Augmented State Research Articles

Active Suspension Robust Preview Control by Considering Actuator Delay

Active suspension systems (ASSs) are crucial for realizing the improvement demand of ride comfort in autonomous vehicles (AVs). This paper presents a novel integrated robust preview control (PC) algorithm to further improve the ride comfort by effectively handling actuator delay. An augmented ASS model is first established to consider actuator delay. Then, to obtain the time-domain feedforward disturbance, updating the local spatial road dataset from sensing systems by low-pass filtering and introducing speed for conversion. A predictive control framework that utilizes preview road disturbances is developed to achieve better ride comfort. And assuming parameterized disturbances, it is transformed into a consistent quadratic programming (QP) problem for real-time application in ASS. Furthermore, an innovative design of combined observer provides accurate and robust observations under multiple uncertainties, with which the algorithm can effectively compensate for actuator delay under different road conditions. Finally, the bounded-input bounded-output (BIBO) stability of the algorithm is well demonstrated. Simulation and bench test results indicate that the proposed algorithm can not only significantly improve road holding and ride comfort, but also realize a robust observation of the augmented ASS state. In addition, the solving time of the bench test satisfies the real-time requirements of the algorithm.

3D reconstruction based on hierarchical reinforcement learning with transferability

3D reconstruction is extremely important in CAD (computer-aided design)/CAE (computer-aided Engineering)/CAM (computer-aided manufacturing). For interpretability, reinforcement learning (RL) is used to reconstruct 3D shapes from images by a series of editing actions. However, typical applications of RL for 3D reconstruction face problems. The search space will increase exponentially with the action space due to the curse of dimensionality, which leads to low performance, especially for complex action spaces in 3D reconstruction. Additionally, most works involve training a specific agent for each shape class without learning related experiences from others. Therefore, we present a hierarchical RL approach with transferability to reconstruct 3D shapes (HRLT3D). First, actions are grouped into macro actions that can be chosen by the top-agent. Second, the task is accordingly decomposed into hierarchically simplified sub-tasks solved by sub-agents. Different from classical hierarchical RL (HRL), we propose a sub-agent based on augmented state space (ASS-Sub-Agent) to replace a set of sub-agents, which can speed up the training process due to shared learning and having fewer parameters. Furthermore, the ASS-Sub-Agent is more easily transferred to data of other classes due to the augmented diverse states and the simplified tasks. The experimental results on typical public dataset show that the proposed HRLT3D performs overwhelmingly better than recent baselines. More impressingly, the experiments also demonstrate the extreme transferability of our approach among data of different classes.

Analysis and Compensation of Sun Direction Error on Solar Disk Velocity Difference

Solar disk velocity difference is an emerging celestial navigation measurement acquired through four spectrometers positioned on the four corners of the quadrangular pyramid. The alignment of the pyramid’s axis with the direction from the sun to the spacecraft is crucial. However, the sun sensor measurement error inevitably leads to the sun direction error, which both significantly affect navigation accuracy. To address this issue, this article proposes an augmented state sun direction/solar disk velocity difference integrated navigation method. By analyzing the impact of the sun direction error on sun direction and solar disk velocity difference measurements, the errors of the solar elevation and azimuth angle are extended to the state vector. The navigation method establishes state and measurement models that consider these errors. Simulation results show that the position error and velocity error of the proposed method are reduced by 97.51% and 96.91% compared with those of the integrated navigation with the sun direction error, respectively. The result demonstrates that the proposed method effectively mitigates the impact of sun direction error on navigation performance. In addition, the proposed method can maintain a satisfactory error suppression effect under different sun direction error values.

Fault estimation and active fault‐tolerant control for a class of nonlinear systems with actuator and sensor faults based on unknown input iterative learning

AbstractIn this paper, fault estimation and active fault‐tolerant control are studied for a class of nonlinear systems with simultaneous actuator and sensor faults, as well as unknown external disturbances. Firstly, the state equation of a class of nonlinear systems is transformed into an augmented system state equation by extending the sensor fault as an auxiliary state. Then, a novel fault estimation observer based on iterative learning with unknown inputs is designed to estimate the system state, as well as actuator and sensor faults. Subsequently, by using the fault estimation information, a dynamic output feedback active fault‐tolerant control scheme is proposed to compensate for the influence of faults on the system. Lyapunov stability theory is used to prove the stability of the closed‐loop system and the convergence of the fault estimation observer. The gain matrices of the fault estimation observer and fault‐tolerant controller are obtained by solving linear matrix inequalities. Furthermore, the paper avoids the use of the norm in the convergence proof of the conventional iterative learning algorithm, which reduces the amount of calculation in the derivation process. Finally, the effectiveness and accuracy of the proposed method are verified through simulation of the DC motor angular velocity system.

