Asymptotic Stability Research Articles

Reinforcement learning-adaptive fault-tolerant IGC method for a class of aircraft with non-affine characteristics and multiple uncertainties

Abstract In this paper, a brand-new adaptive fault-tolerant non-affine integrated guidance and control method based on reinforcement learning is proposed for a class of skid-to-turn (STT) missile. Firstly, considering the non-affine characteristics of the missile, a new non-affine integrated guidance and control (NAIGC) design model is constructed. For the NAIGC system, an adaptive expansion integral system is introduced to address the issue of challenging control brought on by the non-affine form of the control signal. Subsequently, the hyperbolic tangent function and adaptive boundary estimation are utilised to lessen the jitter due to disturbances in the control system and the deviation caused by actuator failures while taking into account the uncertainty in the NAIGC system. Importantly, actor-critic is introduced into the control framework, where the actor network aims to deal with the multiple uncertainties of the subsystem and generate the control input based on the critic results. Eventually, not only is the stability of the NAIGC closed-loop system demonstrated using Lyapunov theory, but also the validity and superiority of the method are verified by numerical simulations.

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 integral robust control method (AIRC-AD) 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 step target signals, sinusoidal target signals and triangular wave target signals, AIRC-AD 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-AD has better adaptability. The unit and the method can meet the demand for precise braking force control in high-level autonomous driving.

Research on Voltage Prediction Using LSTM Neural Networks and Dynamic Voltage Restorers Based on Novel Sliding Mode Variable Structure Control

To address the issue of uncertainty in the occurrence time of voltage sags in power grids, which affects power quality, a voltage state prediction method based on LSTM neural networks is proposed for predicting voltage states. For the problem of quickly and accurately compensating for voltage sags, a DVR system based on a new approach law of sliding mode variable structure control is proposed, which significantly reduces chattering, improves response speed, and enhances the robustness of the system. The stability of the system is proven based on Lyapunov stability theory. Simulation experiments are conducted to analyze the voltage state prediction effect based on the LSTM neural network and the compensation effect of the novel reaching law of sliding mode variable structure control under different levels of voltage sag, validating the effectiveness and correctness of the proposed solution.

AQUILA OPTIMIZED NONLINEAR CONTROL FOR DC-DC BOOST CONVERTER WITH CONSTANT POWER LOAD

Constant power loads (CPL) can be operated by tight-controlled power electronic converters, which have negative impedance and absorb continuous power. Constant power load creates instability in an open-loop system because of its negative incremental impedance. To tackle this problem, a discrete sliding-mode (AQO-DSM) nonlinear control technique has been proposed for a DC-DC boost converter fed CPL based on Aquila optimization. In this paper, the proposed AQO-DSM controllers provide the system stability during a steady state and maintain output voltage regardless of input voltage or CPL variations. In this case, the DSM controller of a DC-DC boost converter's characteristics are adjusted using the Aquila optimization method (AQO). The Lyapunov stability concept is utilized to assess the system's overall stability. Under various system operating conditions, an experimental study and simulation are carried out to validate the proposed controller. The existing methods, such as sliding mode controller (SMC), fuzzy-based SMC (F-SMC), and super twisting algorithm (STA)-based SMC strategies, are compared with a proposed plan to demonstrate the superiority of the proposed AQO-DSMC. Simulated and experimental results have shown that the AQO-DSMC achieves the fastest convergence, the smallest steady-state, settling time under loaded conditions, and consistent chatter reduction compared with all contrasted control methods.

Analysis of stochastic epidemic model with awareness decay and heterogeneous individuals on multi-weighted networks.

In the current study, we present a stochastic SAIS (unaware susceptible-aware susceptible-infectious-unaware susceptible) epidemic dynamic model on complex networks with multi-weights. The disease dynamic is influenced by random perturbations to the force of the infection rates, as well as awareness rates. To analyze the problem of extinction, we discuss both the stochastic asymptotic stability in the large and almost surely exponential stability of the trivial solution. Then, we get some sufficient conditions, which guarantee the stochastic persistence of infectious disease. Based on the Erdös-Réyni random graph, the numerical simulations are given. These not only validate our conclusions but also obtain else significative results. Both theoretical results and numerical simulations further reflect that improvement of risk awareness and reduction of decay in awareness are highly effective in preventing disease spread. And then, environmental noises play a significant role in disease transmission.

Intelligent sliding mode fault-tolerant control for aircraft engines with actuator dynamics and faults based on adaptive dynamic programming

Abstract The fault-tolerant control issue of aircraft engines with actuator dynamics and faults is investigated in this paper. By proposing a novel intelligent sliding mode fault-tolerant control (ISMFTC) method, which combines an adaptive dynamic programming (ADP) sliding surface with Grey Wolf Optimizer (GWO) for controller parameter optimisation, the goal is to achieve quality steady-state and dynamic performance in aircraft engines while maintaining strong fault-tolerance properties. Firstly, by considering not only actuator dynamics but also actuator faults, an uncertain nonlinear cascaded model of aircraft engines is developed according to characteristic of aircraft engines and their actuators. Secondly, an ADP-based sliding surface is proposed for considered aircraft engine uncertain nonlinear cascaded system. It can obtain a certain sense of optimised performance, and could be solved by ADP strategy off-line as well. Thirdly, fault-tolerant controller is obtained on the basis of sliding mode theory and adaptive fault estimation law, namely, ADP-based ISMFTC controller. Meanwhile, GWO is integrated into the investigation of ADP-based ISMFTC controller, optimised designable control parameters are obtained subsequently. Besides, robustness analysis is elaborated according to Lyapunov theory, fault estimation error is bounded and states of closed-loop system are uniformly ultimately bounded. Simulation on a twin-shaft turbofan aircraft engine, indicates the effect of proposed ADP-based ISMFTC method.

Comparative analysis of two novel chaotic systems, and validation of hybrid function projective and complete synchronization using active-adaptive control

Abstract This study investigates the nonlinear characteristics of two novel 3D-chaotic models using phase portraits, bifurcation diagrams, Lyapunov exponents, time series analysis, and Poincaré maps. Here, we have examined hybrid-function projective and complete synchronization schemes via adaptive and active control methods. Moreover, the performance of hybrid-function projective synchronization, utilizing sine, cosine, and exponential terms, is compared to complete synchronization through two control strategies. Our designed controllers ensure asymptotic global chaotic synchronization based on Lyapunov stability principles. We have also compared our results with other competitive schemes and validated the theoretical findings through simulations on the MATLAB platform.

Adaptive Integral Sliding Mode Control with Chattering Elimination Considering the Actuator Faults and External Disturbances for Trajectory Tracking of 4Y Octocopter Aircraft

This paper presents a control strategy for a 4Y octocopter aircraft that is influenced by multiple actuator faults and external disturbances. The approach relies on a disturbance observer, adaptive type-2 fuzzy sliding mode control scheme, and type-1 fuzzy inference system. The proposed control approach is distinct from other tactics for controlling unmanned aerial vehicles because it can simultaneously compensate for actuator faults and external disturbances. The suggested control technique incorporates adaptive control parameters in both continuous and discontinuous control components. This enables the production of appropriate control signals to manage actuator faults and parametric uncertainties without relying only on the robust discontinuous control approach of sliding mode control. Additionally, a type-1 fuzzy logic system is used to build a fuzzy hitting control law to eliminate the occurrence of chattering phenomena on the integral sliding mode control. In addition, in order to keep the discontinuous control gain in sliding mode control at a small value, a nonlinear disturbance observer is constructed and integrated to mitigate the influence of external disturbances. Moreover, stability analysis of the proposed control method using Lyapunov theory showcases its potential to uphold system tracking performance and minimize tracking errors under specified conditions. The simulation results demonstrate that the proposed control strategy can significantly reduce the chattering effect and provide accurate trajectory tracking in the presence of actuator faults. Furthermore, the efficacy of the recommended control strategy is shown by comparative simulation results of 4Y octocopter under different failing and uncertain settings.

Consensus analysis for heterogeneous multiagent systems subject to input saturation

AbstractThis paper investigates the consensus problem of heterogeneous multiagent systems (HMASs) consisting of first‐order and second‐order agents, where second‐order linear and second‐order nonlinear agents are included in the second‐order agents. Firstly, the consensus problem of HMASs without input saturation is studied in the first part. However, in practical applications, due to the physical limitations of actuators, saturation often occurs. Therefore, we focus on the consensus problem of HMASs with input saturation in the second part. Then based on the knowledge of Lyapunov stability theory and graph theory, it gives sufficient conditions for these HMASs to reach consensus, which ensures that each agent eventually reaches consensus. Eventually, the effectiveness of the theory is verified by performing simulations.

Partial state-constrained integrated guidance and control for an STT missile with self-adjusting prescribed performance via non-barrier Lyapunov function method

A state-constrained guidance and control law is vital to the flight safety of an aerial interceptor against a maneuvering target. Taking the flight angle limitations, manipulation saturation, and terminal constraints into consideration, a novel integrated guidance and control (IGC) schema with a self-adjusting prescribed performance is proposed. To avoid the feasibility condition via the conventional barrier Lyapunov function-based method, a new state-dependent nonlinear mapping function is designed, based on which the state-constrained IGC system is converted into a constrained-free model. A novel prescribed performance with a self-tuning mechanism is proposed to guarantee satisfied transit and steady guidance performances. The backstepping technique combined with super-twisting integral sliding modes and newly defined predefined-time disturbance observers is implemented to generate state-constrained virtual command signals. All the signals in the closed-loop system are strictly proven to be bounded by Lyapunov stability theory. The simulation results show the effectiveness of the proposed IGC schema.

