Linear State-space Model Research Articles

Model Predictive Control for Tremor Suppressing Exoskeleton

This paper focuses on the application of model-based predictive control (MPC) for a full wrist exoskeleton designed for the alleviation of tremors in patients suffering from Parkinson's Disease and Essential Tremor. The main motivation for using MPC here relies on its ability to incorporate state and input constraints, which are crucial for the user's safety. The forearm-exoskeleton model is successively linearized at each time sample to obtain a linear state space model. The optimal input is then generated by minimizing a convex quadratic cost function. Finally, simulation cases are provided to demonstrate the effectiveness of the control scheme.

Passive IR-UWB Localization System for UAV-Based Electric Facility Inspection During GPS Outage

A practical localization system is proposed for a substation inspection unmanned aerial vehicle (UAV) performing its mission under global positioning system (GPS) signal blockage. The sensor hardware consists of a single transmitter and a cruciform receiver array, which produces the range difference (RD) information used for UAV positioning. The use of impulse-radio ultra wide-band (IR-UWB) devices secures the robustness against RF interference often caused by an exogenous electromagnetic field. With this hardware configuration, the UAV localization can be formulated as the state estimation problem for an uncertain linear state space model and be solved by using the computationally efficient robust weighted least squares (RWLS) estimator. Since the standard RWLS estimator could be sensitive to the imperfectness of prior knowledge on the noise statistic, a geometric constraint expressed in terms of a UAV position is exploited to secure the reliable localization performance in practice. Through experimental results, it is verified that the proposed solution provides reliable UAV positioning performance despite using the imperfect measurement noise statistics for the localization system.

The Nonlinear Dynamic Response of Intrapartum Fetal Heart Rate to Uterine Pressure.

The research objective of our group is to improve the intrapartum detection of cardiotocography tracings associated with an increased risk of developing fetal acidosis and subsequent hypoxic-ischemic encephalopathy (HIE). The detection methods that we aim to develop must be sensitive to abnormal tracings without causing excessive unnecessary interventions. Past studies showed that the dynamic response of fetal heart rate (FHR) to uterine pressure (UP) during the intrapartum could be modelled using linear systems. In this study, we examined the assumption of linearity by comparing the performance of linear dynamic and nonlinear dynamic models of the UP-FHR system. The linear systems were defined by second-order state-space models. The nonlinear systems were defined by Hammerstein models: a cascade of a static nonlinearity and a linear second-order state-space model. Our results showed that nonlinear dynamic models were better than linear systems in 81.8% of UP-FHR segments.

On the herdability of linear time-invariant systems with special topological structures

In this paper we investigate the herdability property, namely the capability of a system to be driven towards the (interior of the) positive orthant, for linear time-invariant state space models. Herdability of certain matrix pairs (A,B), where A is the adjacency matrix of a multi-agent network, and B a selection matrix that singles out a subset of the agents (the “network leaders”), is explored. The cases when the graph associated with A, G(A), is directed and clustering balanced (in particular, structurally balanced), or it has a tree topology and there is a single leader, are investigated.

An intrinsically motivated learning algorithm based on Bayesian surprise for cognitive radar in autonomous vehicles

IntroductionThis paper proposes a Bayesian surprise learning algorithm that internally motivates the cognitive radar to estimate a target's state (i.e., velocity, distance) from noisy measurements and make decisions to reduce the estimation error gradually. The work exhibits how the sensor learns from experiences, anticipates future responses, and adjusts its waveform parameters to achieve informative measurements based on the Bayesian surprise.MethodsFor a simple vehicle-following scenario where the radar measurements are generated from linear Gaussian state-space models, the article adopts the Kalman filter to carry out state estimation. According to the information within the filter's estimate, the sensor intrinsically assigns a surprise-based reward value to the immediate past action and updates the value-to-go function. Through a series of hypothetical steps, the cognitive radar considers the impact of future transmissions for a prescribed set of waveforms–available from the sensor profile library–to improve the estimation process.Results and discussionNumerous experiments investigate the performance of the proposed design for various surprise-based reward expressions. The robustness of the proposed method is compared to the state-of-the-art for practical and risky driving situations. Results show that the reward functions inspired by estimation credibility measures outperform their competitors when one-step planning is considered. Simulation results also indicate that multiple-step planning does not necessarily lead to lower error, particularly when the environment changes abruptly.

Robust Linearly Constrained Kalman Filter for General Mismatched Linear State-Space Models

It is well known that Wiener filter and Kalman filter (KF) like techniques are sensitive to misspecified covariances, uncertainties in the system matrices, filter initialization, or unwanted system behaviors. A possible solution to robustify these estimation techniques is to impose linear constraints (LCs). In this article: 1) we introduce a general class of linearly constrained KF (LCKF), where a set of nonstationary LCs can be set at every time step; 2) explore the use of such LCs to mitigate modeling errors in general mismatched linear discrete state-space models; and 3) provide the theoretical formulation to show that the gain-constrained KF is a particular instance of the proposed LCKF. Because such LCs can be taken into account in any KF generalization, this sets the basis for a new robust filtering framework. An illustrative example is provided to support the discussion.