Energy-efficient adaptive cruise control system with acceleration prediction via long short-term memory

An energy-efficient adaptive cruise control (ACC) system that predicts the preceding state is proposed to meet the demands of driving in different states and working conditions. The long short-term memory (LSTM) network predicts the trajectory of the preceding vehicle’s future acceleration, allowing for an adaptive time headway that takes acceleration into account. The acceleration of the preceding vehicle is also incorporated as an augmented state in the deep deterministic policy gradient (DDPG) algorithm, resulting in a combined algorithm called prediction deep deterministic policy gradient (PDDPG). A multi-objective reward function is constructed based on human driving data to evaluate the performance indexes of vehicle longitudinal control, including efficiency, safety, and economy. The rules for changing the weight of each target performance under various typical cycle conditions are determined through experiments. The Carsim-based urban, suburban and highway conditions together with the Simulink vehicle dynamics model are compared with human driving data and ACC of conventional algorithms. Based on the test results, the proposed algorithm can improve fuel efficiency by 19.36% in urban driving conditions and reduce acceleration fluctuations.

Robust Fusion Kalman Estimator of the Multi-Sensor Descriptor System with Multiple Types of Noises and Packet Loss.

Under the influence of multiple types of noises, missing measurement, one-step measurement delay and packet loss, the robust Kalman estimation problem is studied for the multi-sensor descriptor system (MSDS) in this paper. Moreover, the established MSDS model describes uncertain-variance noises, multiplicative noises, time delay and packet loss phenomena. Different types of noises and packet loss make it more difficult to build the estimators of MSDS. Firstly, MSDS is transformed to the new system model by applying the singular value decomposition (SVD) method, augmented state and fictitious noise approach. Furthermore, the robust Kalman estimator is constructed for the newly deduced augmented system based on the min-max robust estimation principle and Kalman filter theory. In addition, the given estimator consists of four parts, which are the usual Kalman filter, predictor, smoother and white noise deconvolution estimator. Then, the robust fusion Kalman estimator is obtained for MSDS according to the relation of augmented state and the original system state. Simultaneously, the robustness is demonstrated for the actual Kalman estimator of MSDS by using the mathematical induction method and Lyapunov's equation. Furthermore, the error variance of the obtained Kalman estimator is guaranteed to the upper bound for all admissible uncertain noise variance. Finally, the simulation example of a circuit system is examined to illustrate the performance and effectiveness of the robust estimators.

An improved multi-source information fusion method for IMU compensation of missile

AbstractThe conventional SINS/CNS integrated navigation system equipped on ballistic missiles is typically equipped with attitude measurement, which can only estimate the gyro drift and has no effect on accelerometer bias. To address the issue, an improved multi-source information fusion method containing a new nonlinear framework called SINS/RKCNS with the indirect horizon reference and kinematic constraint is proposed, and a MAP-based modified iterated CKF is involved to increase positioning accuracy and system robustness. Furthermore, to reduce the influence of correlated noise, state augmentation is employed in the iterative process. Eventually, experiments are conducted, and the results confirm the effectiveness of the proposed approach.

Analysis of Novel 4D Rabinovich-Fabrikant Continuous Dynamical System with Coexistence Attractors

In this paper a new Rabinovitch-Fabrikant (R-F) four dimensional (4D) continuous time dynamical system was generated from three dimensional (3D) Rabinovitch-Fabrikant dynamical system using the state augmentation technique by adding new state variables u. The system employs thirteen terms includes five cross-product terms and one irreversible function. The dynamical behaviors of the system were investigated which include equilibrium points, stability analysis, wave form analysis, phase space analysis, multistability, Hopf-bifurcation, the Lyapunov exponent and Lyapunov dimension. The values of Lyapunov exponents are:L1 = 14.025946, L2 = 0.295151, L3 = −2.854401, L4 = −13.736833. and Lyapunov dimension is (3.83474), so the system is unstable and hyperchaotic with coexistence attractors. Chaos was handled in two ways: adaptive control and adaptive synchronization, it was found that the new system is stable and achieved good results.

