Search Results (313)

This paper focuses on a class of fractional-order systems with state delays and studies the design problem of the finite-time bounded tracking controller. The error system method in preview control theory is first used. By taking fractional-order derivatives of the state equations and error signals, a fractional-order error system is constructed. This transforms the tracking problem of the original system into an input–output finite=time stability problem of the error system. Based on the output equation of the original system and the error signal, an output equation for the error system is constructed, and a memory-based output feedback controller is designed by means of this equation. Using the input–output finite-time stability theory and linear matrix inequality (LMI) techniques, the output feedback gain matrix of the error system is derived by constructing a fractional-order Lyapunov–Krasovskii function. Then, a fractional-order integral of the input to the error system is performed to derive a finite-time bounded tracking controller for the original system. Finally, numerical simulations demonstrate the effectiveness of the proposed method. Full article

This study focuses on developing a control methodology for exoskeleton robots designed for lower limb rehabilitation, specifically addressing the needs of elderly individuals and pediatric therapy. The approach centers on implementing an affine state-feedback controller to effectively regulate and stabilize the knee-joint exoskeleton robot at a desired position. The robot’s dynamics are nonlinear, accounting for unknown parameters, solid and viscous frictions, and external disturbances. To ensure robust stabilization, the Lyapunov approach is utilized to derive a set of Linear Matrix Inequality (LMI) conditions, guaranteeing the stability of the position error. The derivation of these LMI conditions is grounded in a comprehensive theoretical framework that employs advanced mathematical tools, including the matrix inversion lemma, Young’s inequality, the Schur complement, the S-procedure, and specific congruence transformations. Simulation results are presented to validate the proposed LMI conditions, demonstrating the effectiveness of the control strategy in achieving robust and accurate positioning of the lower limb rehabilitation exoskeleton robotic system. Full article

This study presents an approach to enhancing the robustness of $H_{\infty }$ control in It$\widehat{o}$-type stochastic Markov jump systems, addressing uncertainties in parameters, time-varying delays, and nonlinear perturbations. In this study, the nonlinearities are not exactly known, so an adaptive control strategy is employed. Firstly, an adaptive state observer of full dimension is constructed along with the derivation of error dynamics. Subsequently, different from traditional methods, two linear sliding surfaces are designed, respectively, for the state observer system and error dynamics, resulting in two sliding mode dynamics. Secondly, by employing the linear matrix inequality (LMI) method, sufficient conditions are established to ensure mean-square exponential stability of the closed-loop systems, including observer sliding mode dynamics and error sliding mode dynamics, along with an $H_{\infty }$ attenuation performance index $\gamma$. Thirdly, adaptive sliding mode controllers are proposed, ensuring the finite-time arrival and maintenance of the established sliding surfaces. Finally, the efficacy of the derived outcomes is illustrated utilizing the Tunnel Diode circuit model as a demonstrative case study. In this example, the system’s state responses, sliding surface functions, control input, and estimated parameters are simulated under different operating modes and external disturbances. The results demonstrate that the proposed adaptive sliding mode control strategy ensures faster and better convergence compared to error dynamics without control. Full article

Grid-connected renewable power generation systems (RPGSs) may be disconnected from the grid under a transient process, which may possibly induce large-scale power outage accidents. Optimization of parameters based on transient stability analysis of RPGSs would be a feasible solution to such a problem. However, the accurate stability boundary of a grid-connected RPGS are hard to obtain, as the commonly used transient stability analysis methods have the problems of large computation burden with no quantitative solution (numerical method), low analysis accuracy (equal area method), and complexity or impossibility in implementation (Lyapunov function-based methods). In this paper, a modified transient stability analysis method is proposed. By calculating the largest area of the domain of attraction (LEDA) based on the linear matrix inequality (LMI) method and optimization modelling, and then applying parameter sensitivity analysis to the LEDA, the dominant parameters that have high impacts on the LEDA are revealed. A parameter optimization design method that can improve the system’s transient stability is eventually obtained. A hardware-in-the-loop (HIL) simulation system of a 2 MW grid-connected RPGS is established based on the Typhoon HIL 602 device. The theoretical results are verified by using HIL simulation results. Full article

