This paper investigates the stabilization of switched positive systems whose subsystems are all unstable. A stability framework is proposed based on a continuous switching cost function and a window-based net attenuation condition. Both conditions are formulated as linear inequalities in copositive Lyapunov vectors, enabling efficient verification via linear programming. The switching cost function captures mode-dependent effects, while the net attenuation condition provides a finite-window stability criterion. The framework applies to systems with Metzler matrices, bounded dwell times, and coexistence of stabilizing and destabilizing switches. Numerical simulations confirm that strategic switching can ensure global exponential stability by compensating for destabilizing effects within finite horizons.
Muscle spasms in patients at the flaccid paralysis stage pose a significant challenge for motion control of upper limb rehabilitation robots. These spasms, characterized by complex physiological tremor mechanisms, vary among patients and across different stages of rehabilitation, making uniform modeling and prediction difficult. A control strategy based on a Finite-Time Disturbance Observer (FTDO) is proposed to enhance tracking robustness under muscle spasm-induced disturbances to address this issue. The FTDO constructs a disturbance estimation term based on system state variables and adjustment functions, enabling real-time approximation of spasm disturbances. The estimation is then fed into the control law to ensure accurate system response within a finite time. Theoretical analysis demonstrates the finite-time convergence of the proposed FTDO. Subsequently, the FTDO is integrated with an Integral Terminal Sliding Mode Controller (ITSMC), which has been designed to improve rehabilitation training comfort. Lyapunov stability analysis confirms the boundedness of the trajectory tracking error. Joint experiments validate the method's effectiveness under initial and high-frequency oscillation disturbances. Compared with existing methods, the proposed FTDO improves the system's response rate to spasm disturbances and overall control accuracy.
This paper investigates the mode-dependent state estimation problem for static neural networks subject to time-varying delay. To better capture delay information, an original delayed neural network (DNN) is equivalently formulated as a switched system with four modes, depending on the delay size and the sign of its derivative. Based on the new switched approach, a mode-dependent state estimator is designed, whose gains can switch with each delay mode. Then, by adopting different Lyapunov matrices for each mode, a switched Lyapunov–Krasovskii functional (LKF) is constructed to provide extra degrees of freedom, rather than employing a unified functional structure over the entire delay interval. Using the average dwell time (ADT) technique, two criteria that guarantee both exponential stability and H_∞ performance are derived. Simulation results further validate the feasibility of the proposed approach.
This paper proposes a sliding integral composite control (SICC) scheme to improve the tracking performance of permanent magnet synchronous motors (PMSMs) and avoid overcurrent. First, a torque observer is developed to generate a compensation current that offsets unknown constant load disturbances and alleviates errors arising from mechanical parameter uncertainties. Then, a fixed-time tracking differentiator (FTTD) is designed to generate constrained reference q-axis current and smooth virtual reference speed. Finally, based on the Takagi–Sugeno (T–S) fuzzy model of PMSMs, a sliding integral controller (SIC) and a nonlinear dynamics feedforward controller (NDFC) are designed, respectively. By applying the SIC, the actual currents can track their references quickly with less overshoot. Meanwhile, the non-parallel distributed compensation (non-PDC) strategy is applied to the SIC to reduce the controller design conservatism. Simulations demonstrate that the SICC scheme can achieve good tracking performance and maintain its advantage even in the presence of parameter uncertainties.
This paper presents a deep neural network-based adaptive backstepping control strategy for permanent magnet synchronous motors operating under parametric uncertainties and external disturbances. The proposed controller leverages the universal approximation capability of neural networks together with Lyapunov-based adaptation laws to compensate lumped unmodeled dynamics without requiring precise identification of the full electromechanical model. Embedded within a field-oriented control framework, the design combines an adaptive backstepping speed-control loop with a q-axis current loop augmented by a deep neural network approximation of the total uncertainty in the torque-producing channel. A Lyapunov-based stability analysis establishes boundedness of all closed-loop signals and semi-global asymptotic convergence of the speed and current tracking errors under the stated assumptions and a verifiable gain condition. A hybrid learning strategy is adopted in which the inner layers of the deep neural network are pretrained offline using data collected from a PI-controlled drive, while the output-layer parameters are updated online in real time. The proposed method is validated using numerical simulations and then implemented on a C2000-based embedded motor-drive platform to demonstrate real-time applicability. In simulation, periodic inner-layer retraining using newly collected closed-loop data is also investigated to assess the effect of feature refinement; in the embedded implementation, the inner-layer parameters remain fixed and only the output layer is adapted online due to real-time constraints.
Prostate biopsy is commonly performed under transrectal ultrasound (TRUS) guidance. MRI-guided transrectal biopsy can provide more accurate lesion targeting, but it requires a positioning system capable of operating within the constraints of the MRI environment. This study presents a hexaglide-based positioning robot for MRI-guided transrectal prostate biopsy. Based on an analysis of CT images from n = 30 patients, the clinical design goals were defined in terms of the required angular coverage envelope ( θ = 25^∘ , ϕ = 35^∘ ) for prostate access. A multi-objective optimization framework was used to evaluate design variations defined by link lengths and spherical joint locations, with workspace coverage and dexterity adopted as performance measures to identify solutions that satisfied the angular goal while preserving translational reach to the prostate. Simulation results confirmed feasible needle guide insertion through the RCM and subsequent orientation coverage of the target prostate envelope. Patient-specific analysis was performed to assess the sensitivity of workspace coverage and dexterity to variations ( ± 50 mm) in RCM height. Uncertainty quantification was further conducted using a Jacobian-based sensitivity model with Monte Carlo sampling to evaluate the propagation of geometric tolerances to end effector pose, yielding spatial maps of the 95 ^th percentile error across the workspace. The results indicate that, in simulation, the optimized system satisfies the clinical workspace and accuracy requirements for MRI-guided prostate biopsy.
This study presents a constraint-preprocessing framework for Laguerre-based model predictive control (LMPC) aimed at improving real-time implementability in constrained control. Although LMPC reduces decision variables through input parameterization, the computational burden can remain high due to numerous linear inequality constraints. To address this, we propose a structure-exploiting algorithm that selects a compact set of dominant constraints prior to optimization. The procedure combines normalization, prediction-based screening, row-wise extrema detection, violation analysis of the unconstrained solution, and warm-start propagation. The retained constraint set is selected to represent the dominant part of the original linear inequality set while reducing computational cost. The approach is demonstrated on a numerical study and high-fidelity CarSim-based vehicle simulations. Results indicate near-optimal tracking with reduced computation compared with conventional MPC and alternative input-parameterization baselines. Under matched computational budgets, the proposed LMPC yields the most favorable performance-computation trade-off among the tested reduced-parameterization methods. The framework is useful when execution time is limited by a fixed compute budget and is applicable beyond automotive to other constrained engineering systems.
Existing studies on quadrotor countermeasures have predominantly targeted individual aerial vehicles; by contrast, countermeasure techniques tailored for networked quadrotor swarms remain relatively underdeveloped and pose significant open challenges. This work investigates the directional eviction problem for autonomous quadrotor swarms from the perspective of state deception attacks. First, a novel eviction scheme is developed to steer an autonomous quadrotor swarm away from a protected target, