Control Input Research Articles

Output tracking problem for a class of 3-D hyperbolic PDEs

The output tracking problem (OTP) refers to the procedure of determining an input control that ensures the system output follows a specified trajectory. In this paper, we investigate the OTP for controlled systems governed by a class of 3-D hyperbolic partial differential equations (PDEs), aiming for an exact alignment between the system output and the desired trajectory. Utilizing backstepping techniques, semigroup theory, the Hahn-Banach theorem, Laplace transforms, and Green's functions, our approach begins by establishing the OTP solution as a bounded feedback law, with Green's functions allowing the solution of a Cauchy-Euler equation. This is followed by deriving a detailed formulation for the complete state of the corresponding control problem. Finally, the approach provides an explicit formula for the OTP solution, using the desired trajectory and the solutions of specific kernel PDEs.

Predefined time trajectory tracking control and hardware in loop verification for quadrotor UAV under input delay and disturbances

AbstractThis paper deals with the predefined time trajectory tracking control of quadrotor unmanned aerial vehicle (UAV) system in the presence of input delay and external disturbances. By combining the backstepping with the predefined time nonlinear disturbance observer, the uncertainty caused by the external disturbance is eliminated, enabling the UAV to reach the control target within a predefined time. Moreover, in order to compensate for the impact of the control input delay, an appropriate auxiliary system is introduced. Simulation and hardware‐in‐the‐loop (HIL) experimental are carried out to show the effectiveness of the proposed control scheme.

Asymptotically stable data-driven koopman operator approximation with inputs using total extended DMD

Abstract The Koopman operator framework can be used to identify a data-driven model of a nonlinear system. Unfortunately, when the data is corrupted by noise, the identified model can be biased. Additionally, depending on the choice of lifting functions, the identified model can be unstable, even when the underlying system is asymptotically stable. This paper presents an approach to reduce the bias in an approximate Koopman model, and simultaneously ensure asymptotic stability, when using noisy data. Additionally, the proposed data-driven modeling approach is applicable to systems with inputs, such as a known forcing function or a control input. Specifically, bias is reduced by using a total least-squares, modified to accommodate inputs in addition to lifted inputs. To enforce asymptotic stability of the approximate Koopman model, linear matrix inequality constraints are augmented to the identification problem. The performance of the proposed method is then compared to the well-known extended dynamic mode decomposition (DMD) method and to the newly introduced forward–backward extended DMD method using a simulated Duffing oscillator dataset and experimental soft robot arm dataset.

The Impact of Digital Transformation on Internal Auditing and Financial Performance of Iraqi Banks

This study investigates the extent to which regulatory systems for electronic accounting information systems, with conventional controls, are implemented in banks. The research employs a questionnaire divided into two main sections : the first section focuses on the personal characteristics of the study sample, while the second section is divided into eight themes. These themes cover the bank's commitment to deregulation of electronic accounting systems, regulatory controls on access to information, security and protection of files, documentation and development of the electronic accounting system, input and output controls, operations, and the risks associated with electronic accounting information systems. Key recommendations include improving control procedures, protecting software and hardware, and adopting clear regulations for responsibilities and powers within banks. The study underscores the importance of continuous internal audits and the development of efficient electronic accounting information systems to mitigate risks and enhance the overall performance of Iraqi private banks.