Control-Oriented Low-Order Approximation and Reconstruction of Yaw-Excited Wind Turbine Wake Dynamics

The estimation and reconstruction of complex fluids like wind turbine wake are challenging problems, which require approximating high-dimensional, nonlinear dynamic systems with a limited number of physical measurements. Current works mainly focus on the reduced-order approximation for fluid dynamics like dynamic mode decomposition, or linear stochastic estimation for static mapping. In this article, the problem of yaw-controlled wind turbine wake dynamics approximation and reconstruction are addressed. A Koopman-linear flow estimator is designed, which forms a control-oriented linear dynamic state-space model. The full wake flow is first approximated on its dynamic performances and then reconstructed from low-order physical states. The novelty mainly yields on the added yaw excitation that a control-oriented dynamic model is obtained. The Kalman filter is also involved that measured data in future time could be embedded while the measurement noise is filtered. At last, static and dynamic estimation tests verify the effectiveness of the proposed estimator.

A Semi Linear State Space Model for Error Floor Estimation of LDPC Codes Over the AWGN Channel

In this paper, we propose a novel state-space model to represent the behavior of sum-product algorithm (SPA) in the vicinity of a trapping set (TS) of a low-density parity-check (LDPC) code over the additive white Gaussian noise (AWGN) channel in the error floor region. The proposed model takes into account the non-linear behavior of SPA in the initial iterations using a quadratic approximation, and dynamically adjusts the operating point of the model in accordance to the statistical properties of TS messages. This is in contrast to the existing linear state-space models which linearly approximate the non-linear behavior of SPA at around the operating point of zero in all iterations. Simulation results are provided to demonstrate the higher accuracy of the proposed model in estimating the error floor of LDPC codes compared to the linear state-space model. We also make connections to the semi-analytical code-dependent technique proposed by Richardson for the error floor estimation of LDPC codes, and demonstrate that the proposed state-space model not only is a fully-analytical code-independent counterpart to that method, but also has less complexity and, in some cases, more accuracy.

Modeling and Finite-Horizon MPC for a Boiler-Turbine System Using Minimal Realization State-Space Model

This paper aims to address a finite-horizon model predictive control (MPC) for non-linear drum-type boiler-turbine system using a system-identification method. Considering that the strong state coupling of a non-linear mechanism model, the subspace identification method is first utilized to obtain a linear state-space model, and transformed into an input–output model. By taking the inputs and outputs of the input–output model as system states, an augmented non-minimal state-space (NMSS) model of state measurable is constructed. In order to reduce the computation burden, the augmented NMSS model is further transformed into a canonical formulation by adopting a Kalman decomposition. Based on the minimal realization state-space model, the MPC controller is parameterized as a finite-horizon optimization problem. Finally, simulations are performed and evaluated the performance of the proposed method, and the simulation results show that: the linear model approximate the non-linear system accurately; the proposed MPC method can achieve a satisfactory stable control performance; and the computation time 18.388 s for the overall optimization problem also illustrates the real-time performance effectively.

Continuous Model Predictive Control for the Direct Torque Control of a PM Synchronous Motor

This paper presents the application of the continuous model predictive control (C-MPC) for the direct torque control (DTC) of a permanent magnet synchronous motor (PMSM). The C-MPC is designed for the direct regulation of the components of the stator flux and the electromagnetic torque of the PMSM. A linear state-space model based on a feedback linearization of the PMSM is used to formulate the controller. The control signals are applied to the PMSM via a power inverter through a pulse width modulator (PWM). The proposed controller is formulated as a constrained optimization problem, where the voltage applied to the motor is selected as the control input and restricted to the power inverter's linear region. Simulation results are presented to demonstrate the effectiveness of the proposed control scheme.

Event-Triggered Control of Robotic Fish With Reduced Communication Rate

Underwater robots often need to communicate with external localization sensors. The low bandwidth in such communications is one of the bottlenecks in achieving accurate tracking control. Toward this end, we adopt a novel periodic event-triggered control (PETC) which allows a robotic fish to reduce its communication load in tracking a desired heading angle with position feedback from an external sensor. To design the PETC, a linear state-space model is derived from a nonlinear dynamic model of the robotic fish with a small perturbation assumption. The PETC consists of an observer, state-feedback controller, integrator, event-trigger rule, and predictor. The observer and state-feedback controller are designed to drive the tracking error to zero. The integrator reduces the steady-state error. The event-trigger rule determines when communication is needed while ensuring the efficacy of the state-feedback controller, and the predictor predicts the state vector for the state-feedback controller when communication is not available. For comparison, an observer-based state feedback control (OSFC) and a proportional-integral-derivative (PID) control are implemented in real-time experiments. Simulations and experimental results show that the PETC can dramatically reduce the number of communication instances without significantly degrading tracking performance, thereby saving communication energy and reducing the need for high bandwidth underwater communication.

