Unknown Input Research Articles

Distributed optimal consensus via PI regulation for high‐order nonlinear agents over directed networks

AbstractThis paper studies the optimal consensus problem of high‐order nonlinear agents under digraphs by PI regulation. A new type of adaptive PI variables is proposed for the first time, which is independent of the global information of graphs and complex dynamics. With the proposed variables, a key lemma is derived to transform the optimal consensus problem into a regulation problem, such that classical control techniques are used to regulate the adaptive PI variables for more complex dynamics. We also develop a new kind of distributed control algorithms based on the adaptive PI variables, Nussbaum‐type functions, and neural networks (NN). The proposed algorithms achieve the optimal consensus for high‐order nonlinear agents with nonidentical unknown control directions, bounded disturbances, and input saturation over weight‐unbalanced directed networks. Finally, a simulation example is provided to illustrate the effectiveness of the proposed algorithms.

Performance Guaranteed Robust Tracking Control of MIMO Nonlinear Systems With Input Delays: A Global and Low-Complexity Solution.

This article presents a global performance guaranteed tracking control method for a class of general strict-feedback multi-input and multi-output (MIMO) nonlinear systems with unknown nonlinearities and unknown time-varying input delays. By introducing a novel error transformation embedded with the Lyapunov-Krasovskii functional (LKF), the developed control scheme exhibits several appealing features: 1) it is able to achieve global prescribed performance tracking for uncertain MIMO systems with delayed inputs, while at the same time eliminating the constraint conditions imposing on initial values between the tracking/virtual error and the performance function; 2) there is no need for any a priori knowledge regarding the nonlinearities of the system nor a prior knowledge of time derivatives of the desired trajectory, making the resultant controller simpler in structure and less expensive in computation; 3) the control scheme includes a new differentiable time-varying feedback term, which gracefully compensates the unknown input delays and unknown control gain coefficient matrices; and 4) the controllability condition is relaxed, which enlarges the applicability of the proposed strategy. Finally, a two-link robotic manipulator example is provided to demonstrate the reliability of the theoretical results.

Short-term solar irradiance forecasting under data transmission constraints

We report a data-parsimonious machine learning model for short-term forecasting of solar irradiance. The model follows the convolutional neural network – long-short term memory architecture. Its inputs include sky camera images that are reduced to scalar features to meet data transmission constraints. The model focuses on predicting the deviation of irradiance from the persistence of cloudiness (POC) model. Inspired by control theory, a noise signal input is used to capture the presence of unknown and/or unmeasured input variables and is shown to improve model predictions, often considerably. Five years of data from the NREL Solar Radiation Research Laboratory were used to create three rolling train-validate sets and determine the best representations for time, the optimal span of input measurements, and the most impactful model input data (features). For the chosen validation data, the model achieves a mean absolute error of 74.29 W/m2over a time horizon of up to two hours, compared to a baseline 134.35 W/m2 using the POC model.

A novel strengthened road roughness estimation framework based on the adaptive unbiased minimum variance with unknown input

The accurate acquisition of the strengthened road roughness is significant to vehicle reliability and durability. However, the existing road roughness estimation methods are inapplicable due to the non-Gaussian characteristic of the strengthened road roughness. To fulfil this gap, this work proposes a novel strengthened road roughness estimation framework based on the adaptive unbiased minimum variance with unknown input (AUMV-UI) to accurately estimate the roughness of strengthened roads. The proposed AUMV-UI framework consists of four sub-models, i.e. the quarter suspension model, the vehicle parameter identification model, the road roughness estimation model, and the estimation error correction model. In the road roughness estimation model, the unbiased minimum variance with unknown input (UMV-UI) method is proposed for the first to estimate the strengthened road roughness, and thus the first three sub-models are also integrated as the UMV-UI framework. In the estimation error correction model, the Sage–Husa method is introduced to further correct the potential errors of the UMV-UI method. The AUMV-UI framework is validated and compared to the UMV-UI framework by simulations and experiments. The results show that the AUMV-UI framework can significantly improve the estimation accuracy, which can serve as an elegant tool to accurately acquire the strengthened road roughness.