Event-Triggered Robust Fusion Estimation for Multi-Sensor Time-Delay Systems with Packet Drops

This paper investigates the robust fusion estimation problem for multi-sensor systems with communication constraints, parameter uncertainty, d-step state delays, and deterministic control inputs. The multi-sensor system consists of a fusion center and some sensor nodes with computational capabilities, between which there are random packet drops. The state augmentation method is utilized to transform a time-delay system into a non-time-delay one. The robust state estimation algorithm is derived based on the sensitivity penalty for each sensor node to reduce the impact of modelling errors, and modelling errors here are not limited to a unique form, which implies that the fusion estimator applies to a wide range of situations. An event-triggered transmission strategy has been adopted to effectively alleviate the communication burden from the sensor node to the fusion center. Moreover, the fusion estimator handles packet drops arising from unreliable channels, and the corresponding pseudo-cross-covariance matrix is provided. Some conditions are given to ensure that the estimation error of the robust fusion estimator is uniformly bounded. Two sets of numerical simulations are provided to illustrate the effectiveness of the derived fusion estimator.

State augmentation method for buffeting responses of wind-sensitive structures in wind environments with large turbulence intensity

Recent studies have shown that wind fields with large turbulence intensity are frequently observed in non-synoptic winds such as typhoons and hurricanes. The quadratic terms of the fluctuating wind speed are important for calculating buffeting responses of wind-sensitive structures under high turbulence. In this study, a moment-based method, which is called the state augmentation method, is used to obtain high-order response moments and avoid the large computational cost of the high-order frequency domain method. First, the buffeting force formula with nonlinear velocity terms is established, and the Non-Gaussian buffeting force is further approximated as a polynomial of the Ornstein–Uhlenbeck (OU) process. Then, an augmented state vector is introduced to express the relationship between the statistical moments of each order, and the 1st to 4th response moments can be solved sequentially by a particular set of linear equations. Finally, the extreme responses of a single-degree-of-freedom (SDOF) tower and a long-span suspension bridge are calculated as engineering examples. By comparing the computation results with the frequency method, it is proven that this moment-based method has a sufficient accuracy in analysing quadratic terms. The calculation results also show that quadratic terms under high turbulence significantly amplify the non-Gaussian peak factor and extreme responses.

Secure control scheme for CPSs under DoS attacks via multiple transmission channels and unknown input observer

The paper investigates the secure control problems for cyber–physical systems (CPSs) when the transmission channels suffer from Denial-of-Service (DoS) attacks based on switching observer and unknown input reconstruction (UIR). Firstly, an augmented system whose system state consists of the original system state and the measurement noises is set up, and the preconditions for the original system and augmented system are discussed in detail. Secondly, a full-order observer is constructed to generate the estimations of the augmented system state. Besides, based on the state estimation, an algebraic UIR method is developed and the UIR decouples the control input signal successfully. Thirdly, under the situation that some transmission channels suffer from DoS attacks, an observer-based secure controller is designed based on state estimation feedback and UIR feedback in view of a switching system. The stability of the switching system is analyzed as well. Finally, to verify the effectiveness of the proposed protocols, two simulation examples and the comparison with existing methods are given.

Robust Preview Path Tracking Control of Autonomous Vehicles Under Time-Varying System Delays and Saturation

Realistic uncertainties and disturbances cannot be ignored when striving towards high-performance autonomous driving. Meanwhile, advanced vehicular sensing technology enables more and more self-driving techniques to come out. Against this backdrop, this paper aims to holistically address the system uncertainties and disturbances in the path tracking control of autonomous vehicles (AVs) by the preview control theory to achieve superior control performance. First, unmeasureable multi-uncertainties and the external disturbance are considered simultaneously into the robust gain-scheduling framework with variable longitudinal velocity. Then, by the equivalent delay approach, ineluctable time-varying system delays are effectively handled. Next, the physical constraints of the steering system and direct yaw moment control (DYC) system are considered for practical implementation through robust set invariance theory. The parallel distributed compensation (PDC) technique and auxiliary feedback matrices approach are introduced for reducing design conservatism. After that, by incorporating the road curvature into the augmented system state, the path tracking preview control problem can be solved without online optimization. Thereafter, the closed-loop system stability and guaranteed performance have been proved through the Lyapunov- Krasovski approach. The proposed controller design is finally reformulated as the optimization problem based on linear matrix inequalities (LMIs) via specific convexification techniques. Finally, to verify the validity of the proposed controller, Software in Loop (SIL) tests with Carsim full-vehicle model under different dynamic conditions have been implemented.

Intelligent Modeling for Batch Polymerization Reactors with Unknown Inputs

While system identification methods have developed rapidly, modeling the process of batch polymerization reactors still poses challenges. Therefore, designing an intelligent modeling approach for these reactors is important. This paper focuses on identifying actual models for batch polymerization reactors, proposing a novel recursive approach based on the expectation-maximization algorithm. The proposed method pays special attention to unknown inputs (UIs), which may represent modeling errors or process faults. To estimate the UIs of the model, the recursive expectation-maximization (EM) technique is used. The proposed algorithm consists of two steps: the E-step and the M-step. In the E-step, a Q-function is recursively computed based on the maximum likelihood framework, using the UI estimates from the previous time step. The Kalman filter is utilized to calculate the estimates of the states using the measurements from sensor data. In the M-step, analytical solutions for the UIs are found through local optimization of the recursive Q-function. To demonstrate the effectiveness of the proposed algorithm, a practical application of modeling batch polymerization reactors is presented. The performance of the proposed recursive EM algorithm is compared to that of the augmented state Kalman filter (ASKF) using root mean squared errors (RMSEs). The RMSEs obtained from the proposed method are at least 6.52% lower than those from the ASKF method, indicating superior performance.

Team optimal decentralized estimation by multiple agents with partial history sharing information structure

AbstractIn this paper, we study the team optimal decentralized estimation with partial history sharing information structure. There exist agents that have their own observations and share partial history observations to each other. The main contributions include two aspects: One is to give the iterative equations of the common estimation, which is the conditional expectation of state with respect to the common information for all agents and the innovation of the local information for each agent; the other is to provide the structure of the team optimal decentralized estimation, that is, the linear combination of the common estimation and the innovation of the local information. The novelty lies in that the estimation can be obtained at one time by defining an augmented state. In particular, the result is reduced to the well‐known centralized estimation when all the information is sharing for all the agents.

Online estimation of colored observation‐noise parameters within an ensemble Kalman filtering framework

AbstractThis work addresses the problem of data assimilation in large‐dimensional systems with colored observation noise of unknown statistics, a scenario that will become more common in the near future with the deployment of denser observational networks of high spatio‐temporal coverage. Here, we are interested in the ensemble Kalman filter (EnKF) framework, which has been derived around a white observation noise assumption. Recently, colored observation‐noise aware EnKFs in which the noise was modeled as a first‐order autoregressive (AR) model were introduced. This work generalizes the above‐mentioned filters to learn the statistics of the AR model further online. We follow the state augmentation approach first to estimate the state and the AR model transfer matrix simultaneously, then the variational Bayesian approach to estimate the AR model noise covariance parameters further. We accordingly derive two filtering EnKF‐like algorithms, which estimate those statistics together with the system state. We demonstrate the effectiveness of the proposed colored observation‐noise aware filtering schemes and compare their performance based on several numerical experiments conducted with the Lorenz‐96 model.

Zero-order optimization for Gaussian process-based model predictive control

By enabling constraint-aware online model adaptation, model predictive control using Gaussian process (GP) regression has exhibited impressive performance in real-world applications and received considerable attention in the learning-based control community. Yet, solving the resulting optimal control problem in real-time generally remains a major challenge, due to (i) the increased number of augmented states in the optimization problem, as well as (ii) computationally expensive evaluations of the posterior mean and covariance and their respective derivatives. To tackle these challenges, we employ (i) a tailored Jacobian approximation in a sequential quadratic programming (SQP) approach and combine it with (ii) a parallelizable GP inference and automatic differentiation framework. Reducing the numerical complexity with respect to the state dimension nx for each SQP iteration from O(nx6) to O(nx3), and accelerating GP evaluations on a graphical processing unit, the proposed algorithm computes suboptimal, yet feasible, solutions at drastically reduced computation times and exhibits favorable local convergence properties. Numerical experiments verify the scaling properties and investigate the runtime distribution across different parts of the algorithm.

On Optimizing the Conditional Value-at-Risk of a Maximum Cost for Risk-Averse Safety Analysis

The popularity of Conditional Value-at-Risk (CVaR), a risk functional from finance, has been growing in the control systems community due to its intuitive interpretation and axiomatic foundation. We consider a nonstandard optimal control problem in which the goal is to minimize the CVaR of a maximum random cost subject to a Borel-space Markov decision process. The objective represents the maximum departure from a desired operating region averaged over a given fraction of the worst cases. This problem provides a safety criterion for a stochastic system that is informed by both the <i>probability</i> and <i>severity</i> of the potential consequences of the system&#x0027;s behavior. In contrast, existing safety analysis frameworks apply stage-wise risk constraints or assess the probability of constraint violation without quantifying the potential severity of the violation. To the best of our knowledge, the problem of interest has not been solved. To solve the problem, we propose and study a family of stochastic dynamic programs on an augmented state space. We prove that the optimal CVaR of a maximum random cost enjoys an equivalent representation in terms of the solutions to these dynamic programs under appropriate assumptions. For each dynamic program, we show the existence of an optimal policy that depends on the dynamics of an augmented state under the assumptions. In a numerical example, we illustrate how our safety analysis framework is useful for assessing the severity of combined sewer overflows under precipitation uncertainty.

Improving the Feasibility of Moment-Based Safety Analysis for Stochastic Dynamics

Given a dynamical system modelled via stochastic differential equations (SDEs), we evaluate the safety of the system through its exit time moments. Using appropriate semidefinite positive matrix constraints, an SDP moment-based approach can be used to compute moments of the exit time. However, the approach is impeded when analyzing higher dimensional physical systems as the dynamics are limited to polynomials. Computational scalability is also poor as the dimensionality of the state grows, largely due to the combinatorial growth of the optimization program. We propose methods to make feasible the safety analysis of higher dimensional physical systems. The restriction to polynomial dynamics is lifted by using state augmentation which allows one to generate the optimization for a broader class of nonlinear stochastic systems. We then reformulate the constraints to mitigate the computational limitations associated with an increase in state dimensionality. We employ our methods on two example processes to characterize their safety via exit times and show the ability to handle multi-dimensional systems that were previously unsupported by the existing SDP method of moments.

USV Parameter Estimation: Adaptive Unscented Kalman Filter-Based Approach

In this article, a new kind of adaptive unscented Kalman filter (AUKF) is proposed to deal with the parameter estimation problem for a class of nonlinear unmanned surface vessel (USV) models with unknown statistical characteristics of process noises. Specifically, the considered parameter estimation problem is first transformed into the state estimation problem by extending eighteen parameters and three unknown inputs into augmented states for the USVs. With the help of such a transformation, the unknown inputs including disturbances and modeling errors are estimated effectively, and employed to construct the estimators such that the effect of these unknown inputs on parameter estimation can be significantly suppressed. Under the condition that the structure of the covariance matrix of the process noise is available, an adaptive law is further designed to estimate such a high-dimensional covariance matrix where the covariance estimation errors can be reduced. Finally, the proposed estimation approach is verified via performing the practical experiment as well as numerical simulations.

Nonlinear receding-horizon filter approximation with neural networks for fast state of charge estimation of lithium-ion batteries

An important component of electric vehicles is the Battery Management System (BMS), whose main objective is to monitor the state of charge (SoC) of the battery, which can significantly impact the vehicle’s autonomy. The SoC may be estimated using filtering algorithms; in this context, higher accuracy and computational complexity are of great importance. The present paper aims to propose receding-horizon strategies, namely Moving-Horizon State Estimation (MHSE) and Neural Network Moving-Horizon Estimation (NNMHE), for SoC estimation. MHSE is based on a constrained optimization problem, with information of measured samples along a larger observation window, which ensures high accuracy and robustness but requires a better processing capacity. Simulated results are obtained through this method, and it is demonstrated its capacity to jointly estimate the states and the unknown lumped parameters of the battery model using an augmented states formulation. The accuracy of MHSE in the process is high enough that its results may be used for training the NNMHE, so that a machine learning-based solution, with reduced processing time, is found. In this proposed method, a Neural Network is used to emulate the optimization problem solver, by which faster and approximate results are obtained. This approach is evaluated with an experimental dataset, achieving a coefficient of determination of almost 99% and about 20 times faster, which proves that it is effective and can be readily employed in an embedded systems application requiring less computational resources.