Economics of Seed Spices in Gujarat: Analyzing Parity of Cost, Price, and Income

This study analyzes the cost, price, and income parity in three major seed spices cultivated in Gujarat by examining indices of average input prices, Farm Harvest Prices, cost of production, and gross income to evaluate the profitability and challenges faced by farmers. The secondary data on input cost, cost of production and gross income were collected for the period of eleven years from 2011-12 to 2021-22 from the reports of “The Scheme for Farm Cost Studies of Important Crops in Gujarat State” and “The Scheme for Creating a Permanent Machinery for studying Cost of Cultivation/ Production of Principal crops grown in Gujarat state, further analysis of parity indices were estimated by taking 2011-12 as base year. The results indicate that for cumin crop, input prices grew significantly, while farm harvest prices exhibited a non-significant increase. Parity indices between Farm Harvest Prices and input prices remained below 100, indicating that farm harvest prices did not cover rising input costs. However, in years like 2016-17, 2018-19, and 2021-22, the farm harvest price and gross income were favorable, indicating profitability for farmers. In fennel, input prices and production costs showed significant growth, while farm harvest prices and gross income had minimal increases. Parity indices suggested that farm harvest prices were insufficient to cover rising costs in most years, though 2012-13 and 2021-22 were favorable for farmers in terms of both price and income. Coriander, with significant growth in input prices, showed a slight increase in farm harvest prices and a decrease in production costs. Parity indices indicated that the farm harvest price consistently exceeded input prices and the cost of production, ensuring favorable profitability and encouraging investment in coriander cultivation. Overall, the findings underscore the need for policy interventions to stabilize farm harvest prices and control input cost inflation, ensuring sustained profitability for farmers growing seed spices.

A Class of Pursuit Problems in 3D Space via Noncooperative Stochastic Differential Games

This paper investigates three-dimensional pursuit problems in noncooperative stochastic differential games. By introducing a novel polynomial value function capable of addressing high-dimensional dynamic systems, the forward–backward stochastic differential equations (FBSDEs) for optimal strategies are derived. The uniqueness of the value function under bounded control inputs is rigorously established as a theoretical foundation. The proposed methodology constructs optimal closed-loop feedback strategies for both pursuers and evaders, ensuring state convergence and solution uniqueness. Furthermore, the Lebesgue measure of the barrier surface is computed, enabling the design of strategies for scenarios involving multiple pursuers and evaders. To validate its applicability, the method is applied to missile interception games. Simulations confirm that the optimal strategies enable pursuers to consistently intercept evaders under stochastic dynamics, demonstrating the robustness and practical relevance of the approach in pursuit–evasion problems.

Small-controllability of state-affine nonlinear systems

This paper is concerned with the small-controllability problem of state-affine nonlinear systems, where the control inputs can be sufficiently small. By proposing the characteristic equation, a necessary condition for small-controllability of discrete-time state-affine nonlinear systems is first given, which covers the classical results for bilinear systems. The proposed characteristic equation is also generalized to continuous-time state-affine nonlinear systems. Then, two classes of sufficient conditions for small-controllability of discrete-time state-affine nonlinear systems are formulated by algebraizing the local rank condition. In this way, not only the classical sufficient results applied for the degenerate systems are improved, but also the scope is extended to more general state-affine nonlinear systems. Finally, the sufficient conditions are generalized to the multi-input case and the continuous-time case. Examples are given to illustrate the small-controllability results of this paper.

Coupled differential-algebraic equations framework for modeling six-degree-of-freedom flight dynamics of asymmetric fixed-wing aircraft

This study presents a comprehensive mathematical framework for modeling the flight dynamics of a six-degree-of-freedom fixed-wing aircraft as a rigid body with three control surfaces: rudder, elevators, and ailerons. The framework consists of 35 differential-algebraic equations (DAEs) and requires 30 constants to be specified. It supports both direct and inverse flight dynamics analyses. In direct dynamics, the historical profiles of control inputs (deflection angles and engine thrust) are specified, and the resulting flight trajectory is predicted. In inverse dynamics, the desired flight trajectory and an additional constraint are specified to determine the required control inputs. The framework employs wind axes for linear-momentum equations and body axes for angular-momentum equations, incorporates two flight path angles, and provides formulas for aerodynamic force and moment coefficients. Key advantages include improved computational efficiency, elimination of Euler angle singularities, and independence from symmetry assumptions with regard to the aircraft’s moments of inertia. The model also accounts for nonlinear air density variations with altitude, up to 20 km above mean sea level, making it suitable for accurate and efficient flight dynamics simulations.

A Cross-Layer Game-Theoretic Approach to Resilient Control of Networked Switched Systems Against DoS Attacks.

This article investigates the resilient control strategies of networked switched systems (NSSs) against denial-of-service (DoS) attacks and external disturbance. In the network layer, both the defender and the attacker allocate energy over multiple channels. Considering the impact of switching characteristic in the physical layer on the network layer, a dynamic regulating factor is proposed to adjust the total energy of the defender. To optimize the signal-to-interference-noise ratio and energy consumption simultaneously at each player's side, a multiobjective game problem is formulated. Furthermore, a nondominated sorting genetic algorithm framework is employed, incorporating the knee point selection mechanism to attain the Pareto-Nash equilibrium, based on which the optimal defense strategy can be derived to achieve resilience against DoS attacks. In the physical-layer, taking the dynamic packet loss caused by DoS attacks and external disturbance into account, an H∞ minimax controller containing control inputs and the switching signal is designed to guarantee the optimal performance for NSSs through the dynamic game-theoretic approach. Finally, the networked continuous stirred tank reactor system is provided to verify the effectiveness of the proposed method.

Metal transfer and forming behavior of bypass-coupled variable polarity plasma arc additive manufacturing

This study proposes a novel bypass-coupled variable-polarity plasma arc additive manufacturing process. This process enables independent control of the main current, bypass current, and their polarities, thereby achieving decoupled control of thermal input to the deposited layers and wire melting. Additionally, the variable polarity effectively removes the oxide film on the surface of aluminum alloys, improving defects in aluminum alloy additive manufacturing. The research results indicate that the bypass-coupled variable-polarity plasma arc additive manufacturing presents different metal transfer forms compared to conventional arc additive manufacturing (MIG/TIG arc heat sources). The droplet transfer behavior manifests in various forms at different wire heights, including droplet transfer, Intermittent bridging transfer, and complete bridging transfer. Notably, the complete bridging transfer results in short metal bridge, which weakens the influence of the coupled arc magnetic field and provides a wider process window for shaping. A detailed analysis of the effects of main and bypass EN/EP currents on the formation morphology reveals that the influence of the main EN current on the width of the deposited layer is twice that of the bypass EN current. By adjusting the main EN current, the remelting depth can be effectively controlled, allowing for precise control over the morphology of the deposited layers. This study demonstrates the potential of this process to enhance deposition efficiency, reduce thermal input, and achieve effective shaping control.

A reconfigurable memristor diode based on a CuInP2S6/graphene lateral heterojunction.

The conventional reconfiguration of transistors requires an additional independent terminal for controllable gate input, which complicates the device structure and makes circuit integration difficult. In this work, we propose a reconfigurable diode based on a 2D layered copper indium thiophosphate (CIPS) and graphene (Gr) van der Waals lateral heterojunction, exhibiting distinctively bias-dependent reconfiguration. The reconfiguration characteristics include reversible memristive behaviors with a current on/off ratio of about 103 and switchable rectifying polarity with a rectifying ratio of up to 3 × 103. This reconfigurable mechanism arises from the lateral bias-induced migration of Cu+ ions, effectively modulating the barrier height at the CIPS and Gr interface. This work provides a simplified reconfigurable solution for electrostatically modulated circuits.

Uncertainty analysis in river quality management considering failure probability: controllable and uncontrollable input pollutants

Uncertainty analysis in river quality management considering failure probability: controllable and uncontrollable input pollutants

Gyro-free attitude reorientation control of spacecraft with state and input constraints

This paper introduces an explicit reference governor-based control scheme to address the gyro-free spacecraft attitude reorientation problem, considering specific constraints such as pointing, angular velocity, and input saturation. The proposed control scheme operates in two layers, ensuring the asymptotic stability of the attitude while adhering to the aforementioned constraints. The inner layer employs output feedback control utilizing an angular velocity observer based on immersion and invariance technology. Through an analysis of the geometry associated with the pointing constraint, determination of the upper bound of angular velocity, and optimization of the control input solution, the reference layer establishes a safety boundary described by the invariant set. Additionally, we introduce the dynamic factor related to the angular velocity estimation error into the invariant set to prevent states from exceeding the constraint set due to unmeasurable angular velocity information. The shortest guidance path is then designed in the reference layer. Finally, we substantiate the efficacy of the proposed constrained attitude control algorithm through numerical simulations.