Composite‐observer‐based asynchronous control for hidden Markov nonlinear systems with disturbances

SummaryIn this article, an asynchronous adaptive tracking control approach is presented for a type of hidden Markov jump nonlinear systems with external disturbances. In this joint jump process model, hidden Markov model signifies the dynamics of the actual system, whereas the signal emits from the detector symbolizes the transmitted information. This leads to the phenomenon of asynchronization between the modes of the system and that of the controller. Accordingly, an asynchronous observer is developed by using the mode information from the detector to develop an asynchronous control approach. The observer contains a disturbance estimation part, to compensate the unknown external inputs. Utilizing the backstepping scheme, a strict‐feedback asynchronous tracking controller is formulated, guaranteeing that all signals within the closed‐loop system are semi‐globally uniformly ultimately bounded in probability. Finally, the validity of the presented methodology is illustrated by means of a simulation example.

An Adjustable Parameter-Based Robust Distributed Fault Diagnosis for One-Sided Lipschitz Formation of Clustered Multi-Agent Systems

This paper addresses the challenge of distributed fault diagnosis in the context of the one-sided Lipschitz formation of agents. Each agent integrates an observer to detect and estimate both linear and non-linear faults in its attitude control subsystem. A robust design configuration is also developed to account for external perturbations. The robust observer utilized in this study is an unknown input observer (UIO), designed to mitigate the impact of disturbances on fault and state estimation errors. The observer’s parameters are determined using linear matrix inequalities (LMIs). Furthermore, a UIO incorporating an adjustable parameter (AP) is introduced to enhance fault diagnosis accuracy. Simulation results for two satellite clusters, consisting of five satellites with varying dynamics due to external disturbances, are presented to validate the approach. Instead of equipping every agent with an observer, specific agents can be equipped with observers to detect faults throughout the constellation, thereby reducing computational demands in configurations with numerous agents. Finally, a comparison is made between the proposed AP-based UIO and a standard UIO. The comparison findings reveal a noteworthy average of a substantial 56.61% reduction in root mean square error (RMSE) employing AP-based UIO compared to the utilization of standard robust UIO.

L1 Adaptive Fault-Tolerant Control for Nonlinear Systems Subject to Input Constraint and Multiple Faults

This paper investigates an L1 adaptive fault-tolerant control scheme for nonlinear systems with input constraint, external disturbances, and multiple faults, which include actuator faults and sensor faults. Faults and input constraint are important factors that affect the stability and performance of a control system. Actuators and sensors are the most vulnerable components, with the former receiving more attention in comparison. In this paper, sensor faults are first transformed into pseudo-actuator faults through the augmented matrix approach, which facilitates their handling together with actuator faults. Saturation constraints on the control signal are not conducive to the design of the controller. The conversion of an input-saturated function to a time-varying linear system is completed based on function approximation and Lagrange’s mean value theorem. Moreover, a nonlinear system with unknown input gain and uncertainties is constructed using these methods. Next, an L1 adaptive fault-tolerant controller is designed to cope with uncertainties, including system uncertainties, external disturbances, faults, and approximation errors. In the L1 adaptive controller, the online estimation of the time-varying parameters allows for updating of the system state, while the combination of the two is transmitted to the control law such that it can compensate for the effects of the uncertainties. The stability and performance boundaries are further derived using the Lyapunov theory and the L1 reference system. Finally, simulations are carried out to demonstrate the effectiveness of the proposed controller.

Probabilistic Risk Assessment in Cybersecurity: Bayesian Methods for Quantifying and Mitigating Cyber Risks

