Design Of Nonlinear Systems Research Articles

Deep optimal experimental design for parameter estimation problems

Abstract Optimal experimental design is a well studied field in applied science and engineering. Techniques for estimating such a design are commonly used within the framework of parameter estimation. Nonetheless, in recent years parameter estimation techniques are changing rapidly with the introduction of deep learning techniques to replace traditional estimation methods. This in turn requires the adaptation of optimal experimental design that is associated with these new techniques. In this paper we investigate a new experimental design methodology that uses deep learning. We show that the training of a network as a Likelihood Free Estimator can be used to significantly simplify the design process and circumvent the need for the computationally expensive bi-level optimization problem that is inherent in optimal experimental design for non-linear systems. Furthermore, deep design improves the quality of the recovery process for parameter estimation problems. As proof of concept we apply our methodology to two different systems of Ordinary Differential Equations.

Robust super‐twisting sliding mode control of input‐delayed nonlinear systems using disturbance observers and predictor feedback

AbstractThis paper investigates prediction‐based robust super‐twisting sliding mode controller design for nonlinear systems with input delay and external disturbances. A novel predictor feedback is introduced based on state predictions of the original and transformed models. To cope with the external disturbances, a set of disturbance observers are utilized which estimate the future values of disturbances asymptotically. Super‐twisting sliding mode control is used to avoid chattering phenomenon which is also able to handle external disturbances. Proposed design can handle all external disturbances that their derivatives vanish at infinity. Stability proof of the closed‐loop is given in details ensuring the asymptotic stability of the tracking errors and finite time vanishing of the sliding surface. To illustrate effectiveness and applicability, the proposed design is applied to a two‐link robot and a serial variable stiffness actuator. Simulation results show that input delays of the robot and actuator are compensated, and external disturbances are correctly estimated and attenuated.

Non-fragile observers design for nonlinear systems with unknown Lipschitz constant

Non-fragile observers design for nonlinear systems with unknown Lipschitz constant

Stability analysis of random fractional-order nonlinear systems and its application

The research on stability analysis and control design for random nonlinear systems have been greatly popularized in recent ten years, but almost no literature focuses on the fractional-order case. This paper explores the stability problem for a class of random Caputo fractional-order nonlinear systems. As a prerequisite, under the globally and the locally Lipschitz conditions, it is shown that such systems have a global unique solution with the aid of the generalized Gronwall inequality and a Picard iterative technique. By resorting to Laplace transformation and Lyapunov stability theory, some feasible conditions are established such that the considered fractional-order nonlinear systems are respectively Mittag-Leffler noise-to-state stable, Mittag-Leffler globally asymptotically stable. Then, a tracking control strategy is established for a class of random Caputo fractional-order strict-feedback systems. The feasibility analysis is addressed according to the established stability criteria. Finally, a power system and a mass–spring-damper system modeled by the random fractional-order method are employed to demonstrate the efficiency of the established analysis approach. More critically, the deficiency in the existing literatures is covered up by the current work and a set of new theories and methods in studying random Caputo fractional-order nonlinear systems is built up.

Decentralized control of nonlinear complex systems

Abstract In the paper, a novel approach to decentralized controller design for nonlinear systems is introduced. The proposed method is based on the relationship between the stability of complex nonlinear systems and the stability of their subsystems. The design procedure of the decentralized controller consists of three steps. In the first step, the stability of the complex nonlinear system is calculated. In the second step, stability conditions at the subsystem level are obtained such that guarantee the stability of the complex nonlinear system. Finally, in the third step, a controller design method is used to ensure that the subsystem stability conditions obtained in the second step are met. As an example, to better understanding the proposed method two simple nonlinear models are used to demonstrate the effectiveness of the proposed method.

Design of Nonlinear Delay Differential System for Analyzing Vulnerabilities in Nanoscale Hardware Implants: A Deep Dive into Intelligent Computing Networks

Design of Nonlinear Delay Differential System for Analyzing Vulnerabilities in Nanoscale Hardware Implants: A Deep Dive into Intelligent Computing Networks

Robust control design of uncertain nonlinear systems: a self-compensating and self-tuning approach

ABSTRACT The problem of robust stabilisation is considered for a class of uncertain nonlinear systems with linear control term. It is not required that the unforced nominal (nonlinear) system has to be stable and/or has to be known, which means that its Lyapunov function need not be known and/or found for designing a stabilising control scheme to compensate the effect of uncertainty on the systems like some traditional control design approaches. For such a class of uncertain nonlinear systems, a design approach, called a self-compensating and self-tuning one, is presented whereby some robust state feedback control schemes can be easily synthesised. The proposed design approach can result in a linear state feedback control scheme with a time-varying control gain for such a class of uncertain nonlinear systems, which implies the simplicity of the design approach and control results. In addition, the system uncertainty is also not required to have to satisfy the matching conditions.

Adaptive distributed fault estimation observer design for nonlinear time-delay multi-agent systems with directed graphs

This paper focuses the development of an adaptive observer-based distributed fault estimation observer (DFEO) for multi-agent nonlinear time-delay systems under a directed communication topology. The process involves constructing a fault estimation observer for each agent based on their relative output estimation errors. An adaptive DFEO design is proposed for multi-agent systems with a directed communication topology. Furthermore, investigating the effect of faulty agents on the criteria of fault detection on healthy agents. The proposed design is represented with Linear Matrix Inequalities (LMIs) to establish a systematic design procedure. The study also includes simulation results to demonstrate the effectiveness of the proposed design techniques.

Unknown input observer design for uncertain nonlinear systems with time-varying delay: application to online fault estimation

This paper recommends an unknown input observer (UIO) for uncertain nonlinear time-delay dynamics that enables online fault estimation. The main novelty of this paper is designing UIO to fault estimation for nonlinear systems that include time-varying delays in states and time-varying uncertainties in all matrices of the system. The other advantage of the proposed method is that both abrupt and incipient faults are considered. Furthermore, the state and output disturbances, as well as actuator and sensor faults, are considered. The Lyapunov–Krasovskii concept is used to guarantee the stability of the augmented closed-loop system. Calculating observer gains and stabilisation of estimation error dynamics are accomplished by utilising a new linear matrix inequality (LMI). Finally, an uncertain continuous-stirred tank reactor (CSTR) with a time-varying delay is used to evaluate the performance of the suggested technique.

Observer Design and State-Feedback Stabilization for Nonlinear Systems via Equilibrium Manifold Expansion Linearization

Observer Design and State-Feedback Stabilization for Nonlinear Systems via Equilibrium Manifold Expansion Linearization

Active Adaptive Composite Fault Tolerant Controller Design For Nonlinear Systems

Abstract It can be seen from the public opinion monitoring that there are many cases of death and injury caused by quality problems of mechanical products, which poses a serious threat to people’s lives. Therefore, it is particularly important to analyze the reliability of mechanical products. This study focuses on active adaptive composite fault tolerant controller (ACFTC) design for nonlinear system with actuator fault. Firstly, a novel iterative learning observer (ILO) is proposed to estimate the early potential fault. And then, the ACFTC approach is proposed in order to obtain desired performance in the faulty case based on the fault estimation information from ILO. Finally, simulation of the flexible joint robot system verifies the validity and applicability of the algorithm.

A novel approach to decentralized sampled‐data fuzzy observer design for nonlinear interconnected systems

AbstractThis paper presents the decentralized sampled‐data fuzzy observer design technique for nonlinear interconnected systems based on the Takagi–Sugeno fuzzy model. The interconnected system is considered that the subsystems include uncertain interconnections and are not needed to satisfy stable conditions. Based on the continuous‐time Lyapunov functional approach, the observer design technique is proposed to minimize the interconnection bound to attenuation degree ratio and formulated into the linear matrix inequality formats. Finally, by simulation example, it shows the validity and superiority of the proposed observer design technique.

Optimal synchronization with [formula omitted]-gain performance: An adaptive dynamic programming approach

This paper studies an optimal synchronous control protocol design for nonlinear multi-agent systems under partially known dynamics and uncertain external disturbance. Under some mild assumptions, Hamilton–Jacobi–Isaacs equation is derived by the performance index function and system dynamics, which serves as an equivalent formulation. Distributed policy iteration adaptive dynamic programming is developed to obtain the numerical solution to the Hamilton–Jacobi–Isaacs equation. Three theoretical results are given about the proposed algorithm. First, the iterative variables is proved to converge to the solution to Hamilton–Jacobi–Isaacs equation. Second, the L2-gain performance of the closed loop system is achieved. As a special case, the origin of the nominal system is asymptotically stable. Third, the obtained control protocol constitutes an Nash equilibrium solution. Neural network-based implementation is designed following the main results. Finally, two numerical examples are provided to verify the effectiveness of the proposed method.

Takagi-Sugeno fuzzy sampled-data observer design for nonlinear permanent magnet synchronous generator-based wind turbine systems using auxiliary function-based integral inequality technique

This study focuses on designing the fuzzy sampled-data observer (FSDO) scheme for nonlinear permanent magnet synchronous generator (PMSG)-based wind turbine systems (WTS). The primary objective of this problem is to solve an unmeasurable state problem under the mismatched premise variables conditions among system, observer, and controller, respectively. To do this, firstly, the proposed wind turbine model is described in a Takagi-Sugeno fuzzy model due to the complex nonlinearities in PMSG-based WTS. Next, based on the measured output signals and sampled estimated states, the FSDO is designed to understand some unmeasurable state variables of the studied system. Then, a novel auxiliary function-based integral inequality (AFBII) is presented to approximate the integral quadratic terms related to sampling information. Thanks to the proposed AFBII technique and the introduction of slack variables, several new and less conservative stability requirements are derived in the formulations of linear matrix inequalities (LMIs) using the looped Lyapunov function. Finally, the simulation studies for the considered wind turbine model are validated numerically, and then some comparative results are provided to show the superiority and applicability of the theoretical observations.

Event-Triggered Robust Integrated Observer Design for Nonlinear Interconnected System Based on Multiple Intermediate Estimators

Event-Triggered Robust Integrated Observer Design for Nonlinear Interconnected System Based on Multiple Intermediate Estimators

Temporal coupled-mode theory in nonlinear resonant photonics: From basic principles to contemporary systems with 2D materials, dispersion, loss, and gain

Temporal coupled-mode theory (CMT) is an acclaimed and widely used theoretical framework for modeling the continuous-wave response and temporal dynamics of any integrated or free-space photonic resonant structure. It was initially employed to understand how energy is coupled into and out of a cavity and how it is exchanged between different resonant modes. In the 30 years that followed its establishment, CMT has been expanded to describe a broad range of nonlinear interactions as well (self- and cross-phase modulation, saturable absorption, frequency generation, gain, etc.). In this Tutorial, we thoroughly present the basic principles and the evolution of CMT throughout the years, showcasing its immense capabilities for the analysis and design of linear and nonlinear resonant photonic systems. Importantly, we focus on the examples of modern, open nanophotonic resonators incorporating contemporary bulk or sheet (2D) materials that may be lossy and dispersive. For each linear/nonlinear effect under study, we follow a meticulous, step-by-step approach, starting from an accurate model of the physical phenomenon and proceeding to its introduction in the CMT framework all the way to the efficient solution of the resulting system of equations. Our work highlights the merits of CMT as an efficient, accurate, and versatile theoretical tool. We envision that it can serve both as an introductory reference for any reader and as a comprehensive handbook on how to incorporate a broad range of linear and nonlinear effects in the CMT framework.

Internal Model Control Design for Nonlinear Systems Based on Inverse Dynamic Takagi–Sugeno Fuzzy Model

Internal Model Control Design for Nonlinear Systems Based on Inverse Dynamic Takagi–Sugeno Fuzzy Model

Observer-based adaptive neural network control design for nonlinear systems under cyber-attacks through sensor networks

This paper considers the adaptive neural tracking control for uncertain nonlinear strict-feedback systems under state-dependent cyber-attacks through sensor networks. As a distinctive feature, by constructing a novel adaptive neural observer, the estimates of system states are used for feedback control instead of the compromised system states corrupted by sensor attacks, such that the assumption on the derivative of attack weight can be removed from the adaptive controller design process. Then, an observer-based control scheme is developed such that all the system signals are bounded and the tracking error converges to a small neighborhood of zero. During the procedure of control design, adaptive backstepping technique is combined with radial basis function neural networks (RBFNNs) to construct controllers. Finally, two examples validate the efficacy of the proposed control scheme.

A novel finite-time stability criteria and controller design for nonlinear impulsive systems

The issue of a novel finite-time stability and stabilization design for a class of nonlinear impulsive systems is discussed in this paper. In previous finite-time control designs for impulsive systems, the convergence rate of these control strategies is even less rapid than the exponential convergence rate when the initial state is distant from the origin. To overcome this problem, two sufficient conditions for the novel finite-time stability of impulsive systems are presented, in which the stabilizing impulses and the destabilizing impulses are considered, respectively. Meanwhile, the upper bound of the settling-time is evaluated. In addition, combining Lyapunov functions theory with impulsive control, we design a controller for impulsive dynamical systems to satisfy the novel finite-time stability. Finally, two simulation examples are given, in which the first example demonstrates the superiority of the proposed finite-time stability criterion for nonlinear impulsive systems by comparing it with traditional finite-time stability, and the second example verifies the effectiveness of the presented controller.

Adaptive output feedback control system design for nonlinear systems via neural networks

AbstractAdaptive output feedback control based on output feedback exponential passivity (OFEP) has a simple structure and strong robustness in regard to disturbances and system uncertainties. However, it is difficult for most nonlinear systems to satisfy the conditions of OFEP. Thus, the introduction of a suitable parallel feedforward compensator (PFC) to construct an OFEP‐augmented system with the controlled system has been used, but the control output cannot achieve perfect tracking because of the output of the introduced PFC. As a solution, introducing a feedforward (FF) input to build a 2 degree of freedom (2‐DOF) is a simple and effective way to solve this problem. In this paper, we propose the design schemes for suitable PFC and FF input of nonlinear systems via the use of neural networks (NN), respectively. Besides, to cope with possibly present input disturbances, we also provide a method to achieve disturbance compensation based on NN to reduce their interference. Finally, the effectiveness of all proposed design schemes is confirmed through numerical simulations.