Adaptive Law Research Articles

An Improved Adaptive Sliding Mode Control Approach for Anti-Slip Regulation of Electric Vehicles Based on Optimal Slip Ratio

To optimize the acceleration performance of independently driven electric vehicles with four in-wheel motors, this paper proposes an anti-slip regulation (ASR) strategy based on dynamic road surface observer for more efficient tracking of the optimal slip ratio and enhanced vehicle acceleration. The method uses the Unscented Kalman Filter (UKF) observer to estimate vehicle speed and calculate the actual slip ratio, while a fuzzy controller based on the Burckhardt tire model identifies road surfaces. The road’s peak adhesion coefficient and optimal slip ratio curve are fitted using a Back Propagation Neural Network (BPNN) optimized by Particle Swarm Optimization (PSO). The control strategy further refines torque management through an adaptive sliding mode control (ASMC) that integrates adaptive laws and a super-twisting sliding mode approach to track the optimal slip ratio. Joint simulations with MATLAB/Simulink and Carsim on low-adhesion, joint, and split road surfaces demonstrate that the strategy quickly and accurately identifies the optimal slip ratio across various road surfaces. This enables the tire slip ratio to approach the optimal value in minimal time, significantly improving vehicle dynamic performance. Compared to conventional sliding mode controllers, the optimized ASMC reduces chattering and improves control precision.

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.

Sliding Mode Fault-Tolerant Control for Nonlinear LPV Systems with Variable Time-Delay

This paper presents a robust sliding mode fault-tolerant control (FTC) strategy for a class of linear parameter variant (LPV) systems with variable time-delays and uncertainties. First fault estimation (FE) is conducted using a robust sliding mode observer, synthesized to simultaneously estimate the states and actuator faults of LPV polytopic delayed systems. Second, a sliding mode FTC is developed, ensuring all states of the closed-loop system converge to the origin. This paper presents an integrated sliding mode FTC strategy to achieve optimal robustness between the observer and controller models. The integrated design approach offers several advantages over traditional separated FTC methods. Our novel approach is based on incorporating adaptive law into the design of the Lyapunov–Krasovskii functional to improve both robustness and performance. This is achieved by combining the concept of sliding mode control (SMC) with the Lyapunov–Krasovskii function under the H∞ criteria, which plays a key role in guaranteeing the stability of this class of system. The effectiveness of the proposed method is demonstrated through a diesel engine example, which highlights the validity and benefits of the integrated and separated FTC strategy for uncertain nonlinear systems with time delays and the sliding mode control.

Adaptive Sliding Mode Control for Trajectory Tracking of Quadrotor Unmanned Aerial Vehicles Under Input Saturation and Disturbances

This paper addresses the challenging issue of trajectory tracking for uncertain quadrotor unmanned aerial vehicles (UAVs), particularly under the constraints of input saturation and external disturbances. It introduces adaptive laws for managing uncertainties in mass and inertia moments without requiring prior knowledge, ensuring effective control even with varying system parameters. To counteract the effects of input saturation, the study incorporates an auxiliary system designed to compensate for these limitations. Additionally, a disturbance observer (DO) is utilized to manage and mitigate the impact of time-varying external disturbances. The proposed control strategy integrates a sliding mode adaptive control approach with an inner–outer loop structure, enhancing robustness and adaptability. Numerical simulations demonstrate the effectiveness of the designed control strategy.

Distributed Neural Adaptive Impedance Control for Cooperative Manipulation With Unknown Objects.

Existing cooperative manipulation methods for multiple manipulator systems usually assume that the grasp matrix and the desired trajectory of each manipulator are known in advance. In this work, distributed neural adaptive impedance control (AIC) strategies integrating fully distributed observers are proposed to remove both limitations. Specifically, two fully distributed finite-time observers are designed to estimate the actual and ideal states of the reference point without using global information. The estimates of the grasp matrix and the desired trajectory of each end-effector (EE) are then obtained by kinematic constraints and the estimates of the reference point's states. At the controller development, a distributed adaptive impedance model is established to achieve an adaptive trade-off between tracking performance and compliance. Then, distributed neural network (NN)-based tracking control strategies are developed to asymptotically realize the desired adaptive impedance dynamics in the presence of uncertainties. Additionally, a virtual energy tank (EK) is employed to interact with the impedance system to correct the adaptive impedance laws for system passivity. A simulation for four mobile manipulators tightly cooperative transport an unknown object is carried out to demonstrate the established results.

State of Charge Estimation for Lithium-Ion Battery Based on Fractional-Order Kreisselmeier-Type Adaptive Observer

For the safe and efficient use of lithium-ion batteries, the state of charge (SOC) is a particularly important state variable. In this paper, we propose a method for the online estimation of SOC and model parameters based on a fractional-order equivalent circuit model. Firstly, we constructed a fractional-order battery model that includes pseudo-capacitance and determined the values of the circuit elements offline using the least squares method from actual input–output data based on the driving profile of an automobile. Compared to the integer-order battery model, we confirmed that the proposed fractional-order battery model has higher accuracy. Secondly, we constructed a fractional-order Kreisselmeier-type adaptive observer as an observer that performs state estimation and parameter adjustment simultaneously. Applying the general adaptive law to the battery model results in a redundant design with many adjustable parameters, so we proposed an adaptive law that reduces the number of adjustable parameters without compromising the stability of the observer. The effectiveness of the proposed method was verified through numerical simulations. As a result, the high estimation accuracy and convergence of the proposed adaptive law were confirmed.

Adaptive asymptotic tracking control of constrained nonlinear MIMO systems subject to unknown hysteresis input: A novel network-based strategy

This paper presents a referential adaptive asymptotic tracking control scheme for nonlinear multi-input and multi-output (MIMO) systems with time-varying full-state constraints and unknown hysteresis input. In order to achieve good asymptotic tracking effect, a zero-limit positive continuous function is introduced into the adaptive backstepping design process while thoroughly considering the impact of disturbance-like terms on the tracking effect. Additionally, a new variable is also imported to replace the reciprocal of unknown coefficient of the Bouc–Wen hysteresis model. Then, a new adaptive law about the new variable is added by combining the positive function, which can not only lessen the impact of the unknown hysteresis input on the tracking effect, but also avoid the “singularity” problem. Aiming at the time-varying full-state constraints, a appropriate time-varying log-type barrier Lyapunov function (TLBLF) is constructed to ensure that all the states of the system are restricted within the constraint scope. Finally, a significant adaptive asymptotic tracking scheme is designed based on multi-dimensional Taylor network (MTN) approximation technology. Apart from achieving high-precision asymptotic tracking performance, the proposed scheme ensures the boundedness of all signals of the closed-loop system without violating the full-state constraints. And, three simulations are given to verify the effectiveness of the scheme.

SARIMA Model-Based Maximum Temperature Forecasting in Bangladesh: A Data-Driven Evaluation from 1981 to 2024

Bangladesh is a tropical nation where there are notable seasonal temperature changes. The Seasonal Autoregressive Integrated Moving Average (SARIMA) model is used in this study to forecast Bangladesh's maximum temperature from 2023 to 2042. The objective is to assess how rising temperatures can affect public health, energy consumption, and agriculture. Autocorrelation and partial autocorrelation analysis will be used to improve the model. Analysis was done using historical maximum temperature data spanning from 1981 to 2022. Forecasts were produced using the SARIMA model, whose parameters were chosen in accordance with plots of the autocorrelation function (ACF) and partial autocorrelation function (PACF). The model SARIMA (1,1,2)(0,0,1) is selected based on AIC. In order to account for forecast uncertainty, forecasts were created for the years 2023–2042. 95% prediction ranges were then calculated. Bangladesh's maximum temperatures are predicted by the SARIMA model to rise gradually, from roughly 33.75°C in 2023 to 34.17°C in 2042. With some degree of uncertainty, the 95% prediction intervals show a steady increasing trend between 33.53°C and 34.51°C. The anticipated increase in the highest temperatures has major consequences for Bangladesh. These results highlight how crucial it is to create adaptation plans and laws in order to lessen the effects of warming temperatures and increase resilience.

MPPT control for PMSG based wind turbine: Adaptive dynamic programming approach

This paper proposes an online adaptive dynamic programming-based controller for the variable-speed wind turbine system, ensuring it tracks the maximum power point under uncertain conditions. This control scheme is composed of two components: the adaptive optimal control component and the high-order disturbance observer-based adaptive sliding mode control component. The adaptive optimal control part is designed using the online adaptive dynamic programming technique, which is one of the algorithms of the reinforcement learning method. This control component has the role of achieving the optimal characteristics for the nonlinear system. Likewise, the high-order disturbance observer is established to estimate system uncertainties and external disturbances. These approximated disturbances are then fed to the adaptive sliding mode control component for system disturbance compensation. As a result, the system, which is affected by the unknown disturbances, achieves robust optimal performance. In addition, the convergence of the adaptive laws and the stability of the overall system are ensured through the Lyapunov theory. Finally, comparative simulations are conducted to validate the advantages of the proposed control scheme in comparison to the existing methods.

Fixed‐Time State Observer‐Based Robust Adaptive Neural Fault‐Tolerant Control for a Quadrotor Unmanned Aerial Vehicle

ABSTRACTThis paper presents a fixed‐time state observer‐based robust adaptive neural fault‐tolerant control (RANFTC) for attitude and altitude tracking and control of quadrotor unmanned aerial vehicles (UAVs), considering multiple actuator faults, parametric uncertainty, and unknown external disturbances simultaneously. A novel fixed‐time state error estimation based on sliding mode observer is designed, which is independent of initial conditions. A proportional–integral–derivative (PID) based sliding mode control (SMC) is proposed to handle actuator faults and unknown disturbances in combination with the fixed‐time observer within the fault‐tolerant control (FTC) design scheme. The radial basis function neural network (RBFNN) is employed with the controller to approximate the uncertain parameters of the system. Furthermore, two new adaptive laws are designed to estimate the sudden actuator fault and the unknown upper bound of disturbances independently. Implementing these estimation schemes avoids overestimation, enhances the robustness of the presented controller, and substantially eliminates the control chattering problem. By applying the Lyapunov stability concept, the suggested control strategy guarantees that the states of the quadrotor UAV converge to the origin in a finite time. Finally, simulation studies are conducted to demonstrate the tracking performance and highlight the effectiveness of the proposed FTC design compared to the existing FTC methods.

Thermosensitive double-membrane neurons and their network dynamics

Abstract Cell membrane of biological neurons has distinct geometric structure, and involvement of diffusive term is suitable to estimate the spatial effect of cell membrane on neural activities. The gradient field diversity between two sides of the cell membrane can be approached by using a double-layer membrane model for the neuron. Therefore, two capacitive variables and diffusive terms are used to investigate the neural activities of cell membrane, and the local kinetics is described by a functional circuit composed of two capacitors. The voltages for the two parallel capacitors describe the inner and outer membrane potentials, and the diffusive effect of ions is considered on the membrane surface. The results reveal that neural activities are relative to the capacitance ratio between the inside and outside of the membrane and diffusive coefficient. High-energy periodic external stimulation induces the target waves to spread uniformly, while low-energy chaotic stimulation results in wave fragmentation. Furthermore, when the capacitance ratio exhibits exponential growth under an adaptive control law, the resulting energy gradient within the network induces stable target waves. That is, energy distribution affects the wave propagation and pattern formation in the neuron. The result indicates that the spatial diffusive effect and capacitance diversity between outer and inner cell membranes are important for selection of firing patterns and signal processing during neural activities. This model is more suitable to estimate neural activities than using generic oscillator-like or map neurons without considering the spatial diffusive effect.

Finite-time robust control of morphing aircraft based on time-varying observer

Morphable vehicles have strong nonlinear, strong coupling and strong time-varying characteristics in the process of variation, which brings great challenges to the design of their flight control systems. To address this problem, a time-varying gain extended state observer is proposed to accurately approximate the system coupling terms. Combining adaptive backstepping control technology and finite-time control theory, a finite-time bounded robust adaptive controller is designed. By designing the barrier Lyapunov function, the actual control law and the adaptive network update law are obtained step by step, ensuring that the system command tracking error can converge to a predetermined range within a finite time. Finally, the effectiveness of the designed control system is verified by attitude control simulation. The simulation results show that the morphable vehicle can track the command signal well in the process of variation and is basically not affected by the variation rate.

