Robust Stability Of System Research Articles

Design of LQ regulators with prescribed degree of stability for dual-rate systems based on reinforcement learning

This paper considers dual-rate systems, where the output is measured at a relatively slow rate while the control signal is adjusted at a faster rate. The output sampling time is an integer multiple of the input sampling time. The paper examines dual-rate inferential control systems, which consist of a fast model, a slow model, and a switch. Missing output samples are estimated using the fast single-rate model. The single-rate control algorithm is then implemented at the fast-sampling rate. The fast-sampling discrete-time model is derived from the plant’s continuous-time model using the first-order hold (FOH) element. A discrete LQ regulator is proposed for this plant model, with a prescribed degree of stability (all closed-loop eigenvalues are within the range 0 < λ < 1 in magnitude). The matrix gain is calculated offline, and an online method for calculating the regulator gain is provided. The regulator gain is calculated using policy iteration, specifically Hewer’s algorithm. Finally, it is demonstrated that the presented inferential control system remains effective in the presence of multiplicative unmodeled dynamics. The main contributions of the paper are: (i) Designing the LQ regulator with a prescribed degree of stability using reinforcement learning (RL) (generalized policy iteration); and (ii) Considering the robust stability of the inferential control system in the presence of multiplicative unmodeled dynamics using the lifting technique.

On Robust Stability of Uncertain Control Systems With Time Delay: An Approach Based on the Overlap of Value Sets

On Robust Stability of Uncertain Control Systems With Time Delay: An Approach Based on the Overlap of Value Sets

An optimization‐based method for robust stabilization of linear delay systems

AbstractThis paper investigates the robust stabilization problem of linear delay systems with parametric uncertainty. First, by means of the argument principle, a delay‐dependent sufficient condition is derived for designing a feedback controller, with which the closed‐loop system can achieve robust stability. Then, based on the fundamental matrix of the linear delay systems, a constrained optimization problem is formulated for solving the feedback gain matrices. The effectiveness of the proposed method is verified by some simulation results.

Dynamic output feedback control strategy for a satellite orbital model within negative-imaginary systems theory framework

This article presents the synthesis of a dynamic output feedback controller for a satellite orbital system confronted with uncertainties. The investigated method transforms the closed-loop system, synthesized by the controller, into an α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document}-strictly negative-imaginary system. It utilizes the DC-loop gain condition associated with negative-imaginary systems theory to demonstrate robust stability of the satellite orbital system in the presence of uncertainties. Furthermore, the synthesized negative-imaginary closed-loop system exhibits notable time-domain performance. The numerical simulation outcomes presented in this article validate the investigated synthesis method.

Robust Output Feedback Stabilization and Tracking for an Uncertain Nonholonomic Systems with Application to a Mobile Robot.

This paper presents a novel robust output feedback control that simultaneously performs both stabilization and trajectory tracking for a class of underactuated nonholonomic systems despite model uncertainties, external disturbance, and the absence of velocity measurement. To solve this challenging problem, a generalized normal form has been successfully created by employing an input-output feedback linearization approach and a change in coordinates (diffeomorphism). This research mainly focuses on the stabilization problem of nonholonomic systems that can be transformed to a normal form and pose several challenges, including (i) a nontriangular normal form, (ii) the internal dynamics of the system are non-affine in control, and (iii) the zero dynamics of the system are not in minimum phase. The proposed scheme utilizes combined backstepping and sliding mode control (SMC) techniques. Furthermore, the full-order high gain observer (HGO) has been developed to estimate the derivative of output functions and internal dynamics. Then, full-order HGO and the backstepping SMC have been integrated to synthesize a robust output feedback controller. A differential-drive type (2,0) the wheeled mobile robot has been considered as an example to support the theoretical results. The simulation results demonstrate that the backstepping SMC exhibits robustness against bounded uncertainties.

Disturbance rejections of polynomial fuzzy systems under equivalent-input-disturbance estimator approach

This paper proposes an integrated robust stabilization and anti-disturbance control scheme for nonlinear systems using a polynomial fuzzy model approach. To estimate unknown disturbances, an equivalent-input-disturbance (EID) estimator is employed. The proposed approach incorporates a novel fuzzy model assisted by EID estimator into the sum-of-squares-based approach, utilizing a polynomial fuzzy model-based observer to estimate the disturbance effect. A suitable fuzzy rule-based control law is developed by utilizing the parallel distributed compensation approach and the output of the EID estimator. To ensure stability, fuzzy membership functions are converted into sum-of-square polynomials using a polynomial curve fitting approach, allowing their exact shape information to be used in the stability condition. The addressed system is transformed into an augmented system by incorporating the system, observer, and filter states, simplifying the analysis. Gain matrices for the controller and observer are obtained using Lyapunov stability theory and sum-of-squares methods to confirm asymptotic stabilization of the fuzzy system. Two numerical examples are presented to demonstrate the effectiveness of the proposed control design method.

Reliable stabilization of discrete-time nonlinear singular systems with time-varying delays

The problem of delay-dependent reliable control for uncertain discrete-time nonlinear singular system with time-varying delays is investigated. A new set of delay-dependent sufficient conditions are established for the existence of a reliable controller which ensures the singular system to be regular, causal (absence of impulses) and stable for all admissible parameter uncertainties. First, the controller for singular system in the presence of known actuator fault matrix is designed. Further, the result is extended to study the robust stabilization of singular systems with unknown actuator fault matrix. The sensor failures of actuator are considered by a variable, which is varying in a given interval. The conditions for the existence of proposed controller design are established in the form of linear matrix inequality (LMI), which can be easily solved via standard numerical software. Finally, numerical examples with simulation results are provided to illustrate the usefulness of control design and results are compared with existing results to show the less conservatism of the proposed theory.

Robust stabilization of polytopic systems via fast and reliable neural network‐based approximations

AbstractWe consider the design of fast and reliable neural network‐based approximations of traditional stabilizing controllers for linear systems with polytopic uncertainty, including control laws with variable structure and those based on a (minimal) selection policy. Building upon recent approaches for the design of reliable control surrogates with guaranteed structural properties, we develop a systematic procedure to certify the closed‐loop stability and performance of a linear uncertain system when a trained rectified linear unit (ReLU)‐based approximation replaces such traditional controllers. First, we provide a sufficient condition, which involves the worst‐case approximation error between ReLU‐based and traditional controller‐based state‐to‐input mappings, ensuring that the system is ultimately bounded within a set with adjustable size and convergence rate. Then, we develop an offline, mixed‐integer optimization‐based method that allows us to compute that quantity exactly.

Robust fuzzy adaptive stabilization for uncertain nonlinear systems with quantized input and output constraints

In this paper, we study the problem of robust fuzzy adaptive output feedback stabilization for a class of nonlinear systems with quantized input and output constraints. The system under consideration has these characteristics: unknown state mismatch uncertainties and unknown disturbances, and unknown measurement noises. By employing the output filtering transformation, the fuzzy logic system (FLS) approximator, the backstepping, and the high gain observer technique, a non-fragile robust fuzzy adaptive observer and a hyperbolic tangent adaptive controller are presented to guarantee that the closed-loop system is ultimately uniformly bounded and the output is constricted in a prescribed performance curve. The effectiveness of the scheme is verified by numerical simulations.

Closing the gap from nominal to robust asymptotic stabilization of time delay systems

SummaryThe control problem of a general class of perturbed linear invariant time‐delay systems within the Sliding Mode Control framework is addressed. We introduce a novel class of sliding manifolds with a structure not previously reported in the literature, which constructively emerges from complete type functionals of the corresponding nominal time‐delay systems and depends on the whole state of the system. A fundamental conclusion derived from this proposal is that every time‐delay system with matched perturbations, whose associated nominal system is exponentially stabilizable, is robustly asymptotically stabilizable. In fact, the introduced sliding manifold enables to construct discontinuous and continuous sliding mode control‐based algorithms that mitigate different classes of perturbations.

Robust Practical Stabilization of Nonlinear Systems With Saturated Impulsive Control

Robust Practical Stabilization of Nonlinear Systems With Saturated Impulsive Control

Robust state and output feedback stabilization for Lipschitz nonlinear systems in reciprocal state space: Design and real-time validation

In many engineering problems, modelling the state and output derivative variables in reciprocal state space form can be generated more easily than in standard state space one. The formulation of a robust [Formula: see text] control problem using feedback principle for continuous Lipschitz nonlinear systems with uncertainties in reciprocal state space is presented in this article. In contrast to the existing approaches, the considered model is affected by unknown disturbances, parameter uncertainties and derivative Lipschitz nonlinearities. The asymptotic stability based on the proper Lyapunov functions of the closed-loop system is guaranteed. The [Formula: see text] control design resolution problem is ensured through the linear matrix inequality technique, the lemmas and the use of new variables with S-procedure. The performance of the proposed approach is shown through the experimental results using real-time implementation with a digital signal processing device (DSpace DS 1104).

Operator-based adaptive robust control for uncertain nonlinear systems by combining coprime factorization and fuzzy control method1

In this paper, the robust stability of nonlinear system with unknown perturbation is considered combining operator-based right coprime factorization and fuzzy control method from the input-output view of point. In detail, fuzzy logic system is firstly combined with operator-based right coprime factorization method to study the uncertain nonlinear system. By using the operator-based fuzzy controller, the unknown perturbation is formulated, and a sufficient condition of guaranteeing robust stability is given by systematic calculation, which reduces difficulties in designing controller and calculating inverse of Bezout identity. Implications of the results related to former results are briefly compared and discussed. Finally, a simulation example is shown to confirm effectiveness of the proposed design scheme of this paper.

On the robust stability of Volterra differential-algebraic systems

On the robust stability of Volterra differential-algebraic systems

System Modeling and Robust Stability Region Analysis for Multi-inverters Based on VSG

System Modeling and Robust Stability Region Analysis for Multi-inverters Based on VSG

A Novel Limited Grid-Forming Strategy to Support Power System Stability under Primary Energy Source Limitations

The available literature on grid-forming converters often assumes an unlimited primary energy source, for example by postulating a constant DC voltage source. However, this assumption is not justified in real-world scenarios as soon as primary energy source limitations are reached. Therefore, it is imperative for grid-forming control strategies to take such limitations into account and ensure that they support robust system stability even under primary source limitations. In this work, a novel concept of limited grid-forming control is introduced that supports the stability of the network, even under primary energy source power as well as energy constraints. Moreover, the control concept also allows for a seamless transition between full grid-forming and limited grid-forming behavior without any control mode switching. The proposed scheme is tested on a modified IEEE 9-bus test system with one synchronous machine replaced by a droop-based grid-forming controlled battery system incorporating the proposed control scheme. The simulation of a couple of dynamic events provides results that demonstrate promising performance, thereby substantiating the feasibility of the proposed control scheme.

Robust Stabilization of Time-Varying Nonlinear Systems With Time-Varying Delays: A Fully Actuated System Approach.

A general time-varying nonlinear uncertain system with time-varying delays is proposed, which is composed of two subsystems: one is an uncertain fully actuated subsystem representing the controllable part in the system, the other is an isolated globally uniformly asymptotically (GUA) stable autonomous subsystem which represents the uncontrollable part in the system. Both the single-order fully actuated system (FAS) and the multiorder FAS representations of the controllable subsystem are introduced. The problem of robust stabilization of such a compound system with full-state feedback can be converted into an input-to-state GUA stabilization problem of the fully actuated subsystem, which is solved for both types of single- and multiorder FASs with very general assumptions on the uncertain perturbed functions. Under certain conditions, the solution reduces to that for robust stabilization with partial-state feedback, and naturally reduce to that for robust stabilization of FASs. Two illustrative examples demonstrate both the effect and the application procedure of the proposed robust stabilization approach.

Converse theorems for the property of negative imaginary systems

This paper deals with the converse problems about the robust stability of finite dimensional negative imaginary systems. Various converse negative imaginary theorems are established for linear time-invariant systems. It is shown that the feedback interconnection stability of a specific system with an arbitrary strictly negative imaginary system implies the negative imaginary property of the specific.

Robust Power System Stability Assessment Against Adversarial Machine Learning-Based Cyberattacks via Online Purification

The increasing complexity associated with renewable generation brings more challenges to power system stability assessment (SA). Data-driven approaches based on machine learning (ML) techniques for stability assessment have received significant research interest and shown their promising performance. However, ML-based models are recognized to be vulnerable to adversarial disturbances, where a slight perturbation to power system measurements could lead to unacceptable errors. To address this issue, this paper develops a novel lightweight mitigation strategy, i.e., robust online stability assessment (ROSA), to enhance the ML-based assessment model against both white-box and the black-box adversarial disturbances (i.e., purification) in the online implementation. The ROSA involves a supervised learning-based module for the primary stability assessment and a self-supervised learning-based module. The two modules are trained jointly with different objective (loss) functions and implemented in sequence. A suitable purification objective and various time-series data augmentation methods are designed for SA applications to tackle adversarial disturbances adaptively. Case studies are performed, and the comparative results have clearly illustrated the competitive, robust accuracy against various adversarial scenarios and verified the effectiveness of the proposed online purification strategy.

Mismatched disturbance compensation enhanced robust H∞ control for systems with nonvanishing uncertainties/disturbances

AbstractThis article proposes a robust control method based on disturbance observer techniques for systems subject to mismatched uncertainties/disturbances. In the existing composite robust control methods with disturbance compensation, only matched uncertainties/disturbances, that is, the uncertainties/disturbances acting on the same channels as the control inputs, are feedforward compensated, while the mismatched ones are only attenuated in a conservative manner. It should be highlighted that if the mismatched uncertainties/disturbances are nonvanishing, the controller generally requires excessive control energy to suppress the effects of uncertainties/disturbances, where the control gains must be designed to ensure robust properties at the expense of sacrificing nominal tracking and/or stabilization performances. To address this problem, this article further introduces the compensation of mismatched uncertainties/disturbances into the robust control. Moreover, to attenuate the effects of observation errors, sufficient conditions for the asymptotic and robust stability of error systems are established. Finally, the proposed controller is applied to a DC–DC buck converter system feeding constant power load. Experimental results confirm its feasibility and efficiency.