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This article investigates the output feedback H∞$$ {H}_{\infty } $$ control problem of linear systems with infinite distributed input delays. An observer‐based output feedback (OBOF) H∞$$ {H}_{\infty } $$ controller is proposed via the predictor feedback approach, and a sufficient condition for the existence of the OBOF H∞$$ {H}_{\infty } $$ controller is given in terms of a set of linear matrix inequalities. It is shown that the resulting closed‐loop system is globally exponentially stable with a prescribed H∞$$ {H}_{\infty } $$ performance. The obtained results include some results on the same problem for linear systems with bounded distributed input delays as special cases. Two numerical examples are finally presented to illustrate the effectiveness of the proposed H∞$$ {H}_{\infty } $$ controller. [ABSTRACT FROM AUTHOR]

The objective of this research is to enable safety‐critical systems to simultaneously learn and execute optimal control policies in a safe manner to achieve complex autonomy. Learning optimal policies via trial and error, that is, traditional reinforcement learning, is difficult to implement in safety‐critical systems, particularly when task restarts are unavailable. Safe model‐based reinforcement learning techniques based on a barrier transformation have recently been developed to address this problem. However, these methods rely on full‐state feedback, limiting their usability in a real‐world environment. In this work, an output‐feedback safe model‐based reinforcement learning technique based on a novel barrier‐aware dynamic state estimator has been designed to address this issue. The developed approach facilitates simultaneous learning and execution of safe control policies for safety‐critical linear systems. Simulation results indicate that barrier transformation is an effective approach to achieve online reinforcement learning in safety‐critical systems using output feedback. [ABSTRACT FROM AUTHOR]

This paper studies the event‐triggered control of switched linear system with state‐dependent switching law. A dynamic term is introduced to the switching law to acclimatize the dynamic mode‐dependent event‐triggered controller. Besides, neither the switching law nor the controller needs continuous detection of the system states. Because of the event‐triggered and sampling behavior of the controller, asynchronous between the controller and the system modes are encountered. A new multiple Lyapunov functional is proposed to appropriately characterize the synchronous and asynchronous working modes of the system, and a sufficient exponential stability condition is obtained, which is applicable for the cases when some modes or all modes of the switched system are unstabilizable. Moreover, the event‐triggered control and switching law parameters are jointly designed using linear matrix inequalities. Numerical and comparison studies are offered to provide the validity and superiority of the result. [ABSTRACT FROM AUTHOR]

In order to achieve robot trajectory tracking in fixed‐time, a novel fixed‐time zeroing neural network model is designed. Initially, the inverse kinematic model of robot trajectory tracking is translated into a time‐varying quadratic programs problem. Subsequently, a novel fixed‐time zeroing neural network is proposed for solving the time‐varying quadratic programs problem. Furthermore, the fixed‐time stability of this model is rigorously established, and an upper bound of convergence time, irrespective of the initial point, is estimated. Finally, numerical simulation results underscore the efficacy of the proposed methodologies. [ABSTRACT FROM AUTHOR]

This paper explores two non‐linear control techniques for designing an effective control system for an omnidirectional autonomous mobile robot with four Mecanum wheels. Due to the unique wheel structure and four separate wheels, the robot has non‐linear dynamics, multiple inputs and outputs. The first technique uses the state‐dependent Riccati equation (SDRE) to address optimal non‐linear control while considering energy and time constraints. The second technique, using an intermediate variable θ$\theta $, has expanded the Hamilton‐Jacobi‐Belman equation in terms of the power series. Consequently, these equations are reduced to a set of recursive Lyapunov algebraic equations, leading to a closed‐form solution for solving the non‐linear optimal control problem. Finally, the maneuverability and path‐tracking capability of the robot are examined by highlighting the non‐linear term through numerical simulation. [ABSTRACT FROM AUTHOR]

This paper proposes a novel solution to the problem of robust ripple‐free hybrid robust regulator ensuring the elimination of intersample ripples. The paper considers a structurally stable regulation approach in the hybrid framework. A regulator is designed using this technique under periodic sampling and is applied to the nonlinear model of a quadrotor. The control of unmanned autonomous vehicles has become a research topic that is important by itself, particularly in the case of multi‐rotor systems due to their versatility in various applications. Tracking a reference signal for such vehicles can be challenging, particularly when the frequency of communication is limited, or the control station is located far away. The proposed controller is hence tested for this challenging application. [ABSTRACT FROM AUTHOR]

In this article, the prescribed‐time global stabilization problem is taken into consideration when it comes to multi‐input‐multi‐output (MIMO) systems with unknown mismatched coupling nonlinear items. It is assumed that the unknown nonlinearities satisfy the linear growth conditions. First, a class of MIMO coupling nonlinear systems with controllable canonical form are considered. Then, by wielding a time‐varying Lyapunov‐like function and properties of parametric Lyapunov equations, a high‐gain linear time‐varying state feedback control law is developed to attenuate the impact of unknown nonlinear terms. Meanwhile, all state signals and control inputs are globally bounded and the target system becomes stable within the prescribed‐time. Finally, the simulation results on an example system with 3 inputs and 11 state variables verify that the developed control mechanism accomplishes the goal of global stabilization in the pre‐defined time. [ABSTRACT FROM AUTHOR]