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.

Distributed Neuroadaptive Formation Control for Aerial Base Station-Assisted Hovercraft Systems with Mixed Disturbances

Effectively addressing the formation control of ABS-assisted hovercraft systems with heterogeneities, unavailable leaders’ convex combination states, nonlinearities, and mixed disturbances poses significant challenges. This paper proposes a distributed neuroadaptive formation tracking strategy of ABS-assisted hovercraft systems for the first time, where aerial base stations (ABSs) are composed of unmanned aerial vehicles (UAVs) for data distribution and computation offloading. Firstly, UAVs are designed to track the virtual-leader while shaping a fixed formation, and the observer is devised for each follower hovercraft to estimate the convex combination states of UAVs. Then, output regulation equations are employed to transform heterogeneous systems into a compact form via the Kronecker product, while neural networks (NNs) are introduced to compensate for model nonlinearities. Furthermore, based on random differential equations (RDEs) combined with Lyapunov theory, the noise-to-state practical stability in probability (NSPS-P) property of the error dynamics under mixed disturbances can be obtained. Finally, simulation examples demonstrate that the outputs of follower hovercrafts rapidly achieve a time-varying formation and rotate around convex combination states of leader UAVs simultaneously.

Towards Sustainable Transportation: Adaptive Trajectory Tracking Control Strategies of a Four-Wheel-Steering Autonomous Vehicle for Improved Stability and Efficacy

The objective of continuous increase in the evolution of autonomous and intelligent vehicles is to attain a trustworthy, economical, and safe transportation system. Four-wheel steering (4WS) vehicles are favored over traditional front-wheel steering (FWS) vehicles because they have excellent dynamic characteristics. This paper exhibits the trajectory tracking task of a two degree of freedom (2DOF) underactuated 4WS Autonomous Vehicle (AV). Because the system is underactuated, MIMO, and has a nontriangular form, the traditional adaptive backstepping control scheme cannot be utilized to control it. For the purpose of rectifying this issue, two-state feedback-based methods grounded on the hierarchical steps of the block backstepping controller are proposed and compared in this paper. In the first strategy, a modified block backstepping is applied for the entire dynamic system. Global stability of the overall system is manifested by Lyapunov theory and Barbalat’s Lemma. In the second strategy, a block backstepping controller has been applied after a reduction of the high-order model into various first-order subsystems, consisting of Lyapunov-based design and stability warranty. A trajectory tracking controller that can follow a double lane change path with high accuracy is designed, and then simulation experiments of the CarSim/Simulink connection are carried out against various vehicle longitudinal speeds and road surface roughness to demonstrate the effectiveness of the presented controllers. Furthermore, a PID driver model is introduced for comparison with the two proposed controllers. Simulation outcomes show that the proposed controllers can attain good response implementation and enhance the 4WS AV performance and stability. Indeed, enhancement of the stability and efficacy of 4WS autonomous vehicles would afford a sustainable transportation system by lessening fuel consumption and gas emissions.

Fractional‐order fast terminal sliding mode trajectory tracking control of quadrotor UAV based on finite time disturbance observer

AbstractIn this paper, a novel trajectory tracking control problem of the quadrotor UAV is addressed, which considers the system uncertainties and unknown external disturbances meanwhile. To ensure a rapid convergence rate of the states, fast terminal sliding mode control (FTSMC) algorithm is improved combining with a fractional order method. In addition, finite‐time observer is designed to handle disturbances and enhance the robustness of the system. The closed‐loop finite‐time stability of the quadrotor UAV system is established using Lyapunov theory in accordance with the novel control law. To evaluate the effectiveness of our proposed strategy, various simulations under different scenarios are conducted respectively. These simulation results clearly demonstrate the superiority of our control scheme, which we refer to as fractional‐order fast terminal sliding mode control (FOFTSMC).

Observer based finite-time adaptive fractional-order sliding mode control of DFIG wind turbines with unknown dynamic parameters

In this study, we investigate adaptive finite-time fractional-order sliding mode control (AFFSMC) of DFIG wind turbines (DWTs) under model uncertainty in finite time. A fractional-order sliding surface is first constructed to develop the concept. A robust terminal adaptive sliding mode controller is then designed for pitch angle control of wind turbine to achieve finite-time stability at high wind speeds to regulate the produced electric power in Zone III of the turbine’s working range. This is all with this assumption that there is no any information about the dynamics of the turbine due to the significant uncertainties. Through the use of a stable adaptive law, the vector of the wind turbine’s unknown dynamic parameters is approximated in this method. An observer is also proposed to estimate both turbine speed and external disturbances term. The closed-loop system’s finite-time stability study and the finite-time convergence of the turbine output were both carried out using the dynamic model of the system and the proposed Lyapunov theory. Some numerical examples are also presented together with a comparison to the standard integer sliding mode control to demonstrate the correctness of the control law.