Control Law Research Articles

Image-Based Visual Servoing of Manipulators With Unknown Depth: A Recurrent Neural Network Approach.

The image-based visual servoing (IBVS) of manipulators is important for intelligent manipulation using visual feedbacks. While the traditional IBVS methods for manipulators require the knowledge of the depth information in the interaction matrix, in this article, we propose a novel IBVS method for manipulators without depth estimation by leveraging the property of the associated image Jacobian. Because of a novel transformation, the IBVS problem is converted into a convex optimization problem subject to the kinematic constraint, joint constraints, and other constraints that are not explicitly related to the depth information. The problem is then solved by developing a recurrent neural network of global asymptotic convergence, and a dynamic neural control law without depth estimation emerges for the IBVS of manipulators. The theoretical guarantee and simulation results are provided to show the efficacy of the proposed method.

Examining Drug Use and Misuse in India, and Evaluating Drug Control Laws

Examining Drug Use and Misuse in India, and Evaluating Drug Control Laws

Adaptive path following control for underactuated surface vessels considering actuator saturation dynamics

ABSTRACT This article studies the path-following problem of underactuated surface vessels with saturated actuator dynamics and unmeasured linear velocities subjected to model uncertainties and unknown environmental disturbances. Firstly, a predictor is designed to estimate linear velocities and an improved predictor-based line-of-sight guidance law is designed to generate a reference heading angle, where the unknown arbitrary sideslip angle is compensated. Secondly, robust adaptive control laws are devised, where auxiliary dynamic systems are introduced to address input saturation and adaptive technique is employed to offset environmental disturbances and model uncertainties. Furthermore, to tackle computational complexity in control design, tracking differentiators are employed. Subsequently, the stability analysis of a closed-loop system is demonstrated by the Lyapunov theory. At last, simulations are applied to verify the validity and superiority of the presented strategy.

Immersion and Invariance Adaptive Control through Polynomial Adaptation

Abstract In conventional immersion and invariance (I&I) adaptive control design, control parameter adaptation is typically linear with respect to the parameter-error-induced perturbation, resulting in quadratic-rate dissipation of energy associated with the off-the-manifold variable. Departing from such a convention, this article contributes a novel strategy - polynomial adaptation. As the name suggests, control parameter adaptation in this approach takes the form of a general polynomial in relation to the perturbation. Accordingly, this new design induces polynomial-rate energy dissipation, which is faster than the quadratic one in the conventional scheme, thereby enhancing closed-loop control performance. The theoretical underpinnings of the new approach are demonstrated through the design of an I&I adaptive tracking control law for a general nth-order, single-input-single-output, parametrically uncertain, nonlinear system in the controllable canonical form. Additionally, a numerical study of the proposed method on the second-order forced Duffing oscillator showcases its improved transient performance in comparison to a baseline controller developed with the standard I&I adaptive control technique.

Dynamic balance of circles with one support point on pommel horse exercise

Double-leg circles on pommel horse exercises require a high degree of dynamic balance. However, theoretical conditions for maintaining dynamic balance are unclear. The purpose of this paper is to propose a simple theoretical model of the dynamic balance of the circles, and to illustrate its qualitative properties. To this end, the body of a gymnast is simply modeled as one rigid body with one support point, and symmetric and constant-velocity circles are assumed in most analyses. The condition that the torques of wrist and shoulder joints are zero is assumed as a dynamic balance condition with minimum strength. A control law is proposed to demonstrate the motion. Various properties of the dynamic balance condition are analyzed as follows. In the symmetric circles, (1) as the period of a circle decrease, the heights and the radius of the toes increase, and (2) the rotation of the body around its longitudinal axis in the double-leg circle has the effect of lifting the toes. (3) The shoulder and wrist torques can change the pose around the dynamic balance condition. In asymmetric circles, (4) the radius of the center of mass (CoM) increases as the angular velocity of the CoM around the support point decreases, and (5) the body angle with respect to the horizontal plane increases as the upward acceleration of the CoM increases. Moreover, mechanical principles of the circles are discussed as follows. (6) The CoM motion during the symmetric circles of the simple model can be related to the conical pendulum. In the simple model, (7) the pommel reaction force should be parallel to the arm segment when the wrist torque and the shoulder torque are equal or zero, and (8) to change the vertical component of the angular momentum of the body around the support point, the wrist torque around the vertical axis is needed. These results provide theoretical and qualitative insights into understanding and improving pommel horse exercise.

Fault tolerant control of uncertain hydraulic system against actuator fault based on redesign Lyapunov approach

The design of stabilizing controller for uncertain nonlinear systems with control constraints is a challenging problem. This paper proposes the design of fault tolerant control for a class of uncertain nonlinear systems with actuator faults based on Lyapunov redesign principle. First, an assumption is introduced to design the control of the nominal system. Then, a new control law has been introduced to handle the difficulty caused by actuator failures. It is shown that the actuator faults can be completely compensated by the proposed nonlinear controller. Finally, the method will be applied to a hydraulic system to show its effectiveness.

Fuzzy inference system enabled neural network feedforward compensation for position leap control of DC servo motor

To improve dynamic performance and steady-state accuracy of position leap control of the direct current (DC) servo motor, a fuzzy inference system (FIS) enabled artificial neural network (ANN) feedforward compensation control method is proposed in this study. In the method, a proportional-integral-derivative (PID) controller is used to generate the baseline control law. Then, an ANN identifier is constructed to online learn the reverse model of the DC servo motor system. Meanwhile, the learned parameters are passed in real-time to an ANN compensator to provide feedforward compensation control law accurately. Next, according to system tracking error and network modeling error, an FIS decider consisting of an FI basic module and an FI finetuning module is developed to adjust the compensation quantity and prevent uncertain disturbance from undertrained ANN adaptively. Finally, the feasibility and efficiency of the proposed method are verified by the tracking experiments of step and square signals on the DC servo motor testbed. Experimental results show that the proposed FIS-enabled ANN feedforward compensation control method achieves lower overshoot, faster adjustment, and higher precision than other comparative control methods.

Command-filtered incremental backstepping attitude control of spacecraft with predefined-time stability

This paper investigates the predefined-time attitude tracking control problem within the theoretical framework of incremental dynamic inversion. The utilization of the Taylor series facilitates the transformation of the attitude control system into a discrete-time plant, with the control input expressed in an incremental form. Additionally, a novel predefined-time stable dynamics system is presented and incorporated into the disturbance observer designing process, serving the purpose of estimating lumped disturbance. It is also employed in a command filter design to approximate the derivatives of the virtual control law within a predefined time. Consequently, an incremental backstepping attitude tracking control scheme is further developed, integrating the proposed predefined-time disturbance observer to ensure the system's robustness and the predefined-time filter to address challenges related to “term explosion” and singularity problem. Rigorous Lyapunov analysis affirms that the attitude control system, when using the incremental backstepping controller, remains predefined-time stable. The effectiveness of the proposed control scheme is subsequently validated through numerical simulations.

Non-collocated control of an anti-stable system of coupled strings under delayed displacements/velocities feedback

In this paper, we consider the non-collocated stabilization of three coupled wave equations with different speeds and joint anti-dampings. These anti-dampings put all eigenvalues of the system in the right complex plane. By designing two invertible transformations, the wave system is converted into an equivalent system with damping terms at the joint points. The feedback controllers with displacements/velocities are designed to obtain the target system. The well-posedness and exponential stability of the closed-loop system are established using the PDE approach, based on the exponential stability of the target system. Simulation results are presented to verify the effectiveness of the feedback control law.

Distributed bipartite time‐varying formation tracking control with prescribed‐time convergence for heterogeneous Euler‐Lagrange systems

AbstractThis paper focuses on the study of the prescribed‐time bipartite time‐varying formation tracking (BTVFT) problem for multiple heterogeneous Euler‐Lagrange systems (HELSs) with external disturbances under directed signed graphs. Considering the fact that the states of leader cannot be accurately obtained, a set of observers which can estimate the states of the leader within a prescribed time, is firstly established according to the time‐varying function. Subsequently, a prescribed‐time distributed control protocol is proposed by employing a terminal sliding surface, aiming to achieve the BTVFT under digraphs within a prescribed time. The theoretical proof utilizes suitable Lyapunov functions to demonstrate that the control law can guide the state trajectories of each follower to the corresponding terminal sliding surface within a predefined time, thus ensuring the solution to the BTVFT problem of HELSs. Finally, simulation results are provided to validate the effectiveness of the derived findings.