A sensor and actuator network (SAN) is a control system where many sensors and actuators are connected through a communication network. In a SAN with redundant sensors and actuators, it is important to consider choosing sensors and actuators used in control design. Depending on applications, it is also important to consider not only the choice of sensors/actuators but also that of communication channels in which some sensors/actuators are connected. In this paper, based on a linear matrix inequality (LMI) technique, we propose a design method for structured sparse feedback controllers. An LMI technique is one of the fundamental tools in systems and control theory. First, the sparse reconstruction problems for vectors and matrices are summarized. Next, two design problems are formulated, and an LMI-based solution method is proposed. Finally, two numerical examples are presented to show the effectiveness of the proposed method. Full article

The fault-tolerant time-varying formation (TVF) trajectory tracking control problem is investigated in this paper for uncertain multi-agent systems (MASs) with external disturbances subject to time delays under semi-Markov switching topologies. Firstly, based on the characteristics of actuator faults, a failure distribution model is established, which can better describe the occurrence of the failures in practice. Secondly, switching the network topologies is assumed to follow a semi-Markov stochastic process that depends on the sojourn time. Subsequently, a novel distributed state-feedback control protocol with time-varying delays is proposed to ensure that the MASs can maintain a desired formation configuration. To reduce the impact of disturbances imposed on the system, the $H_{\infty }$ performance index is introduced to enhance the robustness of the controller. Furthermore, by constructing an advanced Lyapunov–Krasovskii (LK) functional and utilizing the reciprocally convex combination theory, the TVF control problem can be transformed into an asymptotic stability issue, achieving the purpose of decoupling and reducing conservatism. Furthermore, sufficient conditions for system stability are obtained through linear matrix inequalities (LMIs). Eventually, the availability and superiority of the theoretical results are validated by three simulation examples. Full article

This manuscript presents a Luenberger-type state observer for a class of nonlinear systems with multiple delays. Sufficient conditions are provided to ensure practical stability of the error dynamics. The exponential decay of the observation error dynamics is guaranteed through the use of Lyapunov–Krasovskii functionals and the feasibility of linear matrix inequalities (LMIs). Additionally, a time delay SIRS compartmental epidemiological model is introduced, where the time delays correspond to the transition rates between compartments. The model considers that a portion of the recovered population becomes susceptible again after a period that follows its recovery. Three time delays are considered, representing the exchange of individuals between the following compartments: ${\tau }_{1,2,3}$, the time it takes for an individual to recover from the disease, the time it takes for an individual to lose immunity to the disease, and the incubation period associated to the disease. It is shown that the effective reproduction number of the model depends on the rate at which the susceptible population becomes infected and, after a period of incubation, starts to be infectious, and the fraction of the infectious that recovers after a a certain period of time. An estimation problem is then addressed for the resulting delay model. The observer is capable of estimating the compartmental populations of Susceptible $S\left(t\right)$ and Recovered $R\left(t\right)$ based solely on the real data available, which correspond to the Infectious population $I_r\left(t\right)$. The $I_r\left(t\right)$ data used for the state estimation are from a 55-day period of the pandemic in Mexico, reported by the World Health Organization (WHO), before vaccination. Full article

This paper focuses on simultaneous estimation of states and faults for a linear time-invariant (LTI) system observed by sensor networks. Each sensor node is equipped with an observer, which uses only local measurements and local interaction with neighbors for monitoring. The observability of said observer is analyzed where non-local observability of a sensor node is required in terms of the system state and faults. The distributed observers present features of $H_{\infty }$ performance to constrain the influence of disturbances on the estimation errors, for which the global design condition is transformed into a linear matrix inequality (LMI). The LMI is proven to be solvable given collective observability of the system and a suitable $H_{\infty }$ performance index. Moreover, in the case that no disturbances exist, fully distributed observers with adaptive gains are designed to asymptotically estimate the states and faults without using any global information from the network. Finally, the effectiveness of the proposed methods is verified through case studies on a spacecraft’s attitude control system. Full article

This paper introduces a novel observer-based fuzzy tracking controller that integrates disturbance estimation to improve state estimation and path tracking in the lateral control systems of Unmanned Ground Vehicles (UGVs). The design of the controller is based on linear matrix inequality (LMI) conditions derived from a Takagi–Sugeno fuzzy model and a relaxation technique that incorporates additional null terms. The state observer is developed to estimate both the vehicle’s state and external disturbances, such as road curvature. By incorporating the disturbance observer, the proposed approach effectively mitigates performance degradation caused by discrepancies between the system and observer dynamics. The simulation results, conducted in MATLAB and a commercial autonomous driving simulator, demonstrate that the proposed control method substantially enhances state estimation accuracy and improves the robustness of path tracking under varying conditions. Full article