In today's digital world, where everything is linked, privacy dangers are a big problem for businesses, states, and people. When it comes to cybersecurity, traditional ways of assessing risk don't always work because online threats are always changing. By combining statistical models with existing data and expert knowledge, Bayesian methods, on the other hand, look like a potential way to measure and reduce online risks. This essay looks at how Bayesian methods can be used in probabilistic risk assessment (PRA) in the field of hacking. Bayesian reasoning is used by PRA to get a fuller picture of cyber risks by taking into account doubt, variation, and personal opinions during the risk assessment process. By using likelihood functions, posterior distributions, and prior probabilities, Bayesian methods give us a sensible way to update risk predictions as new information comes in. One of the best things about Bayesian PRA is that it can take into account how different online risks and weaknesses are connected and depend on each other. By using statistical modeling to look at these connections, businesses can find possible chain reactions and decide how to best stop them. Additionally, Bayesian methods let you use expert opinions and personal data, which makes it possible to look at online risks in a more complete way than just using numbers. One of Bayesian PRA's strengths is that it can work with little data and unknown input values. When there isn't enough or a lot of good actual data, Bayesian methods let analysts combine information from different sources, like past data, threat intelligence, and expert opinions, in a planned way to get more accurate risk predictions. Bayesian methods can be used to make decisions about how to reduce security risks as well as how to measure those risks. In a probabilistic framework, organizations can figure out the best ways to lower their general cyber risk exposure by modeling the possible results of different mitigating measures. Overall, this study shows how Bayesian methods could help the area of computer risk assessment grow. By accepting doubt and using a variety of information sources, Bayesian PRA provides a powerful set of tools for measuring cyber risks and helping risk managers make decisions in a danger situation that is becoming more complicated.

Distributed fast F‐T control for UAV formation in the presence of unknown input disturbances

Distributed fast F‐T control for UAV formation in the presence of unknown input disturbances

Neural network-based distributed intelligent supervisory control for multi-agent systems with unknown input powers

In this paper, a synchronisation problem is studied for a class of nonlinear leader-following systems. Based on adaptive control with some algebra lemmas, we propose a distributed control scheme. This scheme ensures each follower to asymptotically synchronise with the leader. Compared with the existing works where system input powers are assumed one, the input powers considered in this paper are unknown but larger than one. Based on Graph theory, Lyapunov theory and radial basis function (RBF) networks, we design a distributed adaptive supervisory control method. It is proven that the consensus among the leader and followers are achieved and all the signals including tracking errors asymptotically converge to a small neighbourhood of the origin. Finally, simulation results are displayed to demonstrate the effectiveness of control scheme.

Hamiltonian quantum generative adversarial networks

We propose Hamiltonian quantum generative adversarial networks (HQuGANs) to learn to generate unknown input quantum states using two competing quantum optimal controls. The game-theoretic framework of the algorithm is inspired by the success of classical generative adversarial networks in learning high-dimensional distributions. The quantum optimal control approach not only makes the algorithm naturally adaptable to the experimental constraints of near-term hardware, but also offers a more natural characterization of overparameterization compared to the circuit model. We numerically demonstrate the capabilities of the proposed framework to learn various highly entangled many-body quantum states, using simple two-body Hamiltonians and under experimentally relevant constraints such as low-bandwidth controls. We analyze the computational cost of implementing HQuGANs on quantum computers and show how the framework can be extended to learn quantum dynamics. Furthermore, we introduce a cost function that circumvents the problem of mode collapse that prevents convergence of HQuGANs and demonstrate how to accelerate the convergence of them when generating a pure state. Published by the American Physical Society 2024

3-D Current Density and Magnetic Field of 3-D MR Scanner Gradient Coil

The topic of this paper is to describe the 3-D current density in the windings of a 3-D coil, which fills the volume between two coaxial cylinders at a precisely defined distance from each other, and which serves to generate a magnetic field gradient in the center of the cylinder axis. The 3-D current density is considered an unknown input quantity, which is calculated from the known gradient magnetic field output. It is an inverse problem in mathematics, where the direct problems are the calculation of unknown output quantities based on known input quantities. Fourier series expansion methods in the context of cylindrical coordinates were used to describe the 3-D current density. In that case, Bessel functions are used as development components. The current densities, at each point in space, were lined up to represent current lines. Each power line is associated with a coil winding through which a current of a certain strength flows. After that, the principle of discretization of coil windings was applied. Each winding is divided into a large number of elementary segments that were considered as current elements, which create, based on Bio-Savar's law, an elementary magnetic field. In this way, the total, continuous magnetic field is broken into many elementary components, which come from different current elements. An important result of this process is that each current element can be controlled independently by a current source. This means that the output magnetic field of the gradient can be controlled by current sources, which are the input sizes, and this is what is at the core of the topic of this paper.

