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Optimizing the performance of motion control systems with variations in nonlinear parameters is not an easy task. To accomplish this task, it is important to design the controller using the linear system approach. In this study, a linear parameter varying (LPV) control method is proposed in which nonlinearities are treated as parameter variations for planar motors. The proposed control method consists of the force and torque modulation with the commutation scheme and the nonlinear current controller with H∞ state feedback control in the form of LPV synthesis to improve the position-tracking performance. An interpolated gain-scheduling controller based on LPV synthesis is determined by applying H∞ control to a linear matrix inequality technique. An interpolated gain-scheduling controller can attenuate disturbance without disturbance estimation. The effectiveness of the proposed control method is evaluated using simulation results and compared with the conventional proportional–integral–derivative control to verify both improved position-tracking performance and disturbance attenuation. [ABSTRACT FROM AUTHOR]

This paper proposes a distributed robust frequency control (DRFC) scheme for industrial applications that can effectively adjust the frequency and regulate the active power-sharing ratio of islanded microgrids (MGs). The proposed method also enhances the H∞ performance and the transient response of the MGs by imposing pole placement constraints in the linear matrix inequality (LMI) framework. The proposed scheme utilizes the information on active power and frequency deviations of each distributed generator (DG) and its neighboring DGs to generate an auxiliary control signal implemented by the secondary control layer. The auxiliary control signal improves the input of the droop controller block at the primary control layer, ensuring both frequency regulation and proportional active power-sharing among the DGs. To show the robustness of this novel feature, an AC-islanded MG is simulated under various load and fault scenarios. The simulation results demonstrate the effectiveness and efficiency of the proposed scheme in stabilizing the frequency and damping ratio of the MG while maintaining an active power-sharing balance. [ABSTRACT FROM AUTHOR]

This study aims to explore the problem of H∞ fuzzy control with an adjustable convergence rate for switched nonlinear systems with time-varying delays under the persistent dwell time (PDT) switching. Compared to the widely studied dwell time (DT) switching or average dwell time (ADT) switching in existing literature, PDT switching provides a more comprehensive consideration of the switching frequency and has a broader range of applicability. Subsequently, by combining the interval stability definition, T-S fuzzy model, PDT technique, and Lyapunov-Krasovskii (L-K) functional, a new H∞ fuzzy control criterion for adjusting the convergence rate of switched nonlinear systems with time-varying delays is proposed. This criterion enables the development of a novel method for constructing H∞ fuzzy controllers, which can regulate the system’s convergence rate and achieve the specified H∞ performance. Combining the above methods, an algorithm is introduced to precisely control the convergence rate of the target system. Finally, the effectiveness of this method is validated through a control example of a single-link robot arm. [ABSTRACT FROM AUTHOR]

Abstract This paper studies the H∞ control problem for polynomial time‐varying systems. The H∞ control problem has been much less investigated for time‐varying systems in comparison to the time‐invariant systems. Approximate dynamic programming (ADP) is an optimal method to solve the control problems. Therefore, it is valuable to solve the polynomial time‐varying H∞ control problem with the ADP approach. Considering the time as an independent variable for sum‐of‐squares (SOS) optimization problems, an SOS‐based ADP method is proposed to solve this problem. A policy iteration algorithm is presented, where in its policy evaluation step it is sufficient to solve an optimization problem. Some constraints are added to this optimization problem to guarantee the closed‐loop exponential stability. The convergence and stability properties of the proposed algorithm are stated and proven. Moreover, in order to design an H∞ controller with a smaller disturbance attenuation coefficient, a two‐loop algorithm is suggested. Finally, the effectiveness of the proposed method is demonstrated by simulation examples.

