Asymptotic Stability Research Articles

Adaptive fault-tolerant containment control for heterogeneous uncertain nonlinear multi-agent systems under actuator faults

As modern control systems involve a growing number of actuators, the consequent number of faults occurrence, which may deteriorate the closed-loop system performance, is increasing. Focusing on the containment control problem of generic nonlinear high-order heterogeneous uncertain Multi-Agent Systems, this study proposes a novel distributed adaptive fault-tolerant Proportional-Integral-Derivative control protocol to improve the reliability and the resilience of the whole networked systems against actuator failures. The Lyapunov theory, combined with the Barbalat lemma, provides the design of suitable adaptive mechanisms that adjust the PID control actions to ensure the asymptotic convergence of the closed-loop containment errors for the overall network, hence implying the convergence of each agent state toward the convex region shaped by the multiple leaders, despite the occurrence of actuators faults. The fulfillment of the fault-tolerant containment objective is ensured by requiring a lower computational burden with respect to alternative solutions, hence resulting in more attractive for wider practical engineering applications. Numerical simulation results, also including a comparison analysis with a state-of-the-art controller, corroborate the efficiency and the advantages of the proposed distributed PID controller.

Adaptive finite-time consensus tracking for nonlinear second-order multi-agent systems based on integral sliding mode

This paper delves into the investigation of finite-time consensus for second-order nonlinear multi-agent systems (MASs) with external disturbances under directed topology. The MASs considered in this study consist of n followers and a leader, all of which are subject to bounded disturbances. First, a continuous nonsingular integral terminal sliding mode is designed, which can effectively eliminate the singularity and chattering. Then, a finite-time disturbance observer is introduced to estimate and compensate for disturbances. Subsequently, an integral sliding mode adaptive controller is designed to enhance system’s robustness, improve response speed, and increase tracking accuracy. Furthermore, Lyapunov theory is utilized to demonstrate that the system achieves finite-time consensus under a directed connected topology. Finally, we apply a simulation to verify the efficacy of the proposed consensus control protocol.

Local set stability and target control of probabilistic Boolean networks

This paper analyzes the local set stability of probabilistic Boolean networks (PBNs), including local finite-time set stability with probability one (FSSPO) and local asymptotic set stability with probability one (ASSPO). Firstly, a necessary and sufficient condition is proposed for the local FSSPO of PBNs. Then, a reachable set with probability one is constructed, based on which, the largest domain of attraction for the local FSSPO of PBNs is determined. Secondly, by constructing two parameterized sets, the transition probability matrix of PBNs is properly partitioned, and the largest domain of attraction for the ASSPO is depicted. Finally, for PBNs which are locally stable, the target control is introduced to achieve the global FSSPO and global ASSPO of PBNs, respectively.

Robust bilinear tracking control of a parabolic trough solar collector via saturation

This paper investigates the problem of robust tracking control of heat transport in a Parabolic Trough Solar Collector (PTSC), where the output has to track a desired reference trajectory. In this work, the PTSC is modeled by state-space bilinear dynamics. The manipulated variable is the pump volumetric flow rate, and the source term, i.e., solar irradiance, is assumed to be unmeasured. In addition, the actuator’s physical constraints induce saturation bounds on the manipulated variable and need to be considered explicitly in the controller design. To deal with these challenges, we first propose a saturated state-feedback law that meets the control objectives. Then, we reconstruct the unknown time-varying source term using an adaptive estimator. Later, through Lyapunov stability analysis, we prove that the closed-loop system and the output tracking error are uniformly ultimately stable. Numerical simulations attest to the performance of the proposed control strategy.

General Lyapunov Stability and its Application to Time-Varying Convex Optimization

General Lyapunov Stability and its Application to Time-Varying Convex Optimization

Distributed Nash equilibrium seeking for quadratic games in discrete-time systems with bounded control inputs

This paper considers the distributed Nash equilibrium seeking problem for quadratic games in discrete-time systems with bounded control inputs. First, a saturation gradient algorithm is proposed to seek the Nash equilibrium without considering the limitations of communication. Then the case that players can only communicate with their neighbors is considered, a distributed Nash equilibrium seeking algorithm is designed where a consensus protocol is adapted for information sharing. In the proposed distributed algorithm, each player has an estimate on others’ actions and the consensus of players’ estimates is achieved. By Lyapunov stability theory for discrete-time systems, it is shown that the Nash equilibrium of the game is globally asymptotically stable under certain conditions. Moreover, distributed Nash equilibrium seeking problem in hybrid systems with bounded control inputs is solved. Finally, two numerical examples are presented to verify the effectiveness of the proposed algorithms.

Boundedness and asymptotic stability of solutions in an alopecia areata chemotaxis system with signal-dependent sensitivity

Boundedness and asymptotic stability of solutions in an alopecia areata chemotaxis system with signal-dependent sensitivity

Consensus-Based Power System State Estimation Algorithm Under Collaborative Attack

Due to its vulnerability to a variety of cyber attacks, research on cyber security for power systems has become especially crucial. In order to maintain the safe and stable operation of power systems, it is worthwhile to gain insight into the complex characteristics and behaviors of cyber attacks from the attacker’s perspective. The consensus-based distributed state estimation problem is investigated for power systems subject to collaborative attacks. In order to describe such attack behaviors, the denial of service (DoS) attack model for hybrid remote terminal unit (RTU) and phasor measurement unit (PMU) measurements, and the false data injection (FDI) attack model for neighboring estimation information, are constructed. By integrating these two types of attack models, a different consensus-based distributed estimator is designed to accurately estimate the state of the power system under collaborative attacks. Then, through Lyapunov stability analysis theory, a sufficient condition is provided to ensure that the proposed distributed estimator is stable, and a suitable consensus gain matrix is devised. Finally, to confirm the viability and efficacy of the suggested algorithm, a simulation experiment on an IEEE benchmark 14-bus power system is carried out.

Nonlinear Adaptive Neural Control of Power Converter‐Driven DC Motor System: Design and Experimental Validation

ABSTRACTThis article presents an intelligent adaptive neural control scheme to track the output speed trajectory in power converter‐driven DC motor system. The proposed technique integrates an adaptive polynomial‐neural network with a backstepping strategy to yield a robust control system for output tracking in DC motor. Such a unification of online neural network‐based estimation and adaptive control, results in effective regulation of the output across a wide load torque uncertainties, besides yielding a promising transient and steady‐state performance. The stability of the entire closed‐loop system is ensured through Lyapunov stability criterion. The efficacy of the proposed strategy is revealed through an extensive experimental investigation under various operating points during start‐up, step‐reference tracking, and external step‐load torque disturbances. The real‐time experimentation is conducted on a laboratory prototype of power converter‐driven DC motor of 200 W, using dspace DS1104 control board with MPC8240 processor. The results obtained confirm an improvement in the transient response of the output speed by significantly reducing the settling time to and yielding a steady state behavior with no peak over/undershoots during load disturbances, in contrast to other similar works presented in the literature intended for same the application.

Discrete‐time full‐order sensorless control of high‐speed interior permanent magnet synchronous motor in electric vehicle traction system

AbstractA discrete‐time full‐order sensorless control strategy for high‐speed interior permanent magnet synchronous motor (IPMSM) used in electric vehicle (EV) traction system is designed in this paper. While most speed and position observer (SPO) methods are developed in the continuous‐time domain, the presence of a unit‐time‐delay block existed in feedback loop and discretisation of the algorithm can lead to performance degradation during digital implementation. In this work, speed and angle are observed using the discrete‐time four‐order IPMSM model. A quadrature phase‐locked loop model with compensation is introduced, and its stability condition is established for the first time. Furthermore, to address the potential for sudden speed changes in vehicle applications, the parameter range is further refined to keep the estimation error within a specified range. The sliding mode observer is discretised and its stability is analysed using discrete Lyapunov theory. Additionally, the time sequence of interactive signals between SPO and field‐oriented control is thoroughly examined to ensure accurate time cycle. Finally, the proposed control strategy is validated and demonstrated through bench tests and real EV (LS6 of IM Motors) tests with a 190 kW IPMSM, which can improve the accuracy by 0.3 radians at 8000 rpm compared to traditional methods, and achieve stable control at 15,000 rpm on the test bench and at 120 kph with the EV.

Dynamics and event-triggered control of rumor propagation model with saturated incidence and time delay on heterogeneous networks

Considering the impact of user’s cognitive ability in rumor propagation, this paper proposes a new susceptible infection recovery (2SIR) rumor propagation model with saturation incidence and time delay on heterogeneous networks. First, the existence of the equilibria is discussed by using mean field theory and basic reproduction number. Second, the dynamic behaviors of the rumor-free and persistent equilibria are analyzed via the local linearization method, Lyapunov stability theory and irreducible matrix properties. Furthermore, an event-triggered impulsive control strategy is proposed to control the rumor spreaders and some corresponding control conditions are given. Finally, some numerical simulation results and a practical example are presented to verify the correctness of the theoretical results and reflect the impact of cognitive ability and time delay on rumor propagation.