StocIPNet: A novel probabilistic interpretable network with affine-embedded reparameterization layer for high-dimensional stochastic inverse problems

The stochastic inverse problem (StocIP), which aims to align push-forward and observed output distributions by estimating probability distributions of unknown system inputs, often faces optimization challenges and the curse of dimensionality. A novel deep network called StocIPNet which comprises an affine-embedded reparameterization subnetwork (ReparNet) and a complex system metamodeling subnetwork (MetaNet) is proposed to alleviate these issues. The ReparNet subnetwork embeds the affine transformation to convert the statistical parameters of the physical random vector into learnable weights and biases, effectively implementing the reparameterization trick by separating random and deterministic elements in the stochastic sampling operation to preserve differentiability. In parallel, the MetaNet subnetwork offers a computationally efficient alternative to time-consuming forward solvers, facilitating the generation of push-forward distributions. The entire StocIPNet utilizes the kernel maximum mean discrepancy (MMD) as a distribution-free loss function, quantifying the discrepancy between push-forward and observed output distributions. By leveraging the ReparNet’s advantage of reformulating the sampling process as a differentiable transformation and combining two subnetworks seamlessly, the StocIP is reconfigured into a pure network training paradigm preserving differentiability perfectly, which allows for direct modeling and efficient inference of uncertainty within the network using automatic differentiation, backpropagation and gradient-based optimization methods, enabling ease of scaling to high-dimensional problems. The proposed framework has been theoretically demonstrated to be equivalent to the maximum likelihood method, ensuring its solid probabilistic interpretable foundation. The proposed framework is applied to perform stochastic model updating on a numerical and an experimental structure, which effectively demonstrates the framework’s remarkable effectiveness and high efficiency in treating high-dimensional StocIPs.

Positive functional filters synthesis for positive linear systems

Abstract This paper deals with the problem of positive functional $H_{\infty }$ filtering for positive linear systems subject to both bounded disturbances and unknown inputs. The order of the designed $H_{\infty }$ filter is equal to the dimension of the functional to be estimated, that can be useful for control purpose for example. We focus on the design of positive filters which guarantee that the functional (of the state) is always non-negative at any time and converges to the real functional state by minimizing the effect of the disturbances on the estimation error. In fact, we propose a new positive reduced order $H_{\infty }$ filter for positive linear systems for which the states remain in the non-negative orthant of the state space, subject to both disturbances and unknown inputs. This paper is a first attempt to design positive unknown inputs functional $H_{\infty }$ filter for such positive linear systems. The proposed approach is based on the positivity of an augmented system composed of dynamics of both considered system and proposed filter, on the unbiasedness of the estimation error by the resolution of Sylvester equation; then we derive conditions for the establishment of such filters in terms of an optimization problem. An algorithm that summarizes the different steps of the proposed positive functional $H_{\infty }$ filter design is given. Finally, numerical example and simulation results are given to showcase the effectiveness of the proposed design method.

Adaptive neural sliding mode control of an uncertain permanent magnet linear motor system with unknown input backlash in laser processing

In this article, a novel robust and high-precision control scheme is developed for a permanent magnet linear motor system in large-range laser processing subject to unknown system uncertainties and input backlash. First, to enhance the robustness of the controller, an adaptive neural sliding mode control (SMC) scheme is proposed. Besides, to address the system uncertainties, a novel simplified radial basis neural network (RBFNN) is applied in the adaptive SMC scheme. Subsequently, considering that the unexpected chattering introduced by SMC strategy, another RBFNN is employed to approximate the optimal switching gain. In addition, considering that the nonlinear input backlash caused by actuator can also cause the fluctuation of the input signal, an inverse backlash model with the method of reverse compensation is proposed to further minimize the effect of the input backlash on control accuracy. Finally, simulation results, validation experiments, and laser processing experiments are provided to demonstrate that the proposed control scheme significantly reduces the impact of chattering and input backlash. Additionally, it exhibits outstanding control accuracy.