Lyapunov-based prescribed-time stabilisation control of quantum systems

This paper addresses the prescribed-time stabilisation control problem for quantum systems characterised by a single control input. A control law based on the relative state distance is formulated. Through the application of prescribed-time Lyapunov control techniques, the stabilisation of the quantum system to one of the eigenstates of the internal Hamiltonian within a prescribed-time is established. Notably, in contrast to existing quantum system control methods, our proposed approach ensures stabilisation within a specified time, allowing for the flexible selection of the settling-time upper bound according to preference, independent of the initial conditions.

Drone Swarm Robust Cooperative Formation Pursuit through Relative Positioning in a Location Denial Environment

This paper considers the pursuit problem of a moving target by a swarm of drones through a flexible-configuration formation. The drones are modeled by second-order systems subject to uncertain damping ratios, whereas the moving target follows a polynomial-type trajectory whose coefficient vectors are fully unknown. Due to location denial, drones cannot obtain their absolute positions, but they can obtain their positions relative to other neighboring drones and the target. To achieve a robust formation pursuit, a robust cooperative control protocol is synthesized, which comprises three key components, namely, the pseudo drone position estimator, the pseudo target position estimator, and the local internal model control (IMC) law. The pseudo drone position estimator and the pseudo target position estimator aim to recover for each drone the position of itself and the target, respectively, but are subject to some common unknown constant bias in a distributed manner. By subtracting the pseudo target position from the pseudo drone position, each drone can acquire its position relative to the target, which facilitates the design of a local IMC law to fulfill formation pursuit in the presence of system parametric uncertainties. Both pure numerical simulation and hardware-in-the-loop (HIL) simulation are performed to verify the effectiveness of the proposed control protocol.

Analytic optimal control for multi-satellite assembly using linearized twistor-based model

This paper presents Guidance and Control (G&C) systems for multi-satellite assembly in proximity operations. The systems utilize the twistor model, which is linearized through Taylor’s series. Decentralized control laws, designed using Linear Quadratic Regulator (LQR) and Model Predictive Control (MPC), are employed to track an energy-optimal trajectory generated using the Hamiltonian approach. Data exchange between satellites and their neighbors is represented using graph theory. The decentralized MPC framework is implemented using the CasADi package. To ensure collision avoidance between the satellites, a repulsive control law is designed, considering symmetric input saturation in the actuators. The proposed G&C systems are tested using a high-fidelity nonlinear satellite relative motion model that incorporates orbital perturbations. Numerical simulations are performed in a MATLAB® environment, and the results are visualized using STK®. Furthermore, a comparative study is conducted to evaluate tracking performance and fuel consumption between the two control methods. The results demonstrate that the use of an optimal trajectory reduces fuel consumption for both control algorithms.

New Type-2-Fuzzy-Logic-Based Control System for the Cessna Citation X

This paper presents a new control law based on type-2 fuzzy logic system (T2FLS) for the Cessna Citation X aircraft during cruise. This methodology combines three control systems: a T2FLS, a sliding mode control (SMC) system, and an adaptive control system. Differing from conventional controllers, this control system can deal with uncertainties and aircraft dynamics variations using the T2FLS approximator. The approximated functions were updated during the simulation iterations using adaptation laws derived from the Lyapunov theorem. The adaptability characteristic of this controller allows updating the approximated functions while the other design parameters remain unchanged. This fact simplifies the controller design process and eliminates the need to use a group of conventional controllers with different gains to control the aircraft in various flight conditions. In addition, the sliding mode control system helps to guarantee the aircraft’s stability and robustness, along with two other methodologies in the presence and absence of turbulence. The performance of this control methodology was validated with a nonlinear simulation platform developed for the Cessna Citation X business aircraft using accurate flight data derived from a Level D flight simulator at the Research Laboratory in Active Controls, Avionics and AeroServoElasticity (LARCASE).

Disturbance rejection for switched singular systems using state decomposition technique and equivalent-input-disturbance with a dynamic state observer

In this study, an equivalent-input-disturbance (EID) method with a dynamic state observer and a state decomposition technique (SDT) are used to explore the disturbance rejection of a class of linear switched singular systems. The EID approach defines an EID signal, is defined for the control input channel and has the same impact on the system as exogenous disturbances. Additionally, it employs an observer to estimate the EID and achieves good disturbance-rejection performance. However, in the EID method, the coefficient matrix of the observer needs to be consistent with the coefficient matrix of the original system, which limits the application of the method. So, a dynamic state observer is designed to reconstruct the system state and estimate the disturbance in this study. Based on the state feedback control strategy, a disturbance-rejection control law containing disturbance information is designed and a closed-loop control system structure is established. Subsequently, the state equation of the closed-loop system is reorganised and decomposed into an algebraic equation and a differential equation using the SDT. Then, a Lyapunov function with few decision variables is designed to obtain an admissible criterion for the closed-loop system and the controller gains under arbitrary switching signals. Finally, the effectiveness of the presented method is verified via numerical simulations.

Stages and main tasks of the century-long control theory and system identification development. Part VI. Model predictive control

The article is devoted to one of the relatively new areas in the field of control theory and practice, called model predictive control. The ideas underlying it, the connection with the theory of optimal control and numerical methods for solving optimization problems are described. It should be noted that currently the number of problems solved and control systems developed within the framework of this approach has come out on top in comparison with all others. This is evidenced by numerous publications concerning the theory and practical application of control methods and algorithms using a predictive model. The main distinctive feature of this method is that the control is not synthesized in advance, but is calculated directly during the operation of the system, i.e. at the current time. This made it possible, with such control, to implement original feedback that ensures stabilization of the process when the model is inaccurate and there is uncertainty associated with existing disturbances and measurements. It describes how such feedback is organized based on current measurement data. In this case, there is no need to interpret somehow the nature of the disturbances and errors acting on the system. Much attention in the article is paid to the possibilities that are admitted with this method of control. The model predictive control method seems especially attractive for systems with discrete impulse processes that are well described with using cognitive maps. It is considered an example of cognitive modeling of evolutionary demographic processes in Ukraine and the possibility of control them using a predictive model, when the model contains unstable eigenvalues. When solving problems of predictive control, it is proposed to use trajectory models, which directly follow from the Cauchy formula, in particular for discrete systems, instead of a local description in the state space. This makes it possible to take into account, when solving predictive control problems, how well or poorly controlled, observable or identifiable the system is. Non-standard capabilities of this method with a trajectory description appear during terminal control on a sliding interval with a finite horizon. A number of original formulations of terminal control problems are presented in the article and some of their properties are described.

The Role of Financial Oversight in Enhancing the Efficiency of Public Spending in the Kingdom of Saudi Arabia

This study aimed to determine the extent of the impact of financial control on the efficiency of public spending in the Kingdom of Saudi Arabia to regulate corruption, reduce waste of public funds, enhance transparency, and assess the effectiveness of current financial control legislation and agencies, and the procedures included therein, to understand their responsiveness, efficiency, and their impact on diversifying income sources, reducing unemployment rates, and their effect on economic growth through the analysis and study of international and local reports and indicators regarding financial control. Additionally, this study reviews the most distinguished international experiences in financial control and how to benefit from them to enhance the efficiency of control over the implementation of the general budget in the Kingdom. This study adopts the descriptive-analytical approach to reveal the effectiveness of current financial control over the public budget in the Kingdom of Saudi Arabia, and its impact on the efficiency of spending, relying on three important indicators that represent the growth rate, unemployment rate, and diversification of income sources, through the review and analysis of international and local reports and indicators during the period covered by the Open Budget Index in the Kingdom, starting from 2008 to 2023. The study revealed the necessity of financially and administratively independent financial control agencies, granting them the necessary powers to carry out their tasks, making all administrative levels accountable, with the need for continuous updating of financial control legislation and laws in the Kingdom, activating what has recently been introduced of systems, working on integrating control agencies, in addition to the importance of exercising preventive control before preparing the budget to avoid budget deficit crises and preserve public funds. The researcher believes, through what has been discussed, that this study provides a valuable contribution to the development of financial control policies in the Kingdom of Saudi Arabia.

Immersion and Invariance-Based Linear Tracking and Regulation Controller for Depth Position of an AUV

This paper addresses the tracking control challenge in the diving motion system of a specific class of autonomous underwater vehicles (AUVs) characterized by a torpedo-like shape. A decoupled and reduced-order three degrees-of-freedom linearized diving motion model is employed for depth position control. A control law is synthesized using the immersion and invariance (I&I) technique to achieve the control objectives. The primary aim is to attain tracking by immersing a stable, lower-order target (second-order) dynamic system into a three-dimensional manifold, upon which the closed-loop system evolves. We address the regulation problem as a specialized instance of the tracking problem, with the reference input set as a predetermined known depth that requires regulation. The efficacy of the proposed control law is evaluated through simulation studies involving various scenarios. Robustness tests are conducted to assess the control law’s performance under modeling uncertainties and underwater disturbances. The computer simulation employs an AUV named MAYA, utilizing experimentally validated diving motion parameters. A comparative analysis is performed between the proposed control law and other benchmark controllers to gauge its performance. Additionally, the effectiveness of the proposed control law is confirmed by validating its application to the nonlinear model of the diving motion system.

Global stability analysis, stabilization and synchronization of an SEIR epidemic model

In this paper, we investigate an SEIR epidemic model in which recruitment is assumed to be regulated by a constant function. The SEIR model is a widely-used epidemiological framework that categorises the population into four distinct groups: Susceptible, Exposed, Infectious, and Removed. It employs a system of differential equations to describe the transitions of individuals among these groups, making it a valuable tool for understanding and modelling the dynamics of infectious diseases. Mathematical analysis is used to study the dynamic behaviour of this model. We first determine the basic reproduction number, denoted as R 0 , which governs the dynamics of the SEIR model. Our findings reveal that when R 0 is less than 1, the unique disease-free equilibrium is asymptotically stable, and there is no endemic equilibrium. However, when R 0 exceeds 1, the disease-free equilibrium becomes unstable, and a unique, asymptotically stable endemic equilibrium emerges. Furthermore, by constructing appropriate Lyapunov functions, we have studied the global asymptotic stability of the two equilibrium points. On the other hand, we have used the backstepping method to design a control law that stabilises the SEIR model towards the disease-free equilibrium, which means the eradication of the disease from the target population. Next, we have used the same method to synchronise the SEIR drive system and the SEIR response system. This method is used to stabilise the synchronisation error dynamics arising from the mismatch between the drive and response systems. Finally, we presented numerical simulations to illustrate the theoretical results.

Joint buffetings suppression and trajectory tracking by fuzzy-based super-twist sliding mode control: Application to a fast parallel robot for PnP operations

This paper deals with the suppression of robotic joint buffetings for enhanced precision of trajectory tracking by means of fuzzy-based super-twist sliding mode control, which is illustrated with a fast pick-and-place parallel robot for material handling. Prior to control design, the joint motions and torques are measure to identify the dynamic parameters of the robot with recursive least square method, which is experimentally validated for the further model-based control design. In order to suppress the joint buffetings and to improve the tracking accuracy, the control law by integrating fuzzy algorithm and second-order sliding mode control is designed, where the control performance is evaluated by observing the joint dynamics, compared to the classical computed torque control and fuzzy sliding mode variable structure control. The experimental results and comparative study show the effectiveness of the developed control scheme, regarding the joint buffetings suppression and trajectory tracking precision. The main contribution lies in the integrated fuzzy algorithm and second-order sliding mode control for the model-based control design, with acceptable computational cost and trajectory tracking accuracy, from the perspective of actual engineering application.