Stability Of Control System Research Articles

Loop gain response to increased cerebral blood flow at high altitude.

To compare loop gain (LG) before and during pharmacological increases in cerebral blood flow (CBF) at high altitude (HA). Loop gain (LG) describes stability of a negative-feedback control system; defining the magnitude of response to a disturbance, such as hyperpnea to an apnea in periodic breathing (PB). "Controller-gain" sensitivity from afferent peripheral (PCR) and central-chemoreceptors (CCR) plays a key role in perpetuating PB. Changes in CBF may have a critical role via effects on central chemo-sensitivity during sleep. Polysomnography (PSG) was performed on volunteers after administration of I.V. Acetazolamide (ACZ-10mg/kg) + Dobutamine (DOB-2-5 μg/kg/min) to increase CBF (via Duplex-ultrasound). Central sleep apnea (CSA) was measured from NREM sleep. The duty ratio (DR) was calculated as ventilatory duration (s) divided by cycle duration (s) (hyperpnea/hyperpnea + apnea), LG = 2π/(2πDR-sin2πDR). A total of 11 volunteers were studied. Compared to placebo-control, ACZ/DOB showed a significant increase in the DR (0.79 ± 0.21 vs 0.52 ± 0.03, P = 0.002) and reduction in LG (1.90 ± 0.23 vs 1.29 ± 0.35, P = 0.0004). ACZ/DOB increased cardiac output (CO) (8.19 ± 2.06 vs 6.58 ± 1.56L/min, P = 0.02) and CBF (718 ± 120 vs 526 ± 110ml/min, P < 0.001). There was no significant change in arterial blood gases, minute ventilation (VE), or hypoxic ventilatory response (HVR). However, there was a reduction of hypercapnic ventilatory response (HCVR) by 29% (5.9 ± 2.7 vs 4.2 ± 2.8 L/min, P = 0.1). Pharmacological elevation in CBF significantly reduced LG and severity of CSA. We speculate the effect was on HCVR "controller gain," rather than "plant gain," because PaCO2 and VE were unchanged. An effect via reduced circulation time is unlikely, as the respiratory-cycle length did not change.

Well-posedness and properties of the flow for semilinear evolution equations

We derive conditions for well-posedness of semilinear evolution equations with unbounded input operators. Based on this, we provide sufficient conditions for such properties of the flow map as Lipschitz continuity, bounded-implies-continuation property, boundedness of reachability sets, etc. These properties represent a basic toolbox for stability and robustness analysis of semilinear boundary control systems. We cover systems governed by general C0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$C_0$$\\end{document}-semigroups, and analytic semigroups that may have both boundary and distributed disturbances. We illustrate our findings on an example of a Burgers’ equation with nonlinear local dynamics and both distributed and boundary disturbances.

The use of adaptive multiple models for predefined exponential stability of control systems of uncertain discrete‐time nonlinear objects

SummaryIn this work, an adaptive multiple model pre‐assigned exponential convergence control scheme based on the time varying exponential function is demonstrated for a class of discrete‐time nonlinear systems. For coping with the noncausality problem from previous adaptive backstepping design method of nonlinear discrete‐time systems, a first‐order recursive filter is used in controller design procedures and the n‐step prediction model is not needed, thereby reducing the computational burden effectively. The time varying function is employed to force all states variables to convergence to zero with a pre‐defined rate which does not rely on the initial conditions of systems. In addition, the multiple model set is constructed to address unknown parameters problem and further the second level adaptive algorithm of unknown parameters is developed. A characteristic feature of the second‐level multi‐model adaptation algorithm is that it dynamically adapts to time changes in the identified model (it uses identification information better than the switching multiple model control). In a unified framework of second level adaption, a first‐order recursive filter and backstepping technique, a pre‐assigned exponential convergence controller is presented. Finally, the results about discrete‐time pre‐assigned exponential convergence method are compared with other methods using two case studies.