Unknown input observer based neuro-adaptive fault-tolerant control for vehicle platoons with sensor fault and output quantization

Sensor fault and output quantization are common issues acting on vehicle platoon, and they may lead to performance deterioration, instability and even insecurity of the platoon. Therefore, this paper investigates the fault-tolerant control (FTC) problem of vehicle platoons with regard to the above two issues. Considering the probabilistic sensor fault and quantized measurement signals, an unknown input observer (UIO) based fault detection algorithm with adaptive threshold is developed for sensor health status monitoring. Then, an augmented vehicle platoon model is constructed by introducing a low-pass output filter, and a robust UIO is established for state reconstruction. Based on the above results, a fault-tolerant control scheme is exploited by employing the back-stepping control method and adaptive radial basis function neural network (RBF NN) approximation technique, which is proved to be capable of achieving the time-domain string stability (TSS) of vehicle platoons in the presence of sensor fault and output quantization. Simulation results demonstrate the effectiveness of the proposed algorithms.

Observer‐based fixed‐time task‐space cooperative tracking control of networked Lagrangian agents with quantized communication

AbstractIn this article, the task‐space cooperative tracking control (TSCTC) problem of networked Lagrangian agents (NLAs) with quantized communication is investigated in fixed time, where every Lagrangian agent suffers from imprecise dynamics and external disturbances. A hierarchical observer‐based fixed‐time control (HOBFTC) algorithm is proposed, where there are four parts: a prescribed‐time input observer is proposed to recover the unknown input of the leader, a distributed estimator control is designed to force the estimated values to converge the states (position and velocity) of the leader, a fixed‐time disturbance observer is presented to recover the total disturbances of NLAs, and a nonsingular fixed‐time local control is given to guarantee that the task‐space cooperative tracking can be achieved. The salient features are twofold: (1) by employing the hierarchical control strategy, the proposed control algorithm is clearly structured to solve the complex cooperative tracking problem with multiple constraints including quantized communication, imprecise dynamics and external disturbances. (2) the convergence time of the proposed control algorithm can be set freely by selecting some parameters, which are independent of the initial conditions. Some sufficient conditions are obtained and some simulation examples are given to validate the effectiveness of the proposed algorithm.

Finding eigenvectors with a quantum variational algorithm

This paper presents a hybrid variational quantum algorithm that finds a random eigenvector of a unitary matrix with a known quantum circuit. The algorithm is based on the SWAP test on trial states generated by a parametrized quantum circuit. The eigenvector is described by a compact set of classical parameters that can be used to reproduce the found approximation to the eigenstate on demand. This variational eigenvector finder can be adapted to solve the generalized eigenvalue problem, to find the eigenvectors of normal matrices and to perform quantum principal component analysis on unknown input mixed states. These algorithms can all be run with low-depth quantum circuits, suitable for an efficient implementation on noisy intermediate-scale quantum computers and, with some restrictions, on linear optical systems. In full-scale quantum computers, where there might be optimization problems due to barren plateaus in larger systems, the proposed algorithms can be used as a primitive to boost known quantum algorithms. Limitations and potential applications are discussed.

Identification of oscillatory systems with unknown continuous input actions

Identification of oscillatory systems with unknown continuous input actions

Uncertainty disturbance estimator control for delayed linear systems with input constraint

This paper proposes a novel Uncertainty and Disturbance Estimator (UDE) based controller for Multi-Input Multi-Output (MIMO) systems. The controller handles input constraints, time-varying matched uncertainties in state and input matrices, unknown input–output delays, and partial state measurement. The UDE error dynamics are augmented with a time-varying variable to handle input constraints effectively. The proposed controller employs a Proportional Integral Observer (PIO) and a state predictor to accurately estimate the future state of the system with only partial state measurement. We develop sufficient conditions for system stability in tracking a reference model while only an estimation of the total delay is available. Numerical simulations and experiments on a multi-rotor platform validate the proposed controller’s effectiveness, demonstrating improved tracking performance and stability compared to existing methods. The proposed UDE-based controller, with a PIO and state predictor, is capable of handling various matched uncertainties and disturbances in MIMO systems with input constraints and partial state measurement. It offers improved tracking performance and stability compared to existing studies.