Summary: The existence, solution structure, and equivalence of sparse control for linear time‐varying systems are investigated. We proved the existence of the optimal solution of sparse control for the linear time‐varying systems. By using the non‐smooth maximum principle, we are given the necessary conditions for the sparse control optimality for linear time‐varying systems. We proved that the optimal solution of sparse control taking values of ±1$$ \pm 1 $$ and 0. Under the normality of the linear time‐varying systems, we proved an equivalence theorem between the sparse control and L1$$ {L}^1 $$ optimal control. Numerical examples are included to illustrate the effectiveness of the sparse control for linear time‐varying systems. [ABSTRACT FROM AUTHOR]

In renewable energy-sourced power systems, asynchronous motors serve as elements that both produce and consume electricity. The stability and efficiency of the asynchronous motor in renewable energy system should be considered. Although performance optimization studies have been carried out using power circuits that control the asynchronous motor fed with solar energy and control units such as proportional, integral, derivation (PID), and Fuzzy logic; They may be insufficient to eliminate and reduce vibrations in the output values of an induction motor fed with a renewable energy source. Losses occur as the system performance decreases constantly due to oscillations. In this study, an induction motor power system is optimized with the extra control coefficient (ECCA)-PID, which provides semi-linear control for the first time, unlike the power systems controlled by other linear controllers used so far to reduce oscillations, and the vibration losses are eliminated. The speed oscillations, torque oscillations, and oscillation losses of the induction motor in the system are controlled by conventional PID, and Fuzzy logic controllers in order to demonstrate the effectiveness of the proposed method in simulation and experimentation. Then, the results are compared after the proposed method are examined. As a result of the comparisons, while the motor oscillations and losses in the power system continue throughout the control period in traditional control methods, the proposed method reduces the losses to zero in a large part of the control period. [ABSTRACT FROM AUTHOR]

This article investigates the optimal tracking control problem for data-based stochastic discrete-time linear systems. An average off-policy Q-learning algorithm is proposed to solve the optimal control problem with random disturbances. Compared with the existing off-policy reinforcement learning (RL) algorithm, the proposed average off-policy Q-learning algorithm avoids the assumption of an initial stability control. First, a pole placement strategy is used to design an initial stable control for systems with unknown dynamics. Second, the initial stable control is used to design a data-based average off-policy Q-learning algorithm. Then, this algorithm is used to solve the stochastic linear quadratic tracking (LQT) problem, and a convergence proof of the algorithm is provided. Finally, numerical examples show that this algorithm outperforms other algorithms in a simulation. [ABSTRACT FROM AUTHOR]

This paper aims to develop a robust decomposed system control (RDSC) strategy under input constraints for an electro‐mechanical linear actuator (EMLA) facing model uncertainty and external disturbances. At first, a state‐space model of a complex multi‐stage gearbox EMLA system, driven by a permanent magnet synchronous motor (PMSM), is developed, and the non‐ideal characteristics of the ball screw are presented through the model. The result is a four‐order nonlinear strict‐feedback form (NSFF) system decomposed into three subsystems. As the paper's main result, a novel RDSC strategy with uniform exponential stability for controlling subsystem states is presented. This developed controller avoids the "explosion of complexity" problem associated with backstepping by treating the time derivative of the virtual control input as an uncertain system term. The proposed method, despite assuming load disturbances and input constraints with arbitrary bounds, offers a straightforward control approach for a broader range of applications. Further, the controller's performance is evaluated by simulating two distinct duty cycles, each representing different levels of demand on the actuator facing load disturbances near the rated motor performance. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of dissipative-based stabilization for fractional-order nonlinear control systems with uncertainties, time-delay, external disturbances, actuator faults, actuator and sensor saturations. Specifically, a non-fragile reliable dynamic output feedback controller is designed for the purpose of stabilization of the addressed system. Due to the effect of saturation phenomena occurring in both the actuator and sensor, the anti-windup loops framed with the help of the observer design are incorporated into the controller design. Some sufficient conditions are formulated in terms of linear matrix inequalities by choosing a suitable Lyapunov function thereby assuring the dissipative-based stabilization. The derived results are thus validated by two numerical examples including the practical model of two-stage chemical reactor. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of achieving finite‐time fault‐tolerant consensus control for a class of non‐linear fractional‐order multi‐agent systems (NFO‐MAS) using finite‐time fault detection and estimation, as well as a finite‐time state observer. To achieve this, a specific lemma is utilized to rewrite the high‐order model of NFO‐MAS as a lower‐order NFO unique system. By employing new identification rules and introducing a fault estimation method, both the state variables and faults of the agents are estimated within a finite time. Subsequently, a finite‐time sliding mode control law is designed based on the estimated fault and the state variables obtained from the proposed finite‐time observer to achieve consensus within a finite time for the fractional‐order non‐linear MAS. The stability of the fault estimation, state observer, and consensus controller is proven using the finite‐time Lyapunov theory. The effectiveness of the proposed approach is demonstrated through numerical simulations. [ABSTRACT FROM AUTHOR]

This paper investigates the design of a model‐free adaptive iterative learning controller(MFAILC) based on sampled‐data under the presence of denial‐of‐service(DoS) attacks in nonlinear networked control systems. First, the MFAILC is presented only using I/O data, where a compensation mechanism for DoS attacks is proposed. With dynamic linearization techniques, the nonlinear system is transformed into a linear system in the iteration domain. Then an improved MFAILC is designed to actively compensate the lost data caused by DoS attacks, where the estimation of pseudo‐partial derivative (PPD) is improved by establishing the AR model. The proposed algorithm can weaken the adverse effects of the DoS attacks and ensure the excellent tracking performance of the system. Finally, the stability of the method is proved, and the effectiveness of the proposed algorithm is demonstrated by a numerical example. [ABSTRACT FROM AUTHOR]

This article deals with the robust planar rigid formation control problem of three second‐order coleaders with unknown flowfields acting on the velocity and acceleration respectively. To yield the uniform boundedness property of the resulting system, an adaptive projection is introduced to design the novel adaptive neural control law. To avoid the derivatives of Gaussian functions of neural networks, dynamic surface is used. Simulation results are provided to illustrate the effectiveness of the proposed control law. [ABSTRACT FROM AUTHOR]

In biological systems, impulses are often used to model mutations in gene expression. In order to describe the instantaneity of the impulse, this paper employs a hybrid‐index model of impulsive Boolean networks with state‐triggered impulses. Based on this model, the time‐domain output controllability is investigated. Using the quotient mapping method, the hybrid‐domain solutions of this model are mapped to the time‐domain solutions, mathematically. Then a necessary and sufficient condition for output controllability in the time domain is presented. Finally, an example is given to demonstrate the correctness and effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

This paper investigates the linear quadratic regulator (LQR) problem for continuous-time linear systems with redundant control inputs. The LQR control problem has been widely studied, but due to technical difficulties, there is little advance in the study of adding input redundancies. To address this problem, a convergent matrix series, the limit of a monotonically decreasing sequence, is first presented as an upper bound of the symmetric positive definite solution of a class of continuous algebraic Riccati equations (CAREs). Compared with the existing studies on this topic, the obtained bounds are more precise. Moreover, by utilising these upper bounds in the LQR problem of adding input redundancies, a class of sufficient conditions is presented to decrease the quadratic performance index. Finally, the corresponding numerical examples are given to illustrate the effectiveness of our results and compare them with the existing results. Meanwhile, some simulation experiments show that systems with redundant control inputs have good control performance. [ABSTRACT FROM AUTHOR]

Based on the idea of Lyapunov function, we investigate the output finite-time stability of some classes of abstract bilinear systems using feedback control laws. We first design a stabilising feedback control. Then, we study the well-posedness of the system in closed-loop by using the theory of maximal monotone operators. Then we proceed to the question of output finite-time stability in a settling time of the system at hand. The obtained results are also applied to derive output finite time stabilisation results for linear systems. The algorithm of feedback control design is further applied to finite dimension systems and also to PDE of parabolic and hyperbolic types. [ABSTRACT FROM AUTHOR]

Design of feedback control, for a system with slow and fast eigenvalue modes, using single sampling rate results in either information loss (for a larger sampling period) or increased computations (for a smaller sampling period). This paper contributes to designing multirate state feedback controllers for such systems. In this, it is shown that the feedback control for a linear time-invariant system, having slow and fast eigenvalue modes, can be successfully designed by multirate sampling of states in two stages. Multirate sampling refers to sampling slow- and fast-varying states at different rates, that is sampling slow states at a lower rate than the fast states. Here, two approaches for multirate sampling of states are presented, depending on the sampling sequence. In the first approach, fast subsystem states are sampled initially, and then, slow subsystem states are sampled, whereas in the second approach, slow subsystem states are sampled before sampling the fast subsystem states. As far as the two-stage design is concerned, the first stage of the design of feedback control is initiated just after sampling the first subsystem. Then, the left subsystem is sampled, and the second stage of the design of feedback control is accomplished. It is proved that the feedback controls derived with the multirate sampling of states stabilize the full-order system in both approaches. The design and implementation aspects of both approaches are compared. Finally, the applicability of the proposed control is demonstrated by simulating two examples. Simulations are also compared with other methods proposed in the literature. [ABSTRACT FROM AUTHOR]