Analysis of Fractional Order-Adaptive Systems Represented by Error Model 1 Using a Fractional-Order Gradient Approach

In adaptive control, error models use system output error and adaptive laws to update controller parameters for control or identification tasks. Fractional-order calculus, involving non-integer-order derivatives and integrals, is increasingly important for modeling, estimation, and control due to its ability to generalize classical methods and offer improved robustness to disturbances. This paper addresses the gap in the literature where fractional-order gradient methods have not yet been extensively applied in identification and adaptive control schemes. We introduce a fractional-order error model with fractional-order gradient (FOEM1-FG), which integrates fractional gradient operators based on the Caputo fractional derivative. By using theoretical analysis and simulations, we confirm that FOEM1-FG maintains stability and ensures bounded output errors across a variety of input signals. Notably, the fractional gradient’s performance improves as the order, β, increases with β>1, leading to faster convergence. Compared to existing integer-order methods, the proposed approach provides a more flexible and efficient solution in adaptive identification and control schemes. Our results show that FOEM1-FG offers superior stability and convergence characteristics, contributing new insights to the field of fractional calculus in adaptive systems.

Filter‐Based Average Dwell‐Time Tuning Approach for Adaptive Prescribed‐Time Tracking of Uncertain Switched Nonlinear Systems

ABSTRACTThis paper addresses neural‐network‐based adaptive prescribed‐time (PT) tracking for uncertain switched systems with unmatched nonlinearities. A continuously switched adaptive tuning mechanism for neural network learning is developed by applying the average dwell time (ADT). First, a neural‐network‐based PT tracking control design strategy using the ADT‐based adaptive tuning mechanism is established for switched nonlinear systems in strict‐feedback form. A novel adaptive dynamic surface controller is designed recursively using a practical finite‐time scaling function and continuously switched tuning parameters. The switched adaptive tuning laws for neural networks are structured to reduce the conservatism associated with common adaptive laws. Then, a filter‐based tuning approach is employed to ensure the continuity of switched adaptive parameters with ADT in the designed controller. The practical PT stability of the closed‐loop system is demonstrated based on the boundedness of the adaptive parameters. Building upon this foundation, the proposed PT design approach is extended to control switched pure‐feedback nonlinear systems, even in cases where control directions are unspecified. The unknown sign problem encountered with switched virtual and actual control coefficient functions is resolved in the PT control framework. It is shown that the PT performance bound of the tracking error can be reduced by selecting the design parameter of the scaling function. Finally, simulation results illustrate the merits of the proposed theoretical approach.

Adaptive vibration control for stabilisation of the Euler–Bernoulli beam with an unknown payload

In this paper, an adaptive boundary controller is designed to solve the boundary control problem of Euler–Bernoulli beams with an unknown payload. Therefore, a boundary controller with an adaptive law is designed to compensate for the parameter uncertainty of the system. Partial Differential Equations (PDEs) are used to describe the Euler–Bernoulli beam system. The well-posedness of the system under the action of an adaptive boundary controller is proved by using the linear operator semigroup method. Meanwhile, the asymptotic stability of the closed-loop system is derived from the extended Krasovskii–LaSalle invariance principle. The effectiveness and superiority of the proposed method are illustrated by simulation in comparison with the existing results.

Adaptive synchronization and anti-synchronization of Julia sets generated by the competitive model

In this paper, we study the fractal behaviour of a competitive model that describes the interaction of plankton allelopathy. This paper aims to establish synchronization and anti-synchronization of Julia sets of two competitive systems with some different parameters by using an adaptive control strategy. Firstly, a discrete version of the competitive model is obtained, and then the Julia set of the discrete version is generated by using the escape-time algorithm. Adaptive controllers and parameter update laws for unknown parameters are designed to achieve synchronization and anti-synchronization of Julia sets. Furthermore, we can determine unknown parameters of the competitive system by using this adaptive control technique. Here, the adaptive synchronization and anti-synchronization of Julia sets are accomplished by its trajectories synchronization and anti-synchronization due to the close relation of trajectories of the system with the Julia set of the system. Numerical simulations are carried out to validate several key theoretical results as well as the efficacy and accuracy of the applied methodologies. Moreover, with the help of this analysis, we can study other models of a similar type.

Finite-time optimal control for a class of nonlinear systems with performance constraints via critic-only ADP: Theory and experiments

This paper addresses the optimal control problem within the framework of adaptive dynamic programming (ADP) for a class of nonlinear systems subjected to performance constraints. A new finite-time optimal control scheme is developed to stabilize the system by using the critic-only neural network ADP method. Compared with the existing ADP-based optimal control methods with uniformly ultimately bounded stability, the provided control scheme ensures that the controlled system's state and neural network weight estimation error are finite-time stable. It can ensure optimality, prescribed performance, and finite-time stability of the closed-loop control system simultaneously through an integration of ADP, the prescribed performance control technique, and Lyapunov theory. The designed adaptive neural network weight update law can relax the persisting excitation condition. The proposed control scheme is implemented on a robotic experiment platform to achieve trajectory tracking and verify its effectiveness.

Adaptive performance optimal control for flexible-joint robots with random noises: Design and experiment

This study developes a flexible performance optimal control scheme via reinforcement learning strategy and event-triggered mechanism for flexible-joint robots with random noise and non-affine input. It is notable that an event-triggered optimization mechanism is developed, which meets the optimality principle and saves communication resources. Nevertheless, the existing event-triggered strategy is unable to handle non-affine input, which limits the applicability of this method. To overcome the above problems, a modified event-triggered mechanism is proposed. At the same time, the optimal solution of the system is given by an optimized control algorithm based on the improved performance index function. In the controller design, neural network is used to deal with random disturbances and uncertainties, and an adaptive law is designed to replace the identifier structure. Besides, a flexible prescribed performance function is constructed to yield multiple prescribed performance behaviors by adjusting the key parameters, while the tracking error is stayed within a prescribed boundary. Finally, the effectiveness of the proposed control scheme is further demonstrated by simulation and the experiment of the 2-link flexible-joint robot on the Quanser platform.

Disturbance observer based adaptive predefined‐time sliding mode control for robot manipulators with uncertainties and disturbances

AbstractThis article develops a predefined‐time sliding mode control approach for systems with external disturbances and uncertainties through a nonlinear disturbance observer (DO). For addressing predefined‐time stabilization problem of robotic manipulator system, a predefined‐time sliding mode surface is proposed, ensuring system states converge to origin within a predefined‐time once sliding mode surface is attained. Compared to conventional fixed‐time and finite‐time control strategies, a distinctive advantage of this scheme is that system settling time can be explicitly chosen in advance and independent of system states. To achieve predefined‐time performance, a disturbance observer is introduced to generate the disturbance estimate, which can be incorporated into controller to counteract disturbance. To address the systems uncertainty, an adaptive law is employed to estimate the unknown upper boundary of system uncertainties. Finally, the effectiveness and performance of the proposed scheme are illustrated by simulation and experiment.

Adaptive visual servoing control for uncalibrated robot manipulator with uncertain dead-zone constraint

This paper addresses the adaptive visual tracking control problem of an uncalibrated camera robot system with unknown dead-zone inputs. The uncertainties include camera extrinsic and intrinsic parameters, robot dynamic parameters, and feature depth parameters. The control achieves a better performance by establishing a smooth inverse model of the dead-zone input, which eliminates the nonlinear effect of the actuator constraint. A novel adaptive control scheme is presented which does not require a priori knowledge of the parameter intervals of dead-zone model, to update the parameter values online. Furthermore, adaptive laws are provided to estimate the uncertainties that exist both in robot and in camera models. Meanwhile, in order to avoid the singularity of the image Jacobian matrix, a projection algorithm is also introduced. Subsequently, a novel robust adaptive controller together with dead-zone compensation is established so that the tracking error image space converges to the origin. Simulations and experimental studies are conducted to verify the effectiveness of the proposed method.