Stability Analysis for Model-Based Event-Triggered Nonlinear Control Systems Under DoS Attacks

In this paper, we study the stability of a novel nonlinear event-triggered control system under denial-of-service (DoS) attacks based on an ISS-Lyapunov function analysis. A new dual-mode model-based event-triggering strategy is proposed which works based on consistency between the approximate and exact discretization of the nonlinear plant. We combine an event-triggered module with a controller based on the state prediction, together with a packetized transmission at the controller-to-actuator channel to provide the desired stability properties under DoS attacks. We also provide proof of Zeno-free behavior for the event-based system. Our proposed method provides a maximum percentage of time that the system can tolerate attacks without performance degradation. Finally, a numerical example is used to illustrate the effectiveness of the proposed approach.

Practical fixed-time output feedback trajectory tracking control for marine surface vessels with unknown disturbances

This paper proposes a fixed-time output feedback trajectory tracking control scheme based on an extended state observer for marine surface vehicles (MSVs) with uncertain dynamics and unknown disturbances. The scheme utilizes a high-gain fixed-time extended state observer (HGFxESO) to estimate the reconstructed unmeasured velocities and lumped disturbances. The upper bound of the settling time of the HGFxESO is only determined by the design parameters, and the estimation errors can converge to a bounded set within a fixed time. Moreover, a novel fixed-time control law is proposed based on the backstepping technique and “adding a power integrator” (API) technique. The designed continuous control law ensures the trajectory tracking errors of MSVs converge to a neighborhood around the origin within a fixed time. The fixed-time stability of the MSVs trajectory tracking control system is proved using Lyapunov theory. Finally, simulation results are provided to demonstrate the effectiveness of the proposed control scheme.

Adaptive-Dynamic-Programming-Based Robust Control for a Quadrotor UAV with External Disturbances and Parameter Uncertainties

Thiswork addresses the trajectory-tracking-control problem for a quadrotor unmanned aerial vehicle with external disturbances and parameter uncertainties. A novel adaptive-dynamic-programming-based robust control method is proposed to eliminate the effects of lumped uncertainties (including external disturbances and parameter uncertainties) and to ensure the approximate optimal control performance. Its novelty lies in that two radial basis function neural network observers with fixed-time convergence properties were first established to reconstruct the lumped uncertainties. Notably, they tune only the scalar parameters online and have low computational complexities. Subsequently, two actor–critic neural networks were designed to approximate the optimal cost functions and control policies for the nominal system. In this design, two new actor–critic neural network weight update laws are proposed to eliminate the persistent excitation condition. Then, two adaptive-dynamic-programming-based robust control laws were obtained by integrating the observer reconstruction information and the nominal control policies. The uniformly ultimately bounded stability of the closed-loop tracking control systems was ensured using the Lyapunov methodology. Finally, numerical results are shown to verify the effectiveness and superiority of the proposed control scheme.

An improved predictor LOS-based global fixed-time prescribed performance controller for the path following of underactuated marine surface vehicles with input saturation

A fixed-time controller based on improved fixed-time predictor line-of-sight (FxTPLOS) guidance and a nonsymmetrical prescribed performance constrained controller is designed for the path-following of underactuated marine surface vehicles (MSVs) in the presence of unknown external disturbances and uncertainties. First, a fixed-time error prediction model is established, and an internal model-controlled observer is designed to observe the sideslip angle, which can extend the estimated range of the sideslip angle to any range. Second, a nonlogarithmic performance function is introduced that can converge the error to a prescribed range, and a fixed-time controller is designed by error transformation. A new input saturation function is added to solve the problem of input saturation, and a new filter is added to avoid differentiating the virtual control law. Third, a novel fixed-time lumped disturbance observer is proposed for estimating the model uncertainty and external disturbances. It is possible to achieve accurate disturbance compensation. By using Lyapunov theory to analyze the stability of the closed-loop control system, it is proven that the system can be uniformly globally fixed-time stable (UGFxTS). Finally, simulation experiments prove that the control strategy proposed in this paper is effective.

Stability Study of Event Dynamic Systems Based on Discrete Mathematical Random Variable Modeling

This project intends to consider the stability of a nonlinear control system with unknown dynamics. The system is controlled systematically by using the reverse step method based on Lyapunov's stability principle. This paper also gives the conclusion that when the control law is in a steady state, the output signal in this state will reach uniform boundedness or asymptotic convergence. Finally, a numerical simulation is carried out through an example, and the results show that the algorithm is effective.