Iterative learning control (ILC) algorithms appeared in connection with the problems of increasing the accuracy of performing repetitive operations by robots. They use information from previous repetitions to adjust the control signal on the current repetition. Most often, information from the previous repetition only is used. ILC algorithms that use information from several previous iterations are called higher-order algorithms. Recently, interest in these algorithms has increased in the literature in connection with robotic additive manufacturing problems. However, in addition to the fact that these algorithms have been little studied, there are conflicting estimates regarding their properties. This paper proposes new higher-order ILC algorithms for linear discrete and differential systems. The idea of these algorithms is based on an analogy with multi-step methods in optimization theory, in particular, with the heavy ball method. An example is given that confirms the possibility to accelerate convergence of the learning error when using such algorithms. [ABSTRACT FROM AUTHOR]

The large deviations of linear control system trajectories from the equilibrium position during the stabilization process, known as peak-effect, represent a serious obstacle to the design of cascade control systems and to guidance stabilization. Evaluation of such deviations is an important problem not only for control theory but also for other branches of mathematics where similar phenomenon appears as, for example, in numerical analysis, in the study of hydrodynamic stability and transition to turbulence, in the dynamics of vehicular platoons, and many others. The aim of this paper is to improve one of the main results concerning upper bounds for the peak-effect in linear control systems in the work by B.T. Polyak and myself in 2016. As the lower bound for overshoot proved by R.N. Izmailov in 1987 shows, the asymptotic estimate for the upper bound obtained here cannot be improved. [ABSTRACT FROM AUTHOR]

Summary: This paper proposes a systematic framework for stability and guaranteed cost control of linear impulsive systems subject to random time‐ and event‐triggering impulses. Moment stability criteria and design methods of time‐ and event‐triggered controllers with guaranteed quadratic performance for the impulsive system are established. It shows that the proposed event‐triggered controller in the sense that it guarantees at least the same quadratic performance function bound as the designed time‐triggered guaranteed cost controller, however, with a larger, or at most equal, average inter‐transmission time. Based on the proposed framework of random‐impulses systems, a stochastic dynamic event‐triggered control strategy is proposed to solve sampled‐data control systems in the presents of sporadic measurements or stochastic sampling. Numerical simulations illustrate the effectiveness of the proposed theoretical results. [ABSTRACT FROM AUTHOR]

This paper is a review of the results on the real-time optimal control problem for linear systems obtained by the Minsk school by mathematical methods of optimal control. We consider optimal control problems for dynamical objects, their deterministic mathematical models and perfect measurements of states, objects with disturbances and imperfect measurements of the observed input and output signals, the problem of optimal decentralized control of groups of interconnected dynamical objects, and application of real-time optimal control problems and the control principle to solving stabilization problems. [ABSTRACT FROM AUTHOR]

Controlling the Permanent Magnet Synchronous Motor (PMSM) can be challenging due to the nonlinearity of its dynamics, which makes it difficult to design control strategies that are both robust and effective. To address this challenge, this paper presents a novel control strategy rooted in the concept of passivity that combines field‐oriented control (FOC). This strategy compels the PMSM to accurately follow velocity and electrical torque trajectories. The approach, known as passivity‐based control (PBC), entails reshaping the inherent system energy while introducing the necessary damping to attain the desired objectives. A crucial aspect involves identifying workless force terms within the process model. Despite their presence, these terms do not impact the energy balance and stability properties. As a result, eliminating these terms is unnecessary. This simplicity in control architecture not only preserves system stability but also bolsters overall robustness. The system's overall stability and the current tracking error's exponential convergence have both been demonstrated analytically. In order to maintain stability, the controller accounts for the nonlinearities of the plant and approximates the unstructured dynamics of the PMSM. The proposed control is designed using the dq model of the PMSM, which avoids the model's structure destruction due to singularities, since the dq model does not depend explicitly on the rotor angular position. Experimental results shown further, illustrate speed and position control with a desired pair calculated by a filter or a proportional‐integral (PI) controller for speed control and a proportional‐integral‐derivative (PID) controller for position control. Also the correlation between practical and theoretical results is given as well as the robustness test in relation to the uncertainties of the PMSM's inertia moment. The results demonstrates the effectiveness of the proposed strategy in controlling the PMSM under different operating conditions, highlighting its potential for industrial applications. [ABSTRACT FROM AUTHOR]

This manuscript proposes a robust excitation control strategy for synchronous generators using backstepping theory and an artificial neural network with a radial basis function to improve power system performance during disturbances and parametric uncertainties. The artificial neural network is used to estimate unmeasurable quantities and unknown internal parameters of a recursive backstepping control. Lyapunov theory is used to carry out the stability analysis and to deduce the online adaptation laws of artificial neural network parameters (weights, centres and widths). To validate the performance of this approach, simulations are performed on an IEEE 9 bus multi‐machine power system. Different test results, compared with those of an existing non‐linear adaptive controller, confirm the high robustness of the proposed method against disturbances and uncertainties. [ABSTRACT FROM AUTHOR]

