugeno (T–S) fuzzy modeling and control for bilateral teleoperation with dynamic uncertainties and time-varying delays. The Type-2 T–S fuzzy model identified based on input–output data samples describes the nonlinear teleoperation system by a weighted sum of a group of linear local models, which offers a platform to design robust control algorithms by means of mature linear theories. The fuzzy-model-based four-channel control laws are proposed to guarantee the motion synchronization and enhance the operator's force perception for the environment when the time-varying delays and large dynamic uncertainties, especially the gravity of a heavy end effector of the slave, exist. Markov processes are applied to model the time delays. The stability of the closed-loop system is proved by using the Lyapunov–Krasovskii functions. All the conditions are expressed as linear-matrix inequalities (LMI). By using the MATLAB LMI toolbox, the optimized control gains for each of the fuzzy rules are derived to achieve the optimal performance. Finally, experiments based on an experimental platform consisting of two haptic devices prove the superiority of the proposed strategy through comparison with previous work.

Parameter estimation of the fractional‐order Hammerstein–Wiener model using simplified refined instrumental variable fractional‐order continuous time

This study proposes a direct parameter estimation approach from observed input–output data of a stochastic single-input–single-output fractional-order continuous-time Hammerstein–Wiener model by extending a well known iterative simplified refined instrumental variable method. The method is an extension of the simplified refined instrumental variable method developed for the linear fractional-order continuous-time system, denoted. The advantage of this novel extension, compared with published methods, is that the static output non-linearity of the Wiener model part does not need to be invertible. The input and output static non-linear functions are represented by a sum of the known basis functions. The proposed approach estimates the parameters of the linear fractional-order continuous-time subsystem and the input and output static non-linear functions from the sampled input–output data by considering the system to be a multi-input–single-output linear fractional-order continuous-time model. These extra inputs represent the basis functions of the static input and output non-linearity, where the output basis functions are simulated according to the previous estimates of the fractional-order linear subsystem and the static input non-linear function at every iteration. It is also possible to estimate the classical integer-order model counterparts as a special case. Subsequently, the proposed extension to the simplified refined instrumental variable method is considered in the classical integer-order continuous-time Hammerstein–Wiener case. In this paper, a Monte Carlo simulation analysis is applied for demonstrating the performance of the proposed approach to estimate the parameters of a fractional-order Hammerstein–Wiener output model.

Identification of Continuous-Time Systems with Multiple Unknown Time Delays Using an Output Error Method from Sampled Data

This paper deals with simultaneous identification of continuous systems with multiple unknown time delays from sampled input–output data. In order to estimate, simultaneously, the parameters and the time delays of the system, an output errors method using a nonlinear programming algorithm based on sensitivity functions is discussed. Nevertheless, the initial values of the adjustable parameters should be determined from physical insight or guessed by previous methods. The convergence of the proposed method has been analyzed with theorems and proofs. The simulation example indicates that the proposed algorithm can generate highly accurate parameter estimates.

Relationship between sensitivity indices defined by variance- and covariance-based methods

Sensitivity analysis is a challenge to perform with correlated variables, as often occur in practice. The variance-based methods for correlated variables use the same sensitivity indices defined for independent variables. The associate algorithms to determine the sensitivity indices are computationally demanding, and require explicit knowledge of the joint and conditional probability density function (pdf) of the input variables. As an alternative, a method referred to as structural and correlative sensitivity analysis (SCSA) based on a covariance decomposition has also been developed to fully quantify the deterministic and statistical contributions of independent and correlated variables, which can be applied in simulations as well as for laboratory/field data where the explicit forms of the function f(x) and the pdf are unknown. In this paper, we show that the sensitivity indices defined by the variance-based method may be re-expressed in terms of the SCSA sensitivity indices without further numerical computation, if the function f(x) and the pdf are known. If f(x) and the pdf are not known, the indices can still be accurately calculated from a single modest set of input-output data samples with SCSA.

Direct continuous-time approaches to system identification. Overview and benefits for practical applications

This paper discusses the importance and relevance of direct continuous-time system identification and how this relates to the solution for model identification problems in practical applications. It first gives a tutorial introduction to the main aspects of one of the most successful existing approaches for directly identifying continuous-time models of dynamical systems from sampled input–output data. Compared with traditional discrete-time model identification methods, the direct continuous-time approaches have some notable advantages that make them more useful in many practical applications. For instance, continuous-time models are more intuitive to control scientists and engineers in their every-day practice and the related estimation methods are particularly well suited to handle rapidly or irregularly sampled data situations. The second part of the paper describes further recent developments of this reliable estimation technique, including its extension to handle coloured measurement noise situations, time-delay system identification, frequency-domain identification, non-uniformly sampled data, closed-loop and nonlinear model identification. It also discusses the software tools available and illustrates their advantages via simulated and real data examples.

Robust identification of continuous-time models with arbitrary time-delay from irregularly sampled data

This paper presents a new approach to identify continuous-time systems with arbitrary time-delay from irregularly sampled input–output data. It is based on the separable nonlinear least-squares method which combines in a bootstrap manner the iterative optimal instrumental variable method for transfer function model estimation with an adaptive gradient-based technique that searches for the optimal time-delay. Since the objective function may have several local minima with respect to the unknown parameters (especially the time-delay), the initialization requires special attention. Here, a low-pass filtering strategy is used to widen the convergence region around the global minimum. Simulation results are included to show the performance of the proposed method.

A novel approach to integrate artificial potential field and fuzzy logic into a common framework for robots autonomous navigation

Artificial potential field and fuzzy logic are efficient approaches for mobile robots autonomous navigation. However, both have advantages and drawbacks. Their integration into a common control scheme can significantly improve the performances of the resulting hybrid controller. In this article, we propose a novel hybrid approach in order to better exploit their advantages. The present work contributes in three aspects: first, the proposed control scheme integrates interval type-2 fuzzy logic concepts with artificial potential field concepts into a common framework in order to better exploit their advantages. Second, the proposed control scheme is a simple and realizable design for real-time implementation because only 15 fuzzy rules are sufficient to control the mobile robot. Third, the proposed control scheme is a synthesized design which utilizes both heuristic knowledge and the sampled input–output data pairs. An implementation in real-time on an omnidirectional mobile robot validates the effectiveness of the proposed control scheme.

Gradient-based iterative identification for Wiener nonlinear systems with non-uniform sampling

This paper focuses on the identification problem of Wiener nonlinear systems with non-uniform sampling. The mathematical model for the Wiener nonlinear system is established from the non-uniformly sampled input–output data. In order to solve the identification problem of the Wiener nonlinear system with the unmeasurable variables in the information vector, the gradient-based iterative algorithm is presented by replacing the unmeasurable variables with their corresponding iterative estimates. Finally, the simulation results indicate that the proposed algorithm is effective.