Lyapunov Theorem Research Articles

A novel model reference adaptive control approach investigation for power electronic converter applications

This paper demonstrates the viability and effectiveness of a novel adaptive control approach applied to power electronic converters. A methodology based on the formulation of a Lyapunov-based approach is showcased to represent the operation of a new adaptive controller for the regulation of two power converter topologies (Buck and Boost). The models of the Buck and Boost converter topologies include the parasitic parameters that represent the non-ideal components. The basic idea of the control approach is to demonstrate adaptive stabilization for the proposed non-linear system. The most important design specification to stabilize the system is to track the reference trajectory in such a way that the error on the output variable converges asymptotically to zero. This adaptation mechanism is explicitly designed so that the asymptotic stability of the equilibrium condition is guaranteed according to the Lyapunov theorem and sensitivity theory. The details of the design algorithm are explained in the paper. The proposed control approach has been compared to other Lyapunov-based control techniques proposed in literature for the same non-ideal converters. The results show that the proposed controller provides better level of robustness and performance than the other well-established Lyapunov based controllers. To verify the effectiveness of the controller in real time, a test bench has been set up with prototypes of both converters and the controller has been implemented using the Arduino microcontroller and the control system driven through the Matlab/Simulink platform.

Adaptive radial basis function neural network sliding mode control of robot manipulator based on improved genetic algorithm

ABSTRACT Since the trajectory-tracking control performance of multi-joint robot manipulator may be degraded due to modeling errors and external disturbances, this paper designs a new adaptive robot manipulator trajectory tracking control method through improved genetic algorithm and radial basis function neural network sliding mode control (IGA-RBFNNSMC). Firstly, the genetic algorithm (GA) is improved by establishing superior populations centered on individuals with high fitness values and selecting individuals in the superior populations for crossover and variation. Secondly, the improved genetic algorithm (IGA) is used for the optimization of the center vector and width vector of the Gaussian basis function in radial basis function (RBF) neural network. Then, based on the dynamics model of the robot manipulator, the modeling errors are approximated by RBF neural network and eliminated by sliding mode control (SMC), and the Lyapunov theorem is used to prove the stability and convergence of the control system. Finally, a two-joint robot manipulator is taken as the research objective and the simulation results show that IGA can significantly reduce the solution time on the basis of guaranteed accuracy and IGA-RBFNNSMC can make the trajectory tracking control accurate and more efficient, which proves the effectiveness of the proposed control method.

Research on Neural Network Terminal Sliding Mode Control of Robotic Arms Based on Novel Reaching Law and Improved Salp Swarm Algorithm

Modeling errors and external disturbances have significant impacts on the control accuracy of robotic arm trajectory tracking. To address this issue, this paper proposes a novel method, the neural network terminal sliding mode control (ALSSA-RBFTSM), which combines fast nonsingular terminal sliding mode (FNTSM) control, radial basis function (RBF) neural network, and an improved salp swarm algorithm (ALSSA). This method effectively enhances the trajectory tracking accuracy of robotic arms under the influence of uncertain factors. Firstly, the fast nonsingular terminal sliding surface is utilized to enhance the convergence speed of the system and achieve finite-time convergence. Building upon this, a novel multi-power reaching law is proposed to reduce system chattering. Secondly, the RBF neural network is utilized to estimate and compensate for modeling errors and external disturbances. Then, an improved salp swarm algorithm is proposed to optimize the parameters of the controller. Finally, the stability of the control system is demonstrated using the Lyapunov theorem. Simulation and experimental results demonstrate that the proposed ALSSA-RBFTSM algorithm exhibits superior robustness and trajectory tracking performance compared to the global fast terminal sliding mode (GFTSM) algorithm and the RBF neural network fast nonsingular terminal sliding mode (RBF-FNTSM) algorithm.

A Novel Hierarchical Recursive Nonsingular Terminal Sliding Mode Control for Inverted Pendulum

This paper aims to develop a novel hierarchical recursive nonsingular terminal sliding mode controller (HRNTSMC), which is designed to stabilize the inverted pendulum (IP). In contrast to existing hierarchical sliding mode controllers (HSMC), the HRNTSMC significantly reduces the chattering problem in control input and improves the convergence speed of errors. In the HRNTSMC design, the IP system is first decoupled into pendulum and cart subsystems. Subsequently, a recursive nonsingular terminal sliding mode controller (RNTSMC) surface is devised for each subsystem to enhance the error convergence rate and attenuate chattering effects. Following this design, the HRNTSMC surface is constructed by the linear combination of the RNTSMC surfaces. Ultimately, the control law of the HRNTSMC is synthesized using the Lyapunov theorem to ensure that the system states converge to zero within a finite time. By invoking disturbances estimation, a linear extended state observer (LESO) is developed for the IP system. To validate the effectiveness, simulation results, including comparison with a conventional hierarchical sliding mode control (CHSMC) and a hierarchical nonsingular terminal sliding mode control (HNTSMC) are presented. These results clearly showcase the excellent performance of this approach, which is characterized by its strong robustness, fast convergence, high tracking accuracy, and reduced chattering in control input.

Adaptive Fuzzy Quantized Control for a Cooperative USV-UAV System Based on Asynchronous Separate Guidance

This paper focuses predominantly on the multi-tasks carried out by the cooperative unmanned surface vehicle-unmanned aerial vehicle (USV-UAV) system in which the input quantization is considered. The proposed cooperative scheme consists of the asynchronous separate guidance and adaptive fuzzy quantized control algorithm. The proposed guidance law takes full advantage of subsystems whilst considering the maneuverability of these subsystems in order to achieve the goal of executing multi-tasks. In contrast to previous guidance laws, although the same waypoint path is planned, the calculation for guidance law proposed is based on speed rather than time, which in reality is more relevant. As for the controls, an adaptive fuzzy quantized controller was developed to reduce undue exertion on the actuator. By fusing the dynamic surface control (DSC) and fuzzy logic system (FLS), a hysteresis quantizer has been introduced to reduce the transmission load. By properly adjusting the quantization density, the number of quantizations was reduced whilst maintaining a favorable control performance. All of the stated variables are semi-global uniform ultimate bounded (SGUUB) and the stability of the USV-UAV system is proofed through the Lyapunov theorem. Finally, the advantages of the proposed scheme are evaluated by two simulative experiments, exhibiting the favorable tracking accuracy and reduced wear on the actuators.

Experimental evaluation of the backstepping‐based input resistance controller in step‐up DC–DC converter for maximum power point tracking of the thermoelectric generators

AbstractIn this paper, a novel non‐linear model‐based approach is presented for maximum power point (MPP) tracking of thermoelectric generators (TEGs) using the backstepping controller. Considering the output voltage range of the thermoelectric devices, a step‐up DC–DC converter is employed as an interface between the load and input power source. According to the maximum power transfer theorem, if the equivalent input resistance of the converter (Rin) is equal to the internal resistance of the input source (RTEG), the TEG operation at the MPP will be achieved. Hence, defining the RTEG as a reference value and Rin as a feedback variable for a closed‐loop controller, the backstepping non‐linear controller is developed for input resistance control of the boost DC–DC converter. Owing to the non‐linear nature of the error variable in the input resistance control of the converters, conventional linear controllers cannot guarantee the system's closed‐loop stability within an extensive operational range. However, despite changes in generator's open‐circuit voltage (VOC) and RTEG, the designed closed‐loop controller can successfully stabilize the thermoelectric converter in different operational conditions. Considering the Lyapunov theorem and the Barbalat lemma, the asymptotic stability of the backstepping controller is proved. During the steady‐state operation, the actual values of the VOC and RTEG are updated periodically by the measurement of the converter input voltage/current values. To verify the functionality of the designed control method, PC‐based simulations are carried out in MATLAB/Simulink software. Moreover, by using TMS320F28335 digital signal processor from Texas Instruments and a simple thermoelectric simulator, the experimental response of the proposed controller is evaluated in dynamic and steady‐state conditions. The developed closed‐loop system can track the MPP of a TEG with zero steady‐state error, regardless of uncertain parameter variations.

A flocking control algorithm of multi-agent systems based on cohesion of the potential function

Flocking cohesion is critical for maintaining a group’s aggregation and integrity. Designing a potential function to maintain flocking cohesion unaffected by social distance is challenging due to the uncertainty of real-world conditions and environments that cause changes in agents’ social distance. Previous flocking research based on potential functions has primarily focused on agents’ same social distance and the attraction–repulsion of the potential function, ignoring another property affecting flocking cohesion: well depth, as well as the effect of changes in agents’ social distance on well depth. This paper investigates the effect of potential function well depths and agent’s social distances on the multi-agent flocking cohesion. Through the analysis, proofs, and classification of these potential functions, we have found that the potential function well depth is proportional to the flocking cohesion. Moreover, we observe that the potential function well depth varies with the agents’ social distance changes. Therefore, we design a segmentation potential function and combine it with the flocking control algorithm in this paper. It enhances flocking cohesion significantly and has good robustness to ensure the flocking cohesion is unaffected by variations in the agents’ social distance. Meanwhile, it reduces the time required for flocking formation. Subsequently, the Lyapunov theorem and the LaSalle invariance principle prove the stability and convergence of the proposed control algorithm. Finally, this paper adopts two subgroups with different potential function well depths and social distances to encounter for simulation verification. The corresponding simulation results demonstrate and verify the effectiveness of the flocking control algorithm.

Adaptive sliding mode tracking control of underwater vehicle-manipulator systems considering dynamic disturbance

This paper proposes an adaptive sliding mode tracking control method with a nonlinear disturbance observer (NDO-ASMTC) to solve the trajectory tracking problem of the underwater vehicle-manipulator system (UVMS) in the presence of large dynamic uncertainties and severe external disturbances. The proposed NDO-ASMTC method employs an adaptive control law, an improved fractional-order sliding mode, and a nonlinear disturbance observer to achieve excellent tracking performance of the UVMS. To obtain a fast response speed in the sliding mode phase and eliminate static error in the reaching phase, a modified fractional-order sliding mode control scheme is proposed. An adaptive auto-tuning law of switching gains is presented to overcome the problem that the fixed switching gain may lead to obvious tracking performance degradation under lumped uncertainty. In addition, a nonlinear disturbance observer is implemented to maintain the robustness and stability of the control scheme under severe disturbances. Moreover, the proposed adaptive control scheme has been proved to be stable using the Lyapunov theorem. Simulations and experiments show that the proposed control scheme can meet the design requirements of the UVMS in terms of tracking accuracy, system stability, and interference attenuation under the application of external disturbances.

Self-Organizing Robust Fuzzy Neural Network for Nonlinear System Modeling.

Fuzzy neural network (FNN) is a structured learning technique that has been successfully adopted in nonlinear system modeling. However, since there exist uncertain external disturbances arising from mismatched model errors, sensor noises, or unknown environments, FNN generally fails to achieve the desirable performance of modeling results. To overcome this problem, a self-organization robust FNN (SOR-FNN) is developed in this article. First, an information integration mechanism (IIM), consisting of partition information and individual information, is introduced to dynamically adjust the structure of SOR-FNN. The proposed mechanism can make itself adapt to uncertain environments. Second, a dynamic learning algorithm based on the α -divergence loss function ( α -DLA) is designed to update the parameters of SOR-FNN. Then, this learning algorithm is able to reduce the sensibility of disturbances and improve the robustness of Third, the convergence of SOR-FNN is given by the Lyapunov theorem. Then, the theoretical analysis can ensure the successful application of SOR-FNN. Finally, the proposed SOR-FNN is tested on several benchmark datasets and a practical application to validate its merits. The experimental results indicate that the proposed SOR-FNN can obtain superior performance in terms of model accuracy and robustness.

Integrated trajectory planning into automatic berthing control of underactuated ship based on fuzzy-backstepping method

The trajectory planning and automatic berthing control are traditionally studied separately; however, the planned trajectory is indeed required to be the reference trajectory for the automatic berthing control system. In this paper, a novel trajectory planning strategy is presented and integrated into the automatic berthing control of underactuated ship. First, a novel trajectory planning strategy, including the Bezier curve planning, the least square fitting, and the speed assignment mechanism, is presented for the first time herein to provide the differentiable reference trajectory for the automatic berthing control system based on backstepping method. Second, a novel coordinate transformation between the Earth-fixed frame and the berth-fixed frame is established for the first time herein for the arbitrary berth position. Third, the fuzzy logic system is incorporated into backstepping controller to alleviate the influence of the model uncertainty, which is probably introduced by the shallow water and bank effects. The closed-loop signals are proved to be stable based on Lyapunov theorem. Two simulations are conducted to illustrate the effectiveness and advantages of the presented fuzzy-backstepping-based automatic berthing control methodology.

Practical Adaptive Fast Terminal Sliding Mode Control for Servo Motors

Position control of servo motor systems is a challenging task because of inevitable factors such as uncertainties, nonlinearities, parametric variations, and external perturbations. In this article, to alleviate the above issues, a practical adaptive fast terminal sliding mode control (PAFTSMC) is proposed for better tracking performance of the servo motor system by using a state observer and bidirectional adaptive law. First, a smooth-tangent-hyperbolic-function-based practical fast terminal sliding mode control (PFTSM) surface is designed to ensure not only fast finite time tracking error convergence but also chattering reduction. Second, the PAFTSMC is proposed for the servo motor, in which a two-way adaptive law is designed to further suppress the chattering and overestimation problems. More importantly, the proposed adaptive technique can update the switching gain according to the system uncertainties, which can provide high gain in the reaching phase and then decrease to the smallest value in the sliding phase to avoid the monotonically increasing gain that exists in most adaptation methods. Third, the finite-time stability of the closed-loop system is proved based on the Lyapunov theorem. Finally, the simulation studies and experimental tests verify the effectiveness of the proposed control in terms of better tracking, strong robustness, and reduced chattering, compared to existing algorithms.

Non‐singular terminal sliding mode controller design for nonlinear systems with prescribed convergence time guarantees

AbstractThis paper considers the prescribed‐time non‐singular terminal sliding mode control (TSMC) for nonlinear systems with uncertainties bounded by non‐negative functions. At first, a new Lyapunov theorem for prescribed‐time stability is introduced. Then, a novel terminal sliding surface together with a non‐singular TSMC input is constructed by using a time‐varying scaling function. Strict analysis shows that the proposed controller is able to ensure the exact reaching of the sliding surface as well as the system states to zero in a prescribed time independent of the system initial conditions. Moreover, all the state signals and the control input remain uniformly bounded. Finally, simulation comparison with the existing fixed‐ and prescribed‐time TSMC is given to verify the effectiveness of the theoretical results.

Adaptive Robust Control of an Industrial Motor-Driven Stage with Disturbance Rejection Ability Based on Multidimensional Taylor Network

Linear motors are widely used in practical engineering fields, but it is difficult to achieve accurate position control because of model uncertainty, external interference, input nonlinearity and other factors. In this paper, a multidimensional Taylor network (MTN) controller with flexible learning robustness is proposed to realize tracking control and make the motor have excellent antijamming ability. The controller is composed of a robust feedback part, a parameter adaptive part and a multidimensional Taylor network control part. This strategy has good track tracking performance and anti-interference ability. In this control strategy, the input of the multidimensional Taylor network is determined only by the referable trajectories, and no model information is required. In addition, the designed multidimensional Taylor network can accurately describe the relationship between state variables and any complex disturbance, which is the basis of disturbance suppression. Finally, the stability of the controller is proved by the Lyapunov theorem. The unknown interference comparison experiment and numerical simulation experiment are carried out on the industrial linear motor platform, respectively. Experimental results show that compared with NNPID, the proposed algorithm has smaller overshoot and better performance under various error statistical dimensions.

Optical interference phase control method with single photodetector for interference lithography.

This study designs an optical phase control method for interference lithography system accompanied with severe disturbance. The system, which is designed based on the exponential reaching law of sliding mode control(SMCE), could adjust the interference phase with single photodetector. The model of system is derived and then the stability is proved through Lyapunov theorem. This paper also analyzes the behavior of the system under different reference voltages of photodetector. Both theoretical analysis and simulation experiment results suggest that this method can non-periodically achieve interference phase control with single photodetector by the switching module. Finally, the experimental device is set up, and the superiority of the SMCE method in transient response time and disturbance-resisting ability is demonstrated compared with the proportional-integral-derivative(PID) method.

Dual observers based adaptive fuzzy output feedback control of a motor-driven launching platform with input saturation and disturbance rejection

In this paper, the high accuracy motion output feedback control of a kind of launching platforms driven by motors is focused. The launching platform is used to launch kinetic load to hit the target so it is susceptible to external disturbance. In addition, significant issues arise due to limitations on the plant inputs, such as actuator energy limits and velocity state is usually unavailable due to the limitation of system cost and volume. A new adaptive fuzzy output feedback controller based on dual observers is proposed for solving these problems. A smooth and continuous model is established for input saturation to compensate it. A sliding mode observer and a fuzzy observer with proper membership function are combined to estimate the unmeasured system states more accurately. An adaptive robust controller and the fuzzy observer are combined to realize a motion control with disturbance rejection, which allows correct adaptation while the plant input is saturated. Lyapunov theorem proves the bounded stability of the proposed controller when there exists observation error. Extensive comparative simulation and experiment results verify the effectiveness and practicability of the proposed controller and show that the control accuracy can be improved by an order of magnitude compared with the traditional PID controller and better than some other nonlinear controllers.

Hierarchical critic learning optimal control for lower limb exoskeleton robots with prescribed constraints

AbstractThis paper presents a hierarchical critic learning optimal control (H‐CLOC) strategy for a lower limb exoskeleton system with prescribed state constraints. The prescribed state constraints of the exoskeleton are mathematically modeled by means of a state error transition function, which transforms the constrained state into an equivalent new unconstrained state. A hierarchical framework including a high‐level motion trajectory planner and a low‐level critic learning (CL) controller is proposed for optimal control of the exoskeleton. The estimation of human motion intentions is achieved using dynamic movement primitives (DMPs), which are capable of accurately replicating the original training trajectories during motion. The CL algorithm is implemented on the transformed unconstrained system while enhancing the learning capability of the proposed algorithm for the exoskeleton. The optimal control with prescribed constraints is analyzed for stability using the Lyapunov theorem. Finally, simulation results validate the effectiveness of the proposed H‐CLOC strategy for lower limb exoskeletons.

Generalized Lyapunov stability theory of continuous-time and discrete-time nonlinear distributed-order systems and its application to boundedness and attractiveness for networks models

The Lyapunov direct method is a powerful tool for analyzing the stability of nonlinear dynamical systems. However, most existing research has primarily focused on asymptotic stability, neglecting the crucial aspect of boundedness. In light of this, this paper aims to address the issues concerning the generalized Lyapunov stability theory of distributed-order systems and its application to ensure uniform boundedness and global attractiveness for distributed-order Hopfield neural networks (DOHNNs) with time-varying external input. To achieve this, several essential inequalities that form the foundation of our main work are proposed. Subsequently, two stability criteria in the form of generalized distributed-order Lyapunov theorem are derived by employing Laplace transform techniques. Meanwhile, building upon the proposed inequalities and Lyapunov theorem, sufficient conditions that guarantee the uniform boundedness and global attractiveness of DOHNNs with time-varying external input are established. By the way, all our proposed conclusions are presented in both continuous-time and discrete-time cases to present the distinction and relationship between these two cases. Finally, various simulation examples are designed meticulously to validate the correctness of our proposed theorems and the effectiveness to real-world applicability of our approach.

A New Fractional-Order Adaptive Sliding-Mode Approach for Fast Finite-Time Control of Human Knee Joint Orthosis with Unknown Dynamic

This study delves into the implementation of Fast Finite Time Fractional-Order Adaptive Sliding Mode Control (FFOASMC) for knee joint orthosis (KJO) in the presence of undisclosed dynamics. To achieve this, a novel approach introduces a Fractional-Order Sliding Surface (FOSS). In the context of limited knowledge regarding the dynamics of knee joint arthrosis, Fractional-Order Fast Adaptive Sliding Mode Control (FOFASMC) is devised. Its purpose is to ensure both finite-time stability and prompt convergence of the KJO’s state to the desired trajectory. This controller employs adaptive rules to estimate the enigmatic dynamic parameters of KJO. Through the application of the Lyapunov theorem, the attained finite-time stability of the closed loop is demonstrated. Simulation results effectively showcase the viability of these approaches and offer a comparative analysis against conventional integer-order sliding mode controllers.

Predictive control scheme by integrating event-triggered mechanism and disturbance observer under actuator failure and sensor fault

Liquid-level control in an interacting storage-tank system exhibits major challenges due to the effect of interaction and the presence of combustible/flammable liquid as it faces huge threats from the unmeasurable disturbances, irregular geometry and unmodelled dynamics of the process plant. A combination of tanks with multiple geometries may be preferred for storing liquids using common pumps for energy conservation. Continuous improvement of risk assessment, predicting hazardous scenarios and implementation of inherently-safer-control systems ensure process safety and, as a result, ease out the safe operation. From the process analysis, it was observed that the dynamics of the interacting tank are very sensitive to effective parameters like valve coefficient and pump gain. To overcome the loss of inventory or production, we investigate the synthesis of a non-linear model predictive control scheme with an outline of simultaneous state and parameter estimation strategies. This mechanism deals with a stochastic event-trigger cubature Kalman filter scheme to estimate process states while performing servo operations. To mitigate plant uncertainty, reduce the impact of large disturbances and nullify the effect of actuator failure/sensor fault, influential model parameters are estimated simultaneously with the model state(s). Predicted values of the model states/parameters/faults are used to derive an effective control effort. An inferential non-linear model predictive control paradigm is proposed, where the primary variable(s) is (are) measured with the help of measurable secondary state(s). To demonstrate the practical utility and effectiveness of the control framework for safe operation and loss prevention, a complex industrial process (quadrupled tank) is considered for control, where the system dynamics have been structured newly. Realistic simulations such as servo-regulatory compliance and elimination of measurement noise with a state-of-the-art simulator ensures the efficacy of the proposed scheme. The results are analysed further for a comparative study with traditional non-linear model predictive control law. To guarantee convergence of the estimator and stability of the closed-loop controller, the Lyapunov theorem is well blended.

Position-based visual servoing of a 6-RSS parallel robot using adaptive sliding mode control

The trajectory tracking control of parallel robots is challenging due to their complicated dynamics and kinematics. This paper proposes a position-based visual servoing (PBVS) approach for a 6-Revolute-Spherical-Spherical (6-RSS) parallel robot using adaptive sliding mode control in Cartesian space. A photogrammetry sensor C-Track 780 in the eye-to-hand configuration is adopted to measure the real-time pose of the robot end-effector, which can avoid the calculation of robot forward kinematics and provide more flexibility for controller design. An adaptive Kalman filter is utilized to deal with uncertain noises in visual measurements to increase the pose estimation accuracy. A sliding mode controller with strong robustness is designed to cope with system uncertainties, and a radial basis function (RBF) neural network is incorporated to realize the auto-tuning of the control gains, which make the robot effectively track different trajectories with time-varying conditions in real applications. Based on Lyapunov theorem, the stability analysis of the controller has been done. Experiments have been conducted to validate the effectiveness of the proposed strategy and illustrate the superiority of the designed controller.