This article explores the problem of stabilizing continuous-time switched linear autonomous systems under safety-critical constraints. The authors propose a switching law that achieves both stability and safety by characterizing the safe initial set and developing a design procedure. The research focuses on the constructive design of switched linear autonomous systems to achieve physical safety and exponential convergence of state trajectories. The article includes a proof and proposition related to the stability and safety of the switched system, as well as a computational procedure to estimate the safe initial domain. An illustrative example is provided to demonstrate the effectiveness of the design scheme. The work is supported by the National Key R&D Program of China and the Natural Science Foundation of Shandong Province. [Extracted from the article]

This document provides brief biographical information about three individuals involved in the field of mathematics and systems science. The first individual is a professor at the ISS Academy of Mathematics and Systems Science, CAS, with research interests in system modeling, adaptive control, stochastic systems, and multi-agent systems. The second individual is a professor at Beijing Institute of Technology, specializing in adaptive control, quantized control, multi-agent systems control, and their applications to aircraft control systems. The third individual is a Ph.D. student at the Academy of Mathematics and Systems Science, with research interests in quantized control, adaptive control, and sparse identification. [Extracted from the article]

In this paper, we consider an evolution linear control system. First, by using Weiss–Staffans perturbation results we prove that, under suitable conditions, our evolution system is well posed. Next, we give a characterisation of observability of the evolution system via some spectral condition. We also provide sufficient condition to ensure the stability of the system in the periodic case. As applications, we consider concrete problems including wave equation in one dimension. [ABSTRACT FROM AUTHOR]

For periodic linear control systems with bounded control range, an autonomized system is introduced by adding the phase to the state of the system. Here, a unique control set (i.e., a maximal set of approximate controllability) with nonvoid interior exists. It is determined by the spectral subspaces of the homogeneous part which is a periodic linear differential equation. Using the Poincaré sphere, one obtains a compactification of the state space allowing us to describe the behavior "near infinity" of the original control system. Furthermore, an application to quasi-affine systems yields a unique control set with nonvoid interior. [ABSTRACT FROM AUTHOR]

The hybrid minimum principle (HMP) is established for the optimal control of deterministic hybrid systems with both autonomous and controlled switchings and jumps where state jumps at the switching instants are permitted to be accompanied by changes in the dimension of the state space and where the dynamics, the running and switching costs as well as the switching manifolds and the jump maps are permitted to be time varying. First-order variational analysis is performed via the needle variation methodology and the necessary optimality conditions are established in the form of the HMP. A feature of special interest in this work is the explicit presentations of boundary conditions on the Hamiltonians and the adjoint processes before and after switchings and jumps. Analytic and numerical examples are provided to illustrate the results. [ABSTRACT FROM AUTHOR]

In this paper, a theorem is obtained that gives sufficient input-to-state stability conditions for linear systems with control delay and additive disturbances. Stabilizing feedback is considered available in the absence of delay and disturbances. The mathematical tools are the Lyapunov–Krasovskii functional, the Jensen inequality and the double Hadamard inequality. The critical delay is highlighted. [ABSTRACT FROM AUTHOR]

The quadratic matrix equation (QME) Q(X)=AX2+BX+C=0,$$\begin{equation*} Q(X)=AX^{2}+BX+C=0, \end{equation*}$$occurs in the branches such as the quadratic eigenvalue problems and quasi‐birth‐death processes. Also, the numerical solution of QMEs is an essential step in many computational methods for linear‐quadratic and robust control, filtering, controller order reduction, inner‐outer factorization, spectral factorization, and other applications. In this study, schemes are presented to solve the QME based on the Hermitian and skew‐Hermitian splitting (HSS). It is shown that the proposed schemes converge to the solutions of the QME. Finally, some examples are solved to discover the application of the schemes in comparison with Newton's method. [ABSTRACT FROM AUTHOR]

This paper presents a novel input channel gain adaptive active disturbance rejection control (ICGA‐ADRC) framework for the nonlinear control system with large load variation. This paper first introduces the design of ICGA‐ADRC and proves its stability through the rigorous Lyapunov approach. Subsequently, the proposed controller is simulated by subjecting it to a nonlinear mass‐spring‐damping system characterized by significant load variations. Furthermore, the position‐tracking performance of the controller is tested experimentally by using a motor‐driven pendulum system with various loads. Finally, the results of both simulations and experiments show that the ICGA‐ADRC is capable of compensating for system model uncertainty and external perturbation while accurately estimating the system input channel gain in real‐time. The innovation of this paper is that the robustness of active disturbance rejection control (ADRC) to the system load variation is significantly strengthened by integrating robust adaptive finite‐time parameter estimation method into the conventional ADRC control architecture. [ABSTRACT FROM AUTHOR]