In this paper, passive control and H ∞ state feedback based on non-fragile observer are presented for a class of uncertain, nonlinear and input time-delay systems. Firstly, taking uncertainties, nonlinearities and input time-delay into account, non-fragile observer and controller are designed and the perturbations of controller gain and observer gain are processed. Secondly, for the dynamic disturbances, an appropriate non-fragile state feedback controller based on the observation is selected to prove that the states of closed-loop system can be passive and stabilized with H ∞ performance for continuous time system. Moreover, the problems such as time-delay are handled in virtue of Lyapunov method and linear matrix inequalities (LMIs). Finally, the simulation results demonstrate the validity of the proposed control design method. [ABSTRACT FROM AUTHOR]

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This paper studies the H∞ control problem for polynomial time‐varying systems. The H∞ control problem has been much less investigated for time‐varying systems in comparison to the time‐invariant systems. Approximate dynamic programming (ADP) is an optimal method to solve the control problems. Therefore, it is valuable to solve the polynomial time‐varying H∞ control problem with the ADP approach. Considering the time as an independent variable for sum‐of‐squares (SOS) optimization problems, an SOS‐based ADP method is proposed to solve this problem. A policy iteration algorithm is presented, where in its policy evaluation step it is sufficient to solve an optimization problem. Some constraints are added to this optimization problem to guarantee the closed‐loop exponential stability. The convergence and stability properties of the proposed algorithm are stated and proven. Moreover, in order to design an H∞ controller with a smaller disturbance attenuation coefficient, a two‐loop algorithm is suggested. Finally, the effectiveness of the proposed method is demonstrated by simulation examples. [ABSTRACT FROM AUTHOR]

In this paper, an $\textrm{H}_{{\infty }}$ dynamic output feedback controller is experimentally implemented for the position regulation of a fully actuated tilted-rotor octocopter unmanned aerial vehicle (UAV) to improve wind disturbance rejection during station-keeping. To apply the lateral forces, besides the standard tilt-to-translate (attitude-thrust) movement, tilted-rotor UAVs can generate vectored (horizontal) thrust. Vectored-thrust is high-bandwidth but saturation-constrained, while attitude-thrust generates larger forces with lower bandwidth. For the first time, this paper emphasizes the frequency-dependent allocation of weighting matrices in $\textrm{H}_{{\infty }}$ control design based on the physical capabilities of the fully actuated UAV (vectored-thrust and attitude-thrust). A dynamic model of the tilted-rotor octocopter, including aerodynamic effects and rotor dynamics, is presented to design the controller. The proposed $\textrm{H}_{{\infty }}$ controller solves the frequency-dependent actuator allocation problem by augmenting the dynamic model with weighting transfer functions. This novel frequency-dependent allocation utilizes the attitude-thrust for low-frequency disturbances and vectored-thrust for high-frequency disturbances, which exploits the maximum potential of the fully actuated UAV. Several wind tunnel experiments are conducted to validate the model and wind disturbance rejection performance, and the results are compared to the baseline PX4 Autopilot controller on both the tilted-rotor and a planar octocopter. The $\textrm{H}_{{\infty }}$ controller is shown to reduce station-keeping error by up to 50% for an actuator usage 25% higher in free-flight tests. [ABSTRACT FROM AUTHOR]