Selecting age structure in integrated population models

Integrated population modelling is widely used in ecology when data at the individual level are combined with independent time series measuring population abundance. However there is no formal assessment of how to select the best integrated model. Here we focus on the important case of determining the age-structure for annual survival probabilities of wild animals, involving comparing state–space models with different numbers of states. The work is motivated by real data sets, and evaluated by simulation. We reject the naïve use of AIC, and advocate the use of likelihood-ratio tests, based on combined data. We demonstrate using simulation that typical asymptotic chi-square distributions of likelihood-ratio test statistics to compare integrated models apply when the corresponding state–space models have the same state variables. In addition, for linear state–space models with matching initial conditions the correct chi-square distributions may also hold when models apparently have different state–spaces. The results for comparing integrated models also have relevance for state–space modelling alone. A senescence case study is provided which incorporates a step-up approach and illustrates the use of the recommendations of the paper in practice.

Onset Detection of Pulse-Shaped Bioelectrical Signals Using Linear State Space Models

Abstract Bioelectrical signals are often pulse-shaped with superimposed interference signals. In this context, accurate identification of features such as pulse onsets, peaks, amplitudes, and duration is a frequent problem. In this paper, we present a versatile method of rather low computational complexity to robustly identify such features in real-world signals. For that, we take use of two straight-line models fit to the observations by minimizing a quadratic cost term, and then identify desired features by tweaked likelihood measures. To demonstrate the idea and facilitate access to the method, we provide examples from the field of cardiology.

Discrete-Time Model Predictive Controller Using Laguerre Functions for Active Flutter Suppression of a 2D wing with a Flap

In this paper, a discrete-time model predictive controller using Laguerre orthonormal function-based (LMPC) for active flutter suppression of a two-dimensional wing with a flap is presented. In this work, a linear mathematical state-space model for the pitch, plunge, and flap degrees of freedom under unsteady aerodynamics is derived and used to determine the linear flutter velocity and frequency of the parameters of a selected experimental wing. To verify the model, the open-loop simulation results are compared to an experimental study using the same wing from the literature. The state-space system is then discretized and LMPC with a Kalman filter is designed and tuned using the MATLAB® simulation environment at a selected speed in the linear flutter region. The predictive control advantage of dealing with input constraints in a systematic manner is explored through a quantitative analysis of the response of both constrained and unconstrained LMPC controllers. The results indicate that theoretically both cases can give excellent performance. However, the input trajectory generated by the unconstrained LMPC is very aggressive in a way that it is considered impractical when compared to the physical limits of an experimental actuator from the literature. The potential of LMPC to achieve a reasonable performance at a significantly lower computational cost compared to the classical model predictive controller (MPC) is investigated by measuring the time required by the same computer to compute the control trajectory for both controllers. The data suggest that LMPC requires remarkably low computational power, which makes it an excellent choice for fast aeroelastic applications.

Identification of errors in variables linear state space models using iterative principal component analysis

ABSTRACT Development of dynamic process models from input–output data, also known as system identification, is a well-studied problem. The classical approach to system identification assumes that the input variables are measured without error. However, in practice all data collected from evolving processes (inputs and outputs) will contain errors. System identification using noisy inputs and outputs is known as Errors-in-Variables (EIV) identification. Existing methods for EIV model identification assume that the error variances are known and/or assume the system order to be known. We propose a novel approach combining subspace-based identification and a dynamic iterative principal components approach for identifying EIV MIMO models. The proposed method simultaneously estimates process order, delay, model coefficients, and error variances using a rigorous theoretical basis. A benchmark simulation example from literature is used to exhibit the effectiveness of the proposed approach.

An adaptive unknown input approach to brain wave EEG estimation

Objective:Real time, high fidelity estimation and reconstruction of brain wave dynamics is complicated by the nonstationary and nonlinear effects of electroencephalography (EEG) measures. This work aims to introduce a novel state space architecture, which continuously updates a linear brain wave model and estimates the exogenous input to the brain wave system. This continuous update is adaptive, because the estimator continuously monitors its own performance and can modify its own parameters by a closed loop action. This highly nonlinear estimator should reconstruct the EEG measure in real time for analysis and diagnostic information. Methods:The development of this adaptive unknown input estimator focuses on treating the known phenomena of brain waves. The adaptive law accounts for nonlinearities in the EEG measure while the input estimator simultaneously accounts for the exogenous input to the system. The estimator is further robust to general process uncertainty in the plant dynamics. Results:The stability of the adaptive unknown input estimator for EEG measures is shown. This estimator is shown to outperform standard linear models, such as Kalman filtering techniques especially at points where the EEG measure changes sharply. Conclusion:This adaptive unknown input estimator reconstructs unmodeled EEG data in real time by accounting for the nonlinear brain wave dynamics. Because the adaptive law updates a linear model over time, much of the interpretability and intuition of linear state space modeling is preserved.

Markov chain Monte Carlo based adaptive Rauch–Tung–Striebel smoother

For linear state space model, the covariance matrix setting errors of process and measurement noise deteriorate the estimation performance of Rauch–Tung–Striebel (RTS) smoother. To address this problem, the Markov Chain Monte Carlo is utilized to sample the state vector and noise covariance matrices simultaneously in this study. The Gibbs sampler is adopted and the corresponding adaptive RTS smoother is designed. Simulation results confirm the performance of proposed smoother.

A data-driven nonlinear state-space model of the unsteady lift force on a pitching wing

Accurate unsteady aerodynamic models are essential to estimate the forces on rapidly pitching wings and to develop model-based controllers. As system identification is arguably the most successful framework for model predictive control in general, in this paper we investigate whether system identification can be used to build data-driven models of pitching wings. The forces acting on the pitching wing can be considered a nonlinear dynamic function of the pitching angle and therefore require a nonlinear dynamic model. In this work, a nonlinear data-driven model is developed for a pitching wing. The proposed model structure is a polynomial nonlinear state-space model (PNLSS), which is an extension of the classical linear state-space model with nonlinear functions. The PNLSS model is trained on experimental data of a pitching wing. The experiments are performed using a dedicated wind tunnel setup. The pitch angle is considered as the input to the model, while the lift coefficient is considered as the output. Three models are trained on swept-sine signals at three offset angles with a fixed pitch amplitude and a range of reduced frequencies. The three training datasets are selected to cover the linear and nonlinear operating regimes of the pitching wing. The PNLSS models are validated on single-sine experimental data at the respective pitch offset angles. The PNLSS models are able to capture the nonlinear aerodynamic forces more accurately than a linear and semi-empirical models, especially at higher offset angles.

Novel Unbiased Optimal Receding-Horizon Fixed-Lag Smoothers for Linear Discrete Time-Varying Systems

This paper proposes novel unbiased minimum-variance receding-horizon fixed-lag (UMVRHF) smoothers in batch and recursive forms for linear discrete time-varying state space models in order to improve the computational efficiency and the estimation performance of receding-horizon fixed-lag (RHF) smoothers. First, an UMVRHF smoother in batch form is proposed by combining independent receding-horizon local estimators for two separated sub-horizons. The local estimates and their error covariance matrices are obtained based on an optimal receding horizon filter and the smoother in terms of the unbiased minimum variance; they are then optimally combined using Millman’s theorem. Next, the recursive form of the proposed UMVRHF smoother is derived to improve its computational efficiency and extendibility. Additionally, we introduce a method for extending the proposed recursive smoothing algorithm to a posteriori state estimations and propose the Rauch–Tung–Striebel receding-horizon fixed-lag smoother in recursive form. Furthermore, a computational complexity reduction technique that periodically switches the two proposed recursive smoothing algorithms is proposed. The performance and effectiveness of the proposed smoothers are demonstrated by comparing their estimation results with those of previous algorithms for Kalman and receding-horizon fixed-lag smoothers via numerical experiments.

Gain scheduling model predictive controller design for tankless gas water heaters with time-varying delay

• Thermal model with time-varying delay is developed for a tankless gas water heater. • Feedback, feedforward and model predictive controllers are designed. • Controllers are assessed for cold start and water flow rate sudden disturbances. • Impact of temperature overshoots and undershoots are diminished. • Gain scheduling MPC presents superior performance than classic controllers. One of the most significant drawbacks of tankless gas water heaters is the difficulty of controlling the outlet hot water temperature as changes in water demand cannot be predicted. These sudden changes in hot water flow rate, are associated with the system inhered delays, and are responsible for temperature overshoots and undershoots that severely affect the comfort perception of the user. In the present work, a linear model predictive controller (MPC) design is employed for the stabilization of a constrained nonlinear thermal process with time-varying delay, however, control performance degrades significantly when operating far from the linearization operating point. The idea is to design multiple linear MPC controllers, each with its linear state-space model and constant time delay, describing process dynamics at a specific level of operation. Gain scheduling MPC presents improved performance when compared with classic PID and combined feedforward-feedback controllers, reducing the settling time up to two thirds.