This paper investigates the learning and control problem of sampled‐data systems with only output measurements. A unified approach is presented by integrating the sampled‐data observer and deterministic learning. First, an adaptive radial basis function network (RBFN) learning controller with a sampled‐data observer is designed to track a recurrent reference model. Along the trajectory estimated by the observer, it is proven that the RBFN weights can exponentially converge to their ideal values with the satisfaction of a persistent excitation (PE) condition and the closed‐loop dynamics can be accurately learned during the output‐feedback process. Second, by using the learning results, a knowledge‐based output‐feedback controller is developed to improve the tracking performance. Further research shows that choosing appropriate parameters for the observer and RBFN can guarantee learning and control performance. The significance of the proposed approach is that the closed‐loop dynamics of the output‐feedback process can be accurately learned and further utilized to improve control performance. Simulation studies indicate the effectiveness and advantages of the learning control approach. By combining deterministic learning and sampled‐data observer, an adaptive radial basis function network (RBFN) controller is designed to achieve the tracking of a recurrent reference model, which leads to the satisfaction of the PE condition. During the stable tracking process, closed‐loop dynamics can be accurately identified/learned by the RBFN under the PE condition. Based on the learned dynamics, a new knowledge‐based controller is developed for another output feedback task, which reduces computational complexity and improves tracking performance. [ABSTRACT FROM AUTHOR]

Remote control over communication networks with bandwidth-constrained channels has attracted considerable recent attention because it holds the promise of enabling a large number of real-time applications, such as autonomous driving, smart grids, and the industrial internet of things (IIoT). However, due to the limited bandwidth, the sub-packets or even bits have to be transmitted successively, thereby experiencing non-negligible latency and inducing serious performance loss in remote control. To overcome this, we introduce an incremental coding method, in which the actuator acts in real time based on a partially received packet instead of waiting until the entire packet is decoded. On this basis, we applied incremental coding to a linear control system to obtain a remote-control scheme. Both its stability conditions and average linear-quadratic-Gaussian-(LQG) cost are presented. Then, we further investigated a multi-user remote-control method, with a particular focus on its applications in the demand response of smart grids over bandwidth-constrained communication networks. The utility loss due to the bandwidth constraint and communication latency are minimized by jointly optimizing the source coding and real-time demand response. The numerical results show that the incremental-coding-aided remote control performed well in both single-user and multi-user scenarios and outperformed the conventional zero-hold control scheme significantly under the LQG metric. [ABSTRACT FROM AUTHOR]

This article introduces a novel approach named HBA‐dHoSMO, which combines a continuous decentralized higher‐order sliding mode controller‐based observer (dHoSMO) with the honey badger algorithm (HBA), specifically designed for load frequency control in multi‐area power systems (MAPSs). Traditional sliding mode controllers (SMCs) employed in load frequency control of MAPSs often face challenges related to chattering and oscillations, leading to decreased robustness and stability. Additionally, tuning the parameters for these SMC designs to achieve optimal performance in MAPSs can be challenging. The HBA‐dHoSMO is proposed to address the issues of chattering and oscillations, while the optimal parameters for SMC design are obtained using HBA. The stability analysis of the entire system is conducted using linear matrix inequality and the Lyapunov stability theory, affirming the reliability and feasibility of the approach. A comprehensive set of case studies is performed under various configurations and conditions. Additionally, particle swarm optimization and tuna swarm optimization, in conjunction with SMC‐based and proportional–integral–derivative controllers, are examined for performance comparison. Simulation results demonstrate the superior performance of the proposed controller across all case studies. This is evidenced by the lowest integral time absolute error values recorded as 0.0133, 6.45 × 10−4, and 0.0167 for single‐, two‐, and three‐area power systems, respectively. [ABSTRACT FROM AUTHOR]

To address significant disturbances, including sudden air flow variation, model uncertainty, and unavoidable measurement noises during aeroengine transient tests in the intake environmental pressure simulation system (IEPSS), a sliding mode active disturbance rejection controller (SMADRC) is designed. The sliding mode control in SMADRC can deal with unmatched disturbances that are beyond the capabilities of the extended state observer (ESO) in ADRC. And the particle swarm optimization (PSO) algorithm is introduced to tune and optimize the controller parameters to further enhance the performance. To validate the effectiveness of the proposed method, simulations are conducted on the IEPSS software platform. The simulation results clearly demonstrate PSO‐SMADRC can reduce the mean squared error by 60.9%, the input oscillation by 68.7%, and the maximum deviation by 53.9%, compared with LADRC originally applied in the IEPSS. [ABSTRACT FROM AUTHOR]

An algorithm for finding a control of a linear switched system by means of Geometric Algebra is designed. More precisely, we develop a switching path searching algorithm for a two‐dimensional linear dynamical switched system with a non‐singular matrix whose integral curves are formed by two sets of centralized ellipses. It is natural to represent them as elements of Geometric Algebra for Conics and construct the switching path by calculating switching points, i.e., intersections and contact points. For this, we use symbolic algebra operations or, more precisely, the wedge and inner products that are realizable by sums of products in the coordinate form. Therefore, no numerical solver to the system of equations is needed. Indeed, the only operation that may bring in an inaccuracy is vector normalization, i.e., square root calculation. The resulting switching path is formed by pieces of ellipses that are chosen, respectively, from the two sets of integral curves. The switching points are either intersections in the first or final step of our algorithm, or contact points. This choice guarantees the optimality of the switching path with respect to the number of switches. Two examples are provided to demonstrate the search for the intersections of the conics and, consequently, a description is presented of the construction of a switching path in both cases. [ABSTRACT FROM AUTHOR]