Hierarchical-based self-triggered control for linear systems with external disturbances

This paper introduces a hierarchical-based robust self-triggered control mechanism for linear systems with disturbances, with the goal of achieving anti-interference and computational resource saving. To address the potential external interference in the system, the H∞ performance index is introduced, and the self-triggered controller is developed based on this index to guarantee the system’s desired anti-interference capabilities. Furthermore, a hierarchical framework is employed to facilitate collaborative optimization of triggering mechanisms and control strategies. Within this framework, the triggering interval values and control input values are computed sequentially using a cyclic iteration approach. By upholding the H∞ performance standard and incorporating a hierarchical optimization framework, the system’s sampling frequency is notably diminished, anti-interference performance is safeguarded, and the convergence speed of the state trajectory is accelerated. The efficacy of the proposed method is validated through two illustrative examples.

Dynamic event‐triggered‐based adaptive frequency control of microgrids under cyber‐attacks via adaptive dynamic programming

AbstractThe increasing penetration of renewable energy sources (RES) and the development of the cyber‐physical microgrids (CPMs) make greater demands for frequency control of microgrids. The common approach for frequency control is controlling the micro‐turbine to compensate for frequency deviations, with energy storage systems serving as an auxiliary approach. This article proposes an online adaptive frequency control method to control the governor and energy storage to realize the frequency recovery of microgrid, subject to the external unknown disturbances caused by wind turbine, power load and false data injection (FDI) attacks. First, the non‐zero sum (NZS) games of the considered system are modeled in this work, where the unknown disturbances are also taken into account. For the sake of estimating the unknown disturbances, a disturbance observer (DOB) for the microgrid system is introduced. Then, on the basis of the estimated results of the applied DOB, the disturbance compensation input is derived to offset the interference of the unknown disturbance. Meanwhile, the adaptive dynamic programming (ADP) approach is employed to derive the adaptive optimal control input for the NZS games of microgrid system. Besides, the dynamic event‐triggered (DET) control is introduced, reducing the occupation of computing resources. By utilizing the Lyapunov's method, the stability of the closed‐loop system, the convergence of the estimation weight, the estimation disturbances and the system state are guaranteed. The effectiveness of the proposed method is ultimately verified by the simulation results.

Attractor-Transition Control of Complex Biological Networks: A Constant Control Approach.

This article presents attractor-transition control of complex biological networks represented by Boolean networks (BNs) wherein the BN is steered from a prescribed initial attractor toward a desired one. The proposed approach leverages the similarity between attractors and Boolean algebraic properties embedded in the underlying state transition equations. To enhance the clarity of expression regarding stabilization toward the desired attractor, a simple coordinate transformation is performed on the considered BN. Based on the characteristics of transformed state equations, self-stabilizing state variables requiring no control efforts are derived in the first. Next, by applying the feedback vertex set (FVS) control scheme, control inputs stabilizing the remaining state variables are determined. The proposed control scheme exhibits versatility by accommodating both fixed-point and cyclic attractors. We validate the effectiveness of the proposed strategy through extensive numerical experiments conducted on random BNs as well as complex biological systems. In adherence to the reproducible research initiative, detailed results of numerical experiments and all the implementation codes are provided on the authors' website: https://github.com/choonlog/AttractorTransition.

Constraint-oriented formation control of multi-robot system in leaderless consensus under confined conditions

In this paper, constraint-oriented coordination control of a first-order multi-robot system has been considered in a leaderless consensus where rectangular velocity components of participating robots are subject to constraints while also avoiding inter-robots collisions. The desired formation control of different robots and their inter-robots collision avoidance in a team of robots are achieved by solving an optimization problem based on control barrier functions whereas graph theory concepts are used to represent the interaction relations among robots. A devised quadratic programme subject to the velocity and safety conditions, minimizes the desired cost function encoded in the control barrier function and generates separate control inputs for each robot. The rectangular components of the velocity against each robot are kept constrained during the entire operation of the formation control. The optimization-technique-based decentralized controllers were simulated in MATLAB and the corresponding results were recorded. The robots in the team successfully attained the desired formation in a leaderless consensus, deploying themselves in a plane under constrained rectangular velocities without colliding with each other. Several simulation examples with different values of velocity constraints have been shown to illustrate the operation of constrained controllers while ensuring that the desired leaderless-consensus-based formation remains attainable in a safe manner.