This paper is concerned with event-triggered H∞ control of sampled-data systems. Its novelties lie in three aspects: (i) A novel accumulated-state-error-based event-triggered scheme is introduced by comparing the integral of the state error from tk to t with the system state sampled at tk. This condition works well due to the fact that the so-called Zeno behaviour does not occur. (ii) A novel Lyapunov functional is constructed to establish a criterion to ensure some certain H∞ performance of the closed-loop system. This Lyapunov functional is dependent on the integral of the state error involved in the event-triggered scheme. (iii) Under the event-triggered sampling scheme, suitable state-feedback controllers can be designed rather than be given a priori. Moreover, a self-triggered implementation of the proposed event-triggered sampling scheme is presented as well. Finally, a batch reactor model and an inverted pendulum system are given to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Considering overshoot and chatter caused by the unknown interference, this article studies the adaptive robust optimal controls of continuous‐time (CT) multi‐input systems with an approximate dynamic programming (ADP) based Q‐function scheme. An adaptive integral reinforcement learning (IRL) scheme is proposed to study the optimal solutions of Q‐functions. First, multi‐input value functions are presented, and Nash equilibrium is analyzed. A complex Hamilton–Jacobi–Issacs (HJI) equation is constructed with the multi‐input system and the zero‐sum‐game‐based value function. It is a challenging task to solve the HJI equation for nonlinear system. Thus, A transformation of the HJI equation is constructed as a Q‐function. The neural network (NN) is applied to learn the solution of the transformed Q‐functions based on the adaptive IRL scheme. Moreover, an error information is added to the Q‐function for the issue of insufficient initial incentives to relax the persistent excitation (PE) condition. Simultaneously, an IRL signal of the critic networks is introduced to study the saddle‐point intractable solution, such that the system drift and NN derivatives in the HJI equation are relaxed. The convergence of weight parameters is proved, and the closed‐loop stability of the multi‐system with the proposed IRL Q‐function scheme is analyzed. Finally, a two‐engine driven F‐16 aircraft plant and a nonlinear system are presented to verify the effectiveness of the proposed adaptive IRL Q‐function scheme. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of designing an observer-based event-triggered H ∞ controller for a Hamiltonian system with delays incorporated in the underlying network. As our contributions, we first propose an event-triggered scheme which uses the Hamiltonian to decide whether to trigger the event generator at the sampling time. Additionally, when states are not exactly known globally asymptotically stable, we proceed to design an observer-based controller with which the resulting closed-loop system can be transformed into a time-delay Hamiltonian system. Based on the structural characteristic of the Hamiltonian systems, sufficient conditions are given to guarantee the closed-loop system to achieve the H ∞ performance index with external disturbances in available and unavailable states, respectively. Finally, multi-machine power systems as simulation examples are illustrated to validate our proposed results. • Event-triggered H ∞ control is discussed via a Hamiltonian approach. • A discrete event-triggered scheme is proposed for saving communication resources. • An observer is designed for networked Hamiltonian systems with unknown states. • The influence of network-induced delay is considered. [ABSTRACT FROM AUTHOR]

This study investigates the automated transportation control problem of an offshore floating platform that has limited or no maneuverability. The proposed solution involves two tugboats pushing into the platform and two other tugs towing it in the opposite direction. By implementing cooperative control of these tugs, the desired planar motion of the platform is achieved. For this, the proposed control consists of the following components: (1) an observer estimates the environmental disturbances, (2) a platform motion controller acts as the supervisory control, (3) an optimal constrained allocation distributes the required actions over the tugboats, and (4) the tugboats' controller derived the control inputs of the tugs to fulfill these requirements. Simulation studies are conducted where the proposed solution is compared to one based on the robust H∞ control framework. The results prove the efficiency and robustness of the proposed system. [ABSTRACT FROM AUTHOR]

A predefined-time $H_{\mathrm {\infty }}$ trajectory tracking control scheme based on self-adjusting prescribed performance functions and dynamic relative threshold event-triggered mechanism is proposed for a five-degree-of-freedom underactuated autonomous underwater vehicle (AUV) with unknown external disturbances and actuators saturated. First, a new self-adjusting prescribed performance function is designed to ensure that the tracking errors do not exceed the prescribed bounds and to solve the singularity problem of general prescribed performance control (PPC) due to actuator saturation. Second, a predefined-time $H_{\mathrm {\infty }}$ controller combined with a predefined-time dynamic surface control (DSC) method is proposed to guarantee that system signals converge to the neighborhood of zero in a predefined time without adjusting the control parameters and to improve system robustness to uncertain disturbances. Third, an improved dynamic relative threshold event-triggered method is designed to save the communication resources of an underactuated AUV system. Then, the Lyapunov stability proof indicates that all signals in the closed-loop system are predefined-time bounded, and the trajectory tracking errors can converge to the neighborhood of zero within the set desired time. Finally, the simulations not only demonstrate the performance of the proposed controller-controlled system but also verify the effectiveness of the proposed scheme.