This paper investigates partial approximate controllability of fractional linear and semi-linear control systems involving the conformable derivative. First, we derive sufficient and necessary conditions for partial approximate controllability of fractional linear systems over a small interval. Then, we apply a new approach, different from typical methods involving complexity inequalities and fixed point theorems, to obtain sufficient conditions for partial approximate controllability of semi-linear fractional control systems, assuming that the linear part is partially approximately controllable. The effectiveness of these results is demonstrated through an illustrative example. [ABSTRACT FROM AUTHOR]

To develop a high-performance permanent magnet linear servo system, a novel intelligent second-order complementary sliding mode control (ISOCSMC) method is proposed in this paper. First, the mathematical model of permanent magnet linear synchronous motor (PMLSM) with uncertainties is established. To conquer the uncertainties and reduce chattering, a second-order complementary sliding mode control (SOCSMC) with fast convergence and global robustness is developed. However, because the value of lumped uncertainty is difficult to obtain in advance and cannot be adjusted automatically, an intelligent control system using recurrent Gegenbauer fuzzy neural network (RGFNN) based on improved whale optimization algorithm (IWOA) is proposed to further improve the servo performance. RGFNN acts as an estimator to approximate the lumped uncertainty, and IWOA is used to convergence of the output tracking error and improve the convergence speed of RGFNN. Finally, the experimental results demonstrate the proposed controller exhibits high tracking accuracy and strong robustness against the parameter variations and load disturbances in comparison with the recently reported control strategies. [ABSTRACT FROM AUTHOR]

This article presents a chance‐constrained tube‐based model predictive control (MPC) method for tracking linear time‐invariant systems based on data‐driven uncertainty sets. By defining the terminal admissible set to consider all the possible steady‐states and reformulating the stochastic tube‐based MPC framework, the proposed method can systematically hedge against the impact of uncertainties and ensure tracking for all reachable operating setpoints. To reduce the conservatism of control performance while enlarging the feasible region, a data‐driven polyhedral uncertainty set is constructed by using the principal component analysis technique, which can effectively capture correlations among uncertain variables. Since state constraint violations in a certain probability are allowed, a probability uncertainty set is constructed by using statistic limit and cutting plane methods to formulate a stochastic tube to ensure constraint satisfaction. The recursive feasibility and stability can be guaranteed if the uncertainties are bounded. The effectiveness of the proposed method is verified by numerical examples and tracking problems of a thickening process. [ABSTRACT FROM AUTHOR]

The problem of $ L_1 $ L 1 output tracking control of positive linear systems in finite time is addressed in this paper. By constructing a linear copositive Lyapunov–Krasovskii functional, some sufficient conditions are achieved to ensure that the states are finite-time bounded and the measurement outputs have $ L_1- $ L 1 − gain performance for given systems, respectively. Next, a state feedback controller is designed to ensure that the output signals of the tracking system can effectively trace the specified signals of reference model with finite-time boundedness and $ L_1 $ L 1 -gain performance. Finally, an example is given to illustrate the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

This paper investigates reachable set estimation and state-feedback controller design for linear time-delay control systems with bounded disturbances. By constructing an appropriate Lyapunov–Krasovskii functional, we obtain a delay-dependent condition, which determines the admissible bounding ellipsoid for the reachable set of the system we considered. Then, a sufficient condition in the form of liner matrix inequalities is given to solve the problem of controller design and reachable set estimation. Then, by minimizing the volume of the ellipsoid and solving the liner matrix inequality, we obtain the desired ellipsoid and controller gain. A comparative numerical example is given to show the effectiveness of our result. [ABSTRACT FROM AUTHOR]

The non-linear power-current characteristics of a photovoltaic generator (GPV) present a challenge in maximizing power production. To address this issue, Maximum Power Point Tracking (MPPT) methods, such as the Adaptive Neuro-Fuzzy Inference System (ANFIS), are commonly used due to their quick response and minimal oscillation. As well, sliding mode control (SMC) is a popular method for controlling linear and nonlinear systems because of its high robustness. In this study, the principal purpose is to develop a new approach based on the combination of ANFIS and Terminal Robust Sliding Mode Control (ANFIS-TRSMC) to resist the PV system against uncertain conditions and track the optimal power point. The simulation results show that the ANFIS-TRSMC controller has an accurate, fast, and robust response in comparison with other algorithms such as perturb and observe and the maximum power voltage–based TRSMC controller. [ABSTRACT FROM AUTHOR]