Peak-to-Peak Stabilization of Sampled-Data Systems Subject to Actuator Saturation and Its Practical Application to an Inverted Pendulum

This paper investigates the local stability and stabilization criteria of sampled-data control systems, taking into account actuator saturation and peak-bounded exogenous disturbances. Specifically, this study introduces two innovations to extend the maximum upper bound of the sampling interval: two novel time integrals of the weighted state derivative are introduced to formulate an improved looped-functional; second, the introduction of two supplementary zero-equalities to improve the relationship among the components of the augmented state. Building on this, a set of linear matrix inequality-based stabilization conditions is derived. These conditions ensure that a closed-loop sampled-data system can become exponentially stable and achieve a guaranteed peak-to-peak performance in the domain of attraction. Finally, the efficacy of the proposed methodology is substantiated through both simulation and experimental results, focusing on the sampled-data control of an inverted pendulum system.

Non-fragile output-feedback control for time-delay neural networks with persistent dwell time switching: A system mode and time scheduler dual-dependent design

This paper is concerned with non-fragile output-feedback control for time-delay neural networks with persistent dwell time (PDT) switching in a continuous-time setting. The main purpose is to design an output-feedback controller subject to gain fluctuations, guaranteeing both asymptotic stability and L2-gain of the closed-loop control system. To achieve reduced conservatism, the controller is formulated to depend not only on the system mode but also on a time scheduler constructed based on the PDT switching rule and minimum time span. A criterion for the asymptotic stability and L2-gain analysis is established through the application of the Gronwall–Bellman inequality and mathematical induction. Then, a numerically tractable design approach for the desired controller is proposed, utilizing a four-section piecewise time-dependent Lyapunov–Krasovskii functional and several nonlinearity decoupling techniques. For comparative purposes, a simple case, independent of the time scheduler, is also investigated, and the corresponding controller design approach is presented. Finally, a simulation example is given to illustrate the effectiveness and superiority of the proposed system mode and time scheduler dual-dependent controller design approach.

Tradeoff Techniques for Stabilization of Network-Controlled DC Motor Speed Control System with Uncertainties

This paper details the development of a tradeoff techniques using the conventional time-domain method for stability assurance of network-controlled DC motor speed control system with uncertainties. The DC motor controlled using an open communication network introduces time-delays in the control loop. These time-delays are one of the factors that decides the stability and performance of the dynamical systems. Stabilization of network-controlled DC motor is achieved by tuning the network controller with concern to time-delay. The maximum extend of time-delay called delay margin is computed by developing stability criterion using Lyapunov–Krasvoskii functional and linear matrix inequality techniques. The impact of load disturbances on stability delay margins are investigated and further determining the relationship between delay margin and controller gains for network-controlled DC motor gives a tradeoff between stability and dynamic performance. Finally, proposed results for network-controlled DC motors are validated through Matlab simulation and experimental setup.

Finite-time robust formation control of multiple aerial robotic vehicles with uncertainties and time-varying complex perturbations

Formation control of aerial robotic vehicles (ARVs) has a wide range of applications in the battlefield reconnaissance, medical rescue and load transportation, etc. System parameter variations and complex disturbances are inevitable in the formation control of ARVs, and the effects of them on the formation stability control of ARVs are unnegligible. This paper addresses the robust formation control problem of finite-time leader–follower for multiple ARVs suffering from parameter uncertainties and time-varying perturbations. To ensure the states (e.g. position and velocity) of all followers to converge to leader in finite time, a novel finite-time high-order sliding mode consensus control (HOSMCC) scheme is designed. To better cope with the parameter uncertainties and time-varying disturbances, improve formation control accuracy and achieve the robust formation control of finite-time leader–follower in multiple ARV systems, a new finite time high-order sliding mode formation control (HOSMFC) scheme on the basis of finite-time HOSMCC is proposed. The finite-time stability of multi-ARV formation control system is guaranteed, and the desired formation pattern of multi-ARV systems is achieved using Lyapunov stability theorem. Performance comparisons with proportional differential formation controller (PDFC) and sliding mode formation controller (SMFC) are studied on a four-ARV formation control system. The results validate the designed formation control scheme.

Simulation and analysis of stability of UAV control system based on PID control under different wind forces

The four-rotor UAV has attracted the attention of various fields and has been applied in more areas due to its advantages of low cost, high reliability and simple structure. Nowadays, more complex environment and interference factors put forward higher requirements for the accuracy and stability of the flight control system of UAV. At present, the most widely used four-rotor UAV flight control system is PID control system. This paper constructs a UAV control system based on PID algorithm to analyse and study the dynamic stability control effect of UAV under different wind impact scenarios. MATLAB is used to simulate and analyze the system, and the future development is expected according to the simulation results.

Asynchronous Platoon Control for Connected Vehicles With Intermittent and Delayed Information Transmission

This technical note investigates the asynchronous platoon control problem for connected vehicles with intermittent and delayed information transmission under dynamically changing communication topologies. An asynchronous consensus based protocol is proposed for each vehicle based on the state information of its neighbors at discrete times with communication delays, in which the asynchrony means that each agent updates its dynamics at discrete time instants determined by its own clock. The update intervals and the communication delays are allowed to be arbitrary bounded. We employ nonnegative matrix theory and graph theory to prove that the vehicle platoon asymptotically reaches a desired inter-vehicle spacing and a common velocity, if the effective communication topology jointly contains a directed spanning tree. Furthermore, we show that the string stability of the platoon control system is attained under the predecessor-following topology. Finally, we present numerical examples to validate the theoretical results.

Analysis and Design of a Novel LLC CCPS for Repetitive Pulsed Power Applications

This paper presents a novel type of capacitor charging power supply (CCPS) based on LLC resonant DC/DC converter for repetitive pulsed power applications, such as pulsed lasers. Because the load of CCPS is almost capacitive, leading to a quickly varying of output voltage during the charging period, conventional methods are not appropriate and not accurate enough for analyzing the transient characteristics of this proposed LLC CCPS. Thus, an equivalent resistance method based on first harmonics analysis (FHA) method is proposed and parasitic capacitor effect is analyzed too. In order to improve the stability and robustness of the current control system of the proposed LLC CCPS, a PI+LPF type controller combining LUT-based feed-forward is applied. Based on the theories above, a prototype with 200V input and maximum 1kV/2kW output is demonstrated. A peak efficiency of 97.85% and 2A peak average output charging current is achieved and experiments of repetitive pulsed power with 1Hz are carried out. The results prove the superiority of the proposed LLC CCPS. This text explores new topology options for CCPS and aims to improve their performance, the proposed LLC CCPS shows great engineering application value and potential on repetitive pulsed power applications.

Full-Loop AoI-Based Joint Design of Control and Deterministic Transmission for Industrial CPS

For improving the performance of industrial cyber-physical systems (ICPS), the joint design of control and transmission has been demonstrated as an efficient mechanism. However, the existing metrics in recent joint design works lack completeness and accuracy, which leads to the challenge of improving the stability and network resource utilization of ICPS. This paper proposes a full loop age of information (FL-AoI) based control and transmission joint design architecture for multi-subsystem ICPS integrating multi-hop network. The FL-AoI depicts the timeliness of information by state delay, input delay, and event-triggered status in full-loop ICPS. To avoid the instability caused by the input delay, we design an LQR-based controller by the FL-AoI and derive a feasible region of the FL-AoI for guaranteeing the stability of control systems. To ensure the accuracy of FL-AoI, we propose a routing and scheduling policy based on Time Sensitive Networking (TSN) for the deterministic bound of delay. Finally, we propose an optimal event-triggered policy based on FL-AoI for minimizing the data transmission amount while ensuring the system stability. The evaluation results show that our strategy improves the nonlinear and non-scalar control systems' stability while reducing the network burden of TSN compared with the traditional joint design strategies.

Profit enhancement and grid frequency control by energy level scheduling of CAES system in wind-connected electrical system

The maintenance of power balance poses significant challenges in renewable combined deregulated power systems due to the unpredictable nature of renewable energy sources. This situation leads to economic instability within the system. However, an energy storage system can help maintain energy supply and control system stability for renewable incorporated thermal power plants. Unlike in regulated markets, energy prices in deregulated markets are not fixed by any government body or particular company. Instead, the Independent System Operator (ISO) serves as the main entity in the electrical market, gathering tenders from Generation Companies (GENCOs), Distribution Companies (DISCOs), and Transmission Companies (TRANSCOs). The market controller regulates energy prices using Nodal Pricing (NP), which provides economic benefits to both GENCOs and DISCOs. However, the unpredictability of renewable sources often results in a decline in system profit due to the production of an imbalance price (CostIMC) caused by a mismatch in contracted power generation from the renewable power plant. To address these issues, this study proposes a novel combined system that utilizes a suitable scheduling technique for the optimum operation of a wind farm-compressed air energy storage (CAES) system to maximize profit and revenue while maintaining grid frequency. The CAES system’s energy level is divided into four different levels, and an optimal strategy has been developed to efficiently utilize the CAES system to maintain grid frequency. This work has been conducted in both regulated and deregulated environments using a modified IEEE 30-bus system. The proposed method has been compared with an existing approach and has yielded better results in all aspects.

Stability analysis of nonlinear fuzzy hybrid control systems subject to saturation and delays via step‐function method

AbstractWithin the framework of the step‐function method, the stability of a nonlinear fuzzy hybrid control system that incorporates both an impulsive controller and a continuous state feedback controller is investigated. Both the two controllers are assumed to be subject to both actuator saturation and time‐varying delays, which has been given scant attention, if any, in the existing studies. A new assumption is introduced in this article, thereby enabling the use of generalized sector conditions to tackle the double saturation, and the conservatism inherent in stability results is remarkably reduced owing to the improved step‐function approach employed. The stability theorem proposed in this article removes constraints imposed on the time delays of both controllers, which can be also applied to wider scopes of systems, encompassing hybrid control systems with both stabilizing and instabilizing impulses, systems with varying impulsive gain, and systems with Zeno behavior. Numerical simulations of stabilization for different systems by delayed saturated hybrid control have been conducted, which demonstrate the validity of the proposed theorems.

Tikhonov-Tuned Sliding Neural Network Decoupling Control for an Inverted Pendulum

This paper introduces the concept of intelligent control using Tikhonov regularization for nonlinear coupled systems. This research is driven by the increasing demand for advanced control techniques and aims to explore the impact of Tikhonov regularization on these systems. The primary objective is to determine the optimal regularization term and its integration with other control methods to enhance intelligent control for nonlinear coupled systems. Tikhonov regularization is a technique employed to adjust neural network weights and prevent overfitting. Additionally, the incorporation of ReLU activation function in the neural network simplifies thearchitecture, avoiding issues like gradient explosion, and optimizes controller performance. Furthermore, sliding surfaces are designed to improve control system stability and robustness. The proposed Tikhonov-tuned sliding neural network (TSN) controller ensures both stability and superior system performance. The methodology emphasizes the importance of determining optimal neural network weights and regularization terms to prevent overfitting, facilitating accurate predictions in inverted pendulum control system applications. To assess the functionality and stability of TSN, this paper employs simulations and experimental implementations to control both the rotary inverted pendulum and the arm-driven inverted pendulum. The results indicate that the proposed TSN methodologies are effective and feasible.

Adaptive Fractional Prescribed Performance Control for Micro-Electromechanical System Gyros Using a Modified Neural Estimator

In this paper, a neural fractional order prescribed performance control is proposed for micro-electromechanical system (MEMS) gyros. Gyros tend to become smaller in size and more precise in structure with the development of micro-manufacturing technology. The operational security for MEMS gyros in cases of disturbances and parameter uncertainties becomes a challenging problem that has attracted much attention. The proposed method incorporates a prescribed performance technique to accomplish a bounded (within 10% of the vibration amplitude) gyro trajectory tracking error dynamic to secure the gyro’s operation. Meanwhile, fractional calculus is integrated into the controller’s design to provide precise adjustments to the gyro’s motion and thus further improve gyro control performance (shortening error convergence time by 20%). Furthermore, to enlarge the application scope and to improve gyro system robustness, a modified neural network estimator with a constrained input mapping mechanism is proposed to approximate unknown time-varying angular-velocity-related gyro dynamics. Notably, the constrained input mapping mechanism can help guide neural parameter initialization to avoid a time-consuming parameter adjustment process. The stability of the closed-loop gyro control system is proved in the framework of Lyapunov stability theory, and comparisons of simulation results are presented to demonstrate the effectiveness of the proposed method.