A Nonlinear Optimal Control Approach for Dual-Arm Robotic Manipulators

Dual-arm robotic manipulators are used in industry and for assisting humans since they enable dexterous handling of objects and more agile and secure execution of pick-and-place, grasping or assembling tasks. In this paper, a nonlinear optimal control approach is proposed for the dynamic model of a dual robotic arm. In the considered application, the dual-arm robotic system has to transfer an object under synchronized motion of its two end-effectors so as to achieve precise positioning and to compensate for contact forces. The dynamic model of this robotic system is formulated while it is proven that the state-space description of the robot’s dynamics is differentially flat. Next, to solve the associated nonlinear optimal control problem, the dynamic model of the dual-arm robot undergoes approximate linearization around a temporary operating point that is recomputed at each time-step of the control method. The linearization relies on Taylor series expansion and on the associated Jacobian matrices. For the linearized state-space model of the dual-arm robot, a stabilizing optimal (H-infinity) feedback controller is designed. This controller stands for the solution to the nonlinear optimal control problem under model uncertainty and external perturbations. To compute the controller’s feedback gains an algebraic Riccati equation is repetitively solved at each iteration of the control algorithm. The stability properties of the control method are proven through Lyapunov analysis. The proposed nonlinear optimal control approach achieves fast and accurate tracking of reference setpoints under moderate variations of the control inputs.

Quadcopter Trajectory Tracking Based on Model Predictive Path Integral Control and Neural Network

This paper aims to address the trajectory tracking problem of quadrotors under complex dynamic environments and significant fluctuations in system states. An adaptive trajectory tracking control method is proposed based on an improved Model Predictive Path Integral (MPPI) controller and a Multilayer Perceptron (MLP) neural network. The technique enhances control accuracy and robustness by adjusting control inputs in real time. The Multilayer Perceptron neural network can learn the dynamics of a quadrotor by its state parameter and then the Multilayer Perceptron sends the model to the Model Predictive Path Integral controller. The Model Predictive Path Integral controller uses the model to control the quadcopter following the desired trajectory. Experimental data show that the improved Model Predictive Path Integral–Multilayer Perceptron method reduces the trajectory tracking error by 10.3%, 9.8%, and 5.7% compared to the traditional Model Predictive Path Integral, MPC with MLP, and a two-layer network, respectively. These results demonstrate the potential application of the method in complex environments.

A double neural network model predictive control method for series elastic actuator’s motor thermal protection

Abstract Traditional motor protection methods are conservative, neglecting actual thermal conditions and underutilizing the motor’s performance. This paper proposes a novel double neural network model predictive control (DNMPC)-based protection method to maximize motor performance. First, we analyze the system’s thermal properties and propose a thermal lemma to demonstrate that solving the protection problem involves determining the maximum allowable control input boundary. Second, instead of directly measuring the motor temperature, the neural network (NN) method is proposed to establish the system’s thermal model for estimating the motor temperatures. Third, leveraging the NN model, we propose a model predictive control strategy designed to determine the maximum allowable control input boundaries, which we refer to as the neural network model predictive control (NMPC) method. Consequently, this approach has led to the development of an advanced motor protection system. To further reduce the computational burden, we incorporate an additional NN to directly approximate the NMPC controller, thereby forming our proposed DNMPC approach. Finally, comparative experimental validation demonstrates the effectiveness and superiority of the proposed method. The results indicate that the NN model is highly accurate, eliminating the need for direct temperature measurements and enabling the prediction of future motor temperatures. Additionally, the DNMPC-based protection method significantly improves the joint’s peak torque output by 64.3 % compared to conservative continuous current limited protection methods. The computational efficiency is also notable, with the NMPC achieving a runtime of approximately 20 ms, while the DNMPC achieves only 0.2 ms.