In this paper, model‐free finite‐horizon H∞$$ {H}_{\infty } $$ tracking control for discrete‐time linear systems is studied. By formulating an augmented system consisting of the considered linear system and the command generator system, an augmented time‐varying Riccati equation whose solutions can achieve the finite‐horizon H∞$$ {H}_{\infty } $$ tracking control is derived. Then, a time‐varying Q‐function which contains the control input and disturbance input is designed. A time‐varying Q‐function‐based method is developed to learn the solutions of the finite‐horizon H∞$$ {H}_{\infty } $$ tracking control problem without knowing the system model information nor any model identification methods. It is proved that the solutions of the time‐varying Q‐function‐based method converge to the optimal solutions of the augmented time‐varying Riccati equation. At last, simulation examples are provided to show the feasibility and advantages of the time‐varying Q‐function‐based method compared to the infinite‐horizon Q‐learning‐based H∞$$ {H}_{\infty } $$ tracking control method. [ABSTRACT FROM AUTHOR]

In this paper, a composite fixed‐time sliding mode controller is proposed to address the problems of finite‐time escape and large initial error inherent in disturbance observer (DOB) based controllers. The proposed hybrid control strategy utilizes a fixed‐time DOB and is designed to stabilize a class of second‐order systems in the presence of both matched and mismatched disturbances, while ensuring fixed‐time convergence. First, a fixed‐time DOB is developed to estimate both types of disturbances. Second, a robust sliding mode variable with variable exponent coefficient and a former finite‐time sliding mode controller are proposed to guarantee state convergence without using DOB estimation, thereby preventing the state from diverging due to the unknown large initial error caused by DOB and ensuring convergence prior to switching. Third, a latter robust fixed‐time DOB‐based controller is designed after exact estimation of disturbances is achieved and an estimation of the overall convergence time is provided. Furthermore, strict Lyapunov analysis is employed to prove that the disturbed system under the fixed‐time DOB and composite sliding mode controller is fixed‐time stable. Simulation results for a standard planar uncertain system and Buck converter with mismatched disturbance demonstrate the effectiveness of the proposed controller. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the controllability conditions of linear control systems involving distinct local fractional derivatives. Sufficient conditions for controllability using Kalman rank conditions and the Gramian matrix are presented. We show that the controllability of the local fractional system can be determined by the invertibility of the Gramian matrix and the full rank of the Kalman matrix. We also show that the local fractional system involving distinct orders is controllable if and only if the Gramian matrix is invertible. Illustrative examples and an application are provided to demonstrate the validity of the theoretical findings. [ABSTRACT FROM AUTHOR]

In the paper, we investigate the optimal control problem for a linear system of ordinary differential equations with linear boundary conditions. The boundary conditions involve the values of the phase variable both at separate intermediate points and their integral values over individual intervals of the independent variable. In the problem, we determine the controls involved in the differential equations and the values of the right-hand sides of multipoint and integral boundary conditions. The necessary conditions for the existence and uniqueness of the solution to the boundary value problem, the convexity of the objective functional and the necessary optimality conditions for the optimizable parameters are obtained. The conditions contain constructive formulas of the gradient components of the functional. The numerical solution of an illustrative problem is considered. [ABSTRACT FROM AUTHOR]

In this paper, we examine the behavior of phase trajectories of fractional two-dimensional linear systems with control. We focus on the fractional double integrator. Fractional differentiation operators are understood in the sense of Hilfer or Hadamard. Admissible controls are assumed to be norm-bounded; we search for them in the functional class L∞[0, T], T > 0. Based on explicitly specified constraints on the norm of a control, we calculate boundary trajectories of the system, which determine a domain on the phase plane in which all admissible trajectories of the system are localized. We show that the solution of the optimal control problem by the method of moments leads to some minimization problem that does not have an analytical solution in the general case (for arbitrary values of the indices of fractional differentiation in the equations governing the system). We establish conditions under which the minimization problem has a solution and determine subdomains of possible localization of this solution. Exact and approximate analytical solutions of the minimization problem are constructed in some particular cases and the results of numerical computation of the minimum are given. The corresponding solutions of the optimal control problem are obtained and phase trajectories of the system are found. [ABSTRACT FROM AUTHOR]

This study aims to use the theory of iterative control algorithm to learn and extract the semantic structural features of large-scale network data by analyzing and exploring the semantic structural features of large-scale networks with the help of data visualization analysis methods. In addition, it conducts relevant research on the high-quality simplified representation of computer network graphs based on the effective extraction of structural features and combined with graph sampling techniques. An iterative learning control algorithm based on reference trajectory update is proposed for the tracking control problem of discrete linear control system output subject to non-repetitive perturbation. First, the controller is parametrically optimized by constructing a performance index function to track the system output quickly and accurately at the desired point of reference trajectory update. Second, when the system output is affected by a batch of non-repetitive perturbations, a new performance indicator function is further constructed by introducing a Lagrange multiplier algorithm to establish multi-objective performance indicators to optimize the robust iterative learning controller. Finally, the algorithm is applied to a computer network graph design system, and the simulation results verify the reasonableness and effectiveness of the algorithm. These results show that the suggested technique surpassed the existing approaches with accomplishments such as an average degree of 12.5%, a clustering coefficient of 65%, network efficiency of 91%, and higher modularity, community identification, and network embedding scores. [ABSTRACT FROM AUTHOR]