This paper investigates the leader-following $H_{\infty }$ 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 $H_{\infty }$ consensus for FOMASs are provided in $\alpha \in \left(0,1\right)$ and $\left[1,2\right)$, 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. Full article

The large number of joints in a continuum manipulator complicates its dynamic modeling, making model simplification inevitable for practical motion control. However, due to external disturbances and internal noise, a controller based on the simplified dynamic model often struggles to meet the desired dynamic performance. To address this issue, this paper proposes an anti-interference control algorithm for continuum manipulators, designed to compensate for parameter uncertainties, external disturbances, and measurement noise. At the same time, the parameters of the algorithm are obtained in the form of solvability of linear matrix inequalities (LMIs). The simulation results show that the algorithm proposed in the paper provides better transient performance and is not affected by the entire disturbance. Experimental results further confirm the effectiveness and robustness of the algorithm. Full article

The intermittent power generation of renewable energy sources (RESs) interrupts the balance between power generation and demand load due to the increased frequency fluctuation, which challenges the frequency stability analysis and control synthesis of power generation systems. This paper proposes a robust distributed load frequency control (DLFC) scheme for multi-area power systems. Firstly, a multi-area power system is constructed by integrating photovoltaic (PV) and battery energy storage systems (BESSs). Then, by employing the linear matrix inequality (LMI) technique, the sufficient condition capable of ensuring that the proposed controller satisfies $H_{\infty }$ robust performance in the sense of asymptotic stability is derived. Finally, testing is conducted on a four-area renewable power system, and results verify the strong robustness of the proposed controller against load disturbance and intermittence of RESs. Full article

A control design for a linear large-scale interconnected system composed of identical subsystems is presented in this paper. The control signal of all subsystems is sampled. For different subsystems, the sampling times are not identical. Nonetheless, it is assumed that a bound exists for the maximal sampling time. The control algorithm is designed using the Wirtinger inequality, and the non-fragile control law is proposed. The size of the linear matrix inequalities to be solved by the proposed control algorithm is independent of the number of subsystems composing the overall system. Hence, the algorithm is computationally effective. The results are illustrated by two examples. The first example graphically illustrates the function of the proposed algorithm while the second one compares with a method for stabilizing a large-scale system obtained earlier, thus illustrating the improved capabilities of the presented algorithm. Full article

This paper investigates robust $H_{\infty }$-based control for autonomous underwater vehicle (AUV) systems under time-varying delay, model uncertainties, and cyber-attacks. Sensor and actuator cyber-attacks can cause faults in the overall AUV system. In addition, the behavior of the system can be affected by the presence of complexities, such as unknown random uncertainties that occur in system modeling. In this paper, the robustness against unpredictable random uncertainties is investigated by considering unknown but norm-bounded (UBB) random uncertainties. By constructing a proper Lyapunov–Krasovskii functional (LKF) and using linear matrix inequality (LMI) techniques, new stability criteria in the form of LMIs are derived such that the AUV system is stable. Moreover, this work is novel in addressing robust $H_{\infty }$ control, which considers time-varying delay, cyber-attacks, and randomly occurring uncertainties for AUV systems. Finally, the effectiveness of the proposed results is demonstrated through two examples and their computer simulations. Full article

This paper explores the synchronization control issue for a class of fractional-order Complex-valued Neural Networks (FOCVNNs) with additive time-varying delays (TVDs) utilizing a sampled-data-based event-triggered mechanism (SDBETM). First, an innovative free-matrix-based fractional-order integral inequality (FMBFOII) and an improved fractional-order complex-valued integral inequality (FOCVII) are proposed, which are less conservative than the existing classical fractional-order integral inequality (FOII). Secondly, an SDBETM is inducted to conserve network resources. In addition, a novel Lyapunov–Krasovskii functional (LKF) enriched with additional information regarding the fractional-order derivative, additive TVDs, and triggering instants is constructed. Then, through the integration of the innovative FOCVII, LKF, SDBETM, and other analytical methodologies, we deduce two criteria in the form of linear matrix inequalities (LMIs) to ensure the synchronization of the master–slave FOCVNNs. Finally, numerical simulations are illustrated to confirm the validity of the proposed results. Full article