Distributed Improved RILOS Guidance-Based Formation Control of Underactuated ASVs for Cooperative Maritime Search

A distributed improved robust integral line-of-sight (RILOS) guidance-based sliding mode controller is designed for multiple underactuated autonomous surface vessels (ASVs) to perform cooperative maritime search operations. First, a parallel circle search pattern is designed based on the detection range of ASVs, which can provide the reference formation shape. Second, an improved RILOS method is presented by introducing an integral term into the improved robust LOS method, which can counteract the disadvantageous effect of the unknown sideslip angle and kinematic discrepancy simultaneously. Third, distributed improved RILOS guidance is presented by integrating the extended second-order consensus algorithm into the improved RILOS method; then, the desired heading angle and desired velocity are generated for the control system simultaneously. Finally, the fuzzy logic system is integrated into the sliding mode control (SMC) method to approximate the unknown nonlinear function; then, a distributed improved RILOS guidance-based SMC controller is presented for multiple ASVs. The close-loop signals are proved to be stable by the Lyapunov theory. The effectiveness of the presented method is verified by multiple simulations.

Improved FPTPPF-based predefined-time tracking control of a UVMS with actuator faults

In this paper, a new predefined-time control scheme is proposed for the trajectory tracking problem of an underwater vehicle-mechanic system (UVMS) with external disturbances, model uncertainties and actuator faults. First, a predefined-time controller is proposed to achieve convergence in a predefined time so that the convergence time does not depend on the initial value of the system. Second, considering the possible grasping and transportation tasks for the UVMS, an improved flexible predefined-time prescribed performance function (FPTPPF) with self-adjustment capability is proposed to avoid the vulnerabilities of the existing prescribed performance functions. A control framework is constructed for the integral barrier Lyapunov function and FPTPPF, which can achieve good tracking performance. Third, a predefined-time extended state observer (ESO) is constructed to address the problems caused by external disturbances, model uncertainties and actuator faults. For strong sudden disturbances, the H∞ control strategy is designed via the backstepping method, which effectively improves the robustness. Finally, the predefined-time stability of the system is proven via Lyapunov stability theory, where the tracking errors can converge to a small region of the null domain in a predefined time. The performance and superiority of the proposed predefined-time control method are verified via simulation comparisons.

Optimal Energy Management Systems and Voltage Stabilization of Renewable Energy Networks

This paper addresses the challenge of integrating multiple energy sources into a single-domain microgrid, commonly found in urban buildings, while also providing a platform for energy management. A Lyapunov stability analysis of a simple boost converter was used as a basis for designing the dual control loop of the grid. The versatility of the developed control structure allows for the incorporation of an arbitrary number of sources hence achieving scalability. Next, the energy in the microgrid was separated into exogenous energy and actuator energy. This yielded a description of the system that quantified the condition of stability independent of the decision made by a would-be energy management system. This, in turns, liberates the process of designing an optimized energy management system from stability concerns. The acquired theoretical findings were then translated to a simulation model, where multiple components of the grid were simulated under a typical scenario of operation. Once the simulation phase was concluded, a prototype of the designed grid was constructed to emulate the theoretical results. The prototype exhibited promising performance, matching the simulation predictions to a reasonable degree.

Fault-tolerant control of nonlinear networked control systems based on a dynamic event-triggered mechanism under dual cyber attacks

In this paper, the fault-tolerant control problem of actuator failures for nonlinear networked control systems under deception attacks and denial-of-service attacks is investigated based on a dynamic event-triggered mechanism. Firstly, denial-of-service attacks and deception attacks are modeled as two independent variables that conform to the Bernoulli probability distribution, and the fault-tolerant control problem of nonlinear networked control systems is considered under the possible actuator failures. Then, an appropriate Lyapunov-Krasovskii functional is constructed, and sufficient conditions for ensuring asymptotic stability of the closed-loop systems are obtained using Jensen inequality. Meanwhile, the designed fault-tolerant controller can handle possible actuator failures. Finally, the effectiveness of the proposed method is proved through an example.

Design of sliding mode controller for servo feed system based on generalized extended state observer with reinforcement learning

Nonlinear friction, system uncertainty, and external disturbances have a significant impact on the performance of high-precision servo feed systems. In order to achieve higher tracking accuracy, a sliding mode controller based on a generalized extended state observer with the double critic deep deterministic policy gradient algorithm is designed. Firstly, a flexible two mass drive model (FTMDM) is established for the two-axis differential micro-feed system (TDMS). Next, a generalized extended state observer (GESO) is designed to estimate matched interference and mismatched interference. And it is proved that the observation error of GESO is bounded. A sliding mode controller based on GESO is further proposed. The stability of the controller has been proven through Lyapunov theory, and the error is bounded and converges to zero in finite time. The tuning process of controller parameters is simplified by using quadratic optimal control principle. Furthermore, a double critic deep deterministic policy gradient algorithm (DCDDPG) is proposed to achieve dynamic optimization of parameters about GESO. The simulation results show that GESO with DCDDPG can reduce the observation error of step signal and sinusoidal signal, and improve the observation accuracy of nonlinear friction significantly. Finally, experimental results show that the proposed control method achieves more accurate position tracking performance on TDMS.

Improved adaptive robust control of Direct-Drive Pump-Valve cooperative Brake-by-wire unit with disturbance compensation

Abstract Aiming at the needs of high-level autonomous driving, a direct-drive pump-valve coordinated brake-by-wire unit was designed. To improve the response speed, control accuracy, and robustness of the brake-by-wire unit, an improved adaptive robust control method (AIRC-AF) based on a novel adaptive law and disturbance compensation was proposed. By integrating pressure tracking error information and overall parameter estimation error information, a novel parameter adaptive law with fast convergence speed was designed. A finite-time disturbance observer was designed to observe the overall system disturbance, improving the system's anti-disturbance performance. Finally, the stability of the control method was proven using the Lyapunov stability proof method. The results show that under sinusoidal target signals and triangular wave target signals, AIRC-AF has better response speed and control accuracy. In conditions such as increased permanent magnet temperature, increased coil resistance, or reduced flow area due to hydraulic pipeline blockage, AIRC-AF has better adaptability. The unit and the method can meet the demand for precise braking force control in high-level autonomous driving.

An adaptive dynamic surface control strategy for suppressing pathological oscillations in a neural mass model

Pathological oscillations that have a frequency in the [Formula: see text] band are widely recognized to be involved in Parkinson’s disease. Now, we present an adaptive dynamic surface control strategy for suppressing pathological oscillations that exist in the Parkinsonian state. First, the interactions between the subthalamic nucleus and external globus pallidus are fully considered and establish a neural mass model of Parkinson’s disease. Next, by reasonable state transformation, suppressing pathological oscillations can be converted into a tracking control study of a pure-feedback nonlinear system. Moreover, the dynamic surface control technique adopted reduces the dimensionality of the neural network input and effectively eliminates the complexity explosion problem commonly associated with existing methods. By Lyapunov stability analysis, it can be obtained that all the signals of the resulting closed-loop system are bounded, and the tracking error converges to a small neighborhood of zero. Finally, the simulation results demonstrate the effectiveness of the designed control strategy. This work may provide an effective approach to closed-loop deep brain stimulation optimization for the alleviation of the Parkinsonian state.

Dual-Arm Space Robot On-Orbit Operation of Auxiliary Docking Prescribed Performance Impedance Control

The impedance control of a dual-arm space robot in orbit auxiliary docking operation is studied. First, for the closed-chain hybrid system formed by the dual-arm space robot after capture operation, the dynamic equation of position uncontrolled and attitude controlled is established. The second-order linear impedance model and second-order approximate environment model are established for the problem of simultaneous output force/pose control of the end of the manipulator. Then, aiming at the transient performance control requirements of the dual-arm space robot auxiliary docking operation in orbit, a sliding mode controller with equivalent replacement of tracking errors is designed by introducing Prescribed Performance Control (PPC) theory. Next, Radial Basis Function Neural Networks (RBFNN) are used to accurately compensate for the modeling uncertainties of the system. Finally, the stability of the system is verified by Lyapunov stability determination. The simulation results show that the attitude control accuracy is better than 0.5°, the position control accuracy is better than 10−3 m, and the output force control accuracy is better than 0.5 N when it reaches 30 N. It also indicated that the proposed control algorithm can limit the transient performance of the controlled system within the preset range and achieve high-precision force/pose control, which ensures a more stable on-orbit auxiliary docking operation of the dual-arm space robot.

Enhanced composite controller for PV/PMSG/PEMFC and BESS‐based DC microgrids voltage regulation: Integrating integral terminal sliding mode controller and recursive backstepping controller

AbstractThe variability of renewable energy sources due to weather patterns often leads to a mismatch between power generation and consumption within microgrids (MGs). This challenge is exacerbated when integrating bio‐renewable units, complicating stability maintenance in MGs. This research work introduces a novel solution to address this issue: a composite controller merging an integral terminal sliding mode controller with a recursive backstepping controller for direct current MGs (DCMGs). The proposed DCMG incorporates solar photovoltaic units, wind farms based on permanent magnet synchronous generators, proton exchange membrane fuel cells fuelled by hydrogen gas, an electrolyser, battery energy storage systems, and DC loads. First, a comprehensive mathematical model for the components within the DCMG is developed to design the proposed composite controller. This controller not only overcomes the inherent limitations and convergence issues of conventional SMCs but also ensures stable DC‐bus voltage and maintains power balance across various operational conditions. Moreover, a fuzzy logic‐based energy management system is introduced to regulate power flow, considering factors like battery state of charge and renewable energy sources' total power output. The control Lyapunov function confirms the DCMG system's asymptotic stability. Finally, the proposed controller's effectiveness is validated through simulations on both MATLAB/Simulink and Arduino Mega 2650 processor‐in‐the‐loop platforms under various operational conditions. In both platforms, the proposed controller surpasses an existing controller in terms of settling time, overshoot, and tracking error of the DC‐bus voltage.