This study addresses the $H_{\infty }$ control design problem for actively controlled systems with input time delay. A novel control algorithm is proposed to derive the $H_{\infty }$ controller. The core concept involves employing the Chebyshev spectral continuous-time approximation (CHsCTA) and defining specific augmented matrices to reconfigure the original time-delayed system into a transformed system that is free of time delay. Subsequent control design is executed on this transformed system, facilitating the derivation of an $H_{\infty }$ controller. Case studies demonstrate that compared with the existing Lyapunov-Krasovskii (L-K) functional-based algorithms, the proposed control algorithm is distinguished by its reduced conservatism and enhanced $H_{\infty }$ control performance.

This paper proposes an optimal controller and estimator for energy dispatch to balance the power supply and demand considering communication delays. The proposed algorithm involves modeling an autonomous nanogrid (ANG) consisting of distributed energy resources, energy storage systems, loads, an $H_{\infty }$ controller with a reference power modulation technique, and a state estimator. The ANG was developed to express the dynamic supply-demand energy balance of a nanogird system. Reference power modulation was designed to generate the desired ESS power based on the imbalanced energy. Random communication delays were modeled using a stochastic variable satisfying the Bernoulli random binary distribution. The optimal $H_{\infty }$ controller and estimator were developed using a linear matrix inequality approach to exponentially stabilize the closed-loop system. Simulations were performed using real daily demand forecasts obtained from the Korea Meteorological Administration to demonstrate the effectiveness of the proposed real-time optimization algorithm.

This paper investigates the leader-following H∞ consensus of fractional-order multi-agent systems (FOMASs) under input saturation via the output feedback. Based on the bounded real lemma for FOSs, the sufficient conditions of H∞ consensus for FOMASs are provided in α∈0,1 and 1,2, respectively. Furthermore, the iterative linear matrix inequalities (ILMIs) approaches are applied for solving quadratic matrix inequalities (QMIs). The ILMI algorithms show a method to derive initial values and transform QMIs into LMIs. Mathematical tools are employed to transform the input saturation issue into optimal solutions of LMIs for estimating stable regions. The ILMI algorithms avoid the conditional constraints on matrix variables during the LMIs’ construction and reduce conservatism. The approach does not disassemble the entire MASs by transformations to the Laplacian matrix, instead adopting a holistic analytical perspective to obtain gain matrices. Finally, numerical examples are conducted to validate the efficiency of the approach.

Optimizing the performance of motion control systems with variations in nonlinear parameters is not an easy task. To accomplish this task, it is important to design the controller using the linear system approach. In this study, a linear parameter varying (LPV) control method is proposed in which nonlinearities are treated as parameter variations for planar motors. The proposed control method consists of the force and torque modulation with the commutation scheme and the nonlinear current controller with H∞ state feedback control in the form of LPV synthesis to improve the position-tracking performance. An interpolated gain-scheduling controller based on LPV synthesis is determined by applying H∞ control to a linear matrix inequality technique. An interpolated gain-scheduling controller can attenuate disturbance without disturbance estimation. The effectiveness of the proposed control method is evaluated using simulation results and compared with the conventional proportional–integral–derivative control to verify both improved position-tracking performance and disturbance attenuation.

This paper addresses a mode-dependent state-feedback H ∞ control for stochastic descriptor hybrid systems, considering both the absence and presence of actuator saturation. Firstly, the necessary and sufficient conditions for the stochastic admissibility criterion with H ∞ performance γ of the closed-loop system are proposed. Given the proposed non-convex condition, the author reformulates it into linear matrix inequalities (LMIs). Then, to extend the result to the systems with actuator saturation, the actuator-saturated control input is expressed as a linear combination of a given state-feedback control input and a virtual control input that always remains under the saturation level. To verify this expression, the set invariant condition is also suggested by using the singular mode-dependent Lyapunov function candidate. Therefore, the conditions for the existence of both the mode-dependent state-feedback H ∞ control and the ellipsoidal shape invariant sets are successfully derived in terms of LMIs. Two numerical examples demonstrate the effectiveness of the proposed method by solving optimization problems subject to the proposed LMIs that minimize H ∞ performance γ and maximize the invariant set, respectively. [ABSTRACT FROM AUTHOR]

Regenerative chatter deteriorates machining precision and accelerates tool wear, thereby limiting productivity. This paper presents the design, analysis, and verification of a novel finite-frequency band (FFB) H∞ state feedback control strategy, which is dedicated to chatter control of turning processes. In comparison with the available entire-frequency domain (EFD) controllers, one uniqueness of the proposed controller is that it achieves the finite-frequency band optimal control of chatter, and the user can specify the frequency band for optimization according to actual requirements. Dynamics of regenerative delay, cutting model uncertainty, and actuator output constraint are incorporated into the controller design. Utilizing the Lyapunov–Krasovskii functional (LKF) method and the generalized Kalman-Yakubovich-Popov (GKYP) lemma, a set of linear matrix inequalities (LMI) are derived and adopted to synthesize the FFB H∞ controller. The superiority of the developed controller versus EFD controllers is verified by carrying out both simulation and experimental studies. Results demonstrate that the chatter-free region can be substantially enlarged with the proposed method. [ABSTRACT FROM AUTHOR]

The reference model tracking control of an unmanned aerial helicopter (UAH) under outside disturbance is studied, and a tracking control scheme based on the adaptive disturbance observer is proposed. Firstly, the disturbance is modelled as a nonlinear exogenous system with uncertain parameter error based on the available information. Secondly, a state observer and an adaptive disturbance observer (DO) are proposed to estimate the unmeasurable state and disturbance of the UAH system. Thirdly, by combining the reference model control and DO-based control, a composite anti-disturbance control scheme is presented to derive an overall closed-loop system consisting of tracking error and observer error. Fourthly, based on the Lyapunov stability theory, a sufficient condition on H∞ performance index and asymptotic stability is obtained, and a co-design method of the observers, controller, and adaptive law is proposed by resorting to matrix transformation. Finally, numerical simulations demonstrate the effectiveness and superiority of the proposed tracking control algorithm. [ABSTRACT FROM AUTHOR]

Piezoelectric actuators find extensive application in delivering precision motion in the micrometer to nanometer range. The advantages of a broader range of motion, rapid response, higher stiffness, and large actuation force from piezoelectric actuators make them suitable for precision positioning applications. However, the inherent nonlinearity in the piezoelectric actuators under dynamic working conditions severely affects the accuracy of the generated motion. The nonlinearity in the piezoelectric actuators arises from hysteresis, creep, and vibration, which affect the performance of the piezoelectric actuator. Thus, there is a need for appropriate modeling and control approaches for piezoelectric actuators, which can model the nonlinearity phenomenon and provide adequate compensation to achieve higher motion accuracy. The present review covers different methods adopted for overcoming the nonlinearity issues in piezoelectric actuators. This review highlights the charge-based and voltage-based control methods that drive the piezoelectric actuators. The survey also includes different modeling approaches for the creep and hysteresis phenomenon of the piezoelectric actuators. In addition, the present review also highlights different control strategies and their applications in various types of piezoelectric actuators. An attempt is also made to compare the piezoelectric actuator's different modeling and control approaches and highlight prospects. [ABSTRACT FROM AUTHOR]

This paper proposes a robust lateral control scheme for the path tracking of autonomous vehicles. Considering the discrepancies between the model parameters and the actual values of the vehicle and the fluctuation of parameters during driving, the norm-bounded uncertainty is utilized to deal with the uncertainty of model parameters. Because some state variables in the model are difficult to measure, an H∞ observer is designed to estimate state variables and provide accurate state information to improve the robustness of path tracking. An H∞ state feedback controller is proposed to suppress system nonlinearity and uncertainty and produce the desired steering wheel angle to solve the path tracking problem. A feedforward control is designed to deal with road curvature and further reduce tracking errors. In summary, a path tracking method with H∞ performance is established based on the linear matrix inequality (LMI) technique, and the gains in observer and controller can be obtained directly. The hardware-in-the-loop (HIL) test is built to validate the real-time processing performance of the proposed method to ensure excellent practical application potential, and the effectiveness of the proposed control method is validated through the utilization of urban road and highway scenes. The experimental results indicate that the suggested control approach can track the desired trajectory more precisely compared with the model predictive control (MPC) method and make tracking errors within a small range in both urban and highway scenarios.

Abstract This paper proposes a tube‐based robust model predictive control (TMPC) scheme with an optimal tube for disturbance‐affected linear systems. In the literature on TMPC, there is no proper methodology to handle the considerable effects of the tube size on the closed‐loop system performance. There is usually a trade‐off between the disturbance rejection level and the amount of control effort available for the MPC problem. In some applications, it is nearly impossible to find a feasible TMPC to have a sufficient amount of states and inputs feasible sets for the MPC optimization problem. It would be a vital contribution to the TMPC designs if an algorithm is demonstrated which can investigate the suitability of TMPC for a specific system. This paper provides a solution for the mentioned challenges by introducing the concept of Quasi‐H∞ criterion and proposing a constrained optimization problem. The optimization problem is then reformulated and simplified to present an efficient methodology for the TMPC designers. The proposed TMPC scheme could benefit from a larger terminal region and result in a larger region of attraction. The achievements in TMPC designs are shown by simulations and comparisons with the previously used techniquesover numerical case studies.

The well-known H ∞ control design gives robustness to a controller by rejecting perturbations from the external environment, which is difficult to do for completely unknown affine nonlinear systems. Accordingly, the immediate objective of this paper is to develop an on-line real-time synergetic learning algorithm, so that a data-driven H ∞ controller can be received. By converting the H ∞ control problem into a two-player zero-sum game, a model-free Hamilton–Jacobi–Isaacs equation (MF-HJIE) is first derived using off-policy reinforcement learning, followed by a proof of equivalence between the MF-HJIE and the conventional HJIE. Next, by applying the temporal difference to the MF-HJIE, a synergetic evolutionary rule with experience replay is designed to learn the optimal value function, the optimal control, and the worst perturbation, that can be performed on-line and in real-time along the system state trajectory. It is proven that the synergistic learning system constructed by the system plant and the evolutionary rule is uniformly ultimately bounded. Finally, simulation results on an F16 aircraft system and a nonlinear system back up the tractability of the proposed method. • A model-free Hamiltonian–Jacobi–Isaacs equation is derived for H ∞ control problems. • A real-time on-line evolutionary rule for tuning neural network weights is developed. • The system and neural network approximation errors achieve synergetic learning. [ABSTRACT FROM AUTHOR]

Wheeled Mobile Robots (WMRs) are systems with multiple industrial and civilian applications. Trajectory tracking is essential in many applications, such as surveillance, monitoring, and autonomous driving. However, in practical applications, a WMR is always affected by kinematic disturbances, state estimation error, and measurement noise, which may diminish the system's performance. Hence, this work proposes a novel observer-based H ∞ controller that is robust against matched and unmatched disturbances. The proposed methodology compensates for disturbances through a disturbance observer, transforming the closed-loop system into a new one affected by uniformly bounded disturbances. Then, an H ∞ controller is designed to make the WMR track a desired reference signal. A formal stability proof demonstrates the feasibility of the new proposal. Also, feedback and finite-time controllers are used to assess the novel controller. Numerical simulations and experimental results with a scaled autonomous car-like robot demonstrate the novel controller's efficiency and outstanding performance, despite disturbances when compared against finite-time and feedback controllers. [Display omitted] • An observer-based H ∞ controller for trajectory tracking of wheeled mobile robots is developed. • The kinematic model is transformed into decoupled systems, simplifying the control design stage. • The disturbances affecting the system are compensated through an observer. • Robust performance is achieved despite matched and unmatched disturbances. • The controller is validated through numerical simulations and experimental results. [ABSTRACT FROM AUTHOR]

Sensorless speed control of a brushless DC (BLDC) motor, basically a combined control‐observer design, plays a crucial role in several industries, including electrical and aerospace applications. The key idea is to use only electrical (current) sensors and the remaining mechanical states (speed and rotor position) to be estimated using square‐root extended H∞$\text{H}_\infty$ filter (SREH∞$\text{H}_\infty$F) for a BLDC motor. These estimated states are then fed‐back to the controller. In most of the designs, it is assumed that the BLDC motor plant parameters are constant; however, in reality, their parameters vary due to various intrinsic and extrinsic conditions. Compared to the conventional extended Kalman filter or its square‐root version, the proposed SREH∞$\text{H}_\infty$F for the BLDC motor has an inherent tendency to deal with parameter uncertainties and hence improves the robustness of the overall system. The robustness of the proposed scheme is tested at various reference speeds for a closed‐loop BLDC drive; further parametric uncertainties in stator resistance, detuning of inductance, and change in load are considered. The proposed control‐observer strategy using SREH∞$\text{H}_\infty$F is compared with its counterpart square‐root extended Kalman filter (SREKF), and the experimental results validate the efficacy of SREH∞$\text{H}_\infty$F for speed control of BLDC motor drive during the nominal conditions and in the presence of parametric uncertainties. [ABSTRACT FROM AUTHOR]

This paper considers the problem of admissibility and admissibilization of 2D singular continuous systems described by the Roesser model. A necessary and sufficient admissibility condition is first proposed for 2D singular continuous systems in terms of a strict Linear Matrix Inequality (LMI). Then, a necessary and sufficient condition is established for the closed-loop system to be admissible (i.e., stable, regular, and impulse-free). Moreover, the stability condition is completed to give a sufficient condition to ensure a specified H∞ disturbance attenuation level for the state feedback closed loop. To illustrate the effectiveness of the proposed methodology, a numerical example is given to illustrate an admissibilization of a state feedback closed-loop system.

This paper concentrates on the finite-time H∞ control problem for a type of stochastic discrete-time Markovian jump systems, characterized by time-delay and partly unknown transition probabilities. Initially, a stochastic finite-time (SFT) H∞ state feedback controller and an SFT H∞ observer-based state feedback controller are constructed to realize the closed-loop control of systems. Then, based on the Lyapunov–Krasovskii functional (LKF) method, some sufficient conditions are established to guarantee that closed-loop systems (CLSs) satisfy SFT boundedness and SFT H∞ boundedness. Furthermore, the controller gains are obtained with the use of the linear matrix inequality (LMI) approach. In the end, numerical examples reveal the reasonableness and effectiveness of the proposed designing schemes.

This study investigates the automated transportation control problem of an offshore floating platform that has limited or no maneuverability. The proposed solution involves two tugboats pushing into the platform and two other tugs towing it in the opposite direction. By implementing cooperative control of these tugs, the desired planar motion of the platform is achieved. For this, the proposed control consists of the following components: (1) an observer estimates the environmental disturbances, (2) a platform motion controller acts as the supervisory control, (3) an optimal constrained allocation distributes the required actions over the tugboats, and (4) the tugboats’ controller derived the control inputs of the tugs to fulfill these requirements. Simulation studies are conducted where the proposed solution is compared to one based on the robust H∞ control framework. The results prove the efficiency and robustness of the proposed system.

The small-signal stability of a hybrid (DC/AC) microgrid is highly affected by the direction and amount of power flow through the interlinking converter (IC). This article proposes an invariant-set design of non-droop tracker (to follow the desired time-varying reference) for controlling the power flow in hybrid microgrids in both inversion and rectification modes. The proposed tracker provides fast response, zero steady state error, and robustness against system uncertainty. Since the invariant-set is difficult to calculate, it is approximated using a bounding ellipsoid (being a linear function, and the problem reduces to convex optimization, easy to solve). A novel linear matrix inequality-based theorem is established to obtain the optimal trackers. The hybrid microgrid has been modelled and linearized in the two modes of operation. In Mode I, the interlink converter acts as an inverter, transferring power from the DC side to the AC side. During Mode II, the interlink converter acts as a rectifier, transferring the AC power to the DC side. The suggested trackers' performance has been compared to that of the H∞ trackers in various operational scenarios. The results show that the proposed controller is much faster and has much less overshoot than the H∞ controller. Moreover, the proposed technique can be considered a platform for hybrid microgrid systems since it is easy, straightforward to be implemented, and computationally inexpensive compared to other corresponding techniques in the literature.

This paper proposes a tube‐based robust model predictive control (TMPC) scheme with an optimal tube for disturbance‐affected linear systems. In the literature on TMPC, there is no proper methodology to handle the considerable effects of the tube size on the closed‐loop system performance. There is usually a trade‐off between the disturbance rejection level and the amount of control effort available for the MPC problem. In some applications, it is nearly impossible to find a feasible TMPC to have a sufficient amount of states and inputs feasible sets for the MPC optimization problem. It would be a vital contribution to the TMPC designs if an algorithm is demonstrated which can investigate the suitability of TMPC for a specific system. This paper provides a solution for the mentioned challenges by introducing the concept of Quasi‐H∞ criterion and proposing a constrained optimization problem. The optimization problem is then reformulated and simplified to present an efficient methodology for the TMPC designers. The proposed TMPC scheme could benefit from a larger terminal region and result in a larger region of attraction. The achievements in TMPC designs are shown by simulations and comparisons with the previously used techniquesover numerical case studies. [ABSTRACT FROM AUTHOR]

This paper considers H∞ anti-synchronization (HAS) for uncertain neural networks subject to time-varying delay. An output-feedback-based adaptive control scheme is used to ensure the HAS of the considered networks. An existence condition and update laws of the unknown parameters for the desired controller are developed by resorting to the Lyapunov-Krasovskii functional theory, Bessel-Legendre inequality, as well as reciprocal convex combination. Then, a linear-matrix-inequalities-based design method is developed for the output-feedback gain by decoupling nonlinear terms. Finally, a numerical example is given to illustrate the lower conservatism and effectiveness of the present HAS control method. [ABSTRACT FROM AUTHOR]

This paper investigates the adaptive control problem for a class of Euler-Lagrangian (EL) systems with uncertain parameters and external disturbances. While the EL system is one of the most classical system models, the dynamics of exoskeleton motion rehabilitation robots (EMRR) can be modeled as an EL system by the Lagrangian approach. First, in the absence of uncertainties, it is shown that an effective controller can be designed easily such that the system state tracks the reference signal. Second, for the case where uncertainties exist, a neural network (NN) is introduced to approximate the uncertain terms, and a novel adaptive controller design strategy is proposed to improve the resilience against disturbance by taking $H_{\infty} $ performance into account. Moreover, based on the constructed adaptive controller, an effective stability analysis technique is also proposed for the cases where intermittent measurements are collected. Finally, an EMRR system example is provided to demonstrate the effectiveness of the proposed method.

In this article, a method that applies event‐triggered (ET) mechanism H∞ control to continuous‐time (C‐T) nonlinear systems with asymmetric constraints based on dual heuristic dynamic programing (DHP) structure is proposed. At first, we derive ET mechanism from traditional time‐triggered and give the Hamilton–Jacobi–Isaacs (HJI) equation. Second, we give the triggering condition and prove the stability of system under ET mechanism. Then, two neural networks (NNs) are introduced, one of which is the critic network, which is designed to approximate the partial derivatives of value function with respect to inputs, and approximate disturbance policy. The other is the action network, which is used to acquire the estimation optimal control policy. Furthermore, we choose a suitable Lyapunov candidate function to prove that the system and NNs weight estimation errors are uniformly ultimately bounded (UUB). Besides, it is important that we prove that Zeno phenomenon can be avoided. Finally, simulation results are shown that the proposed method is feasible. [ABSTRACT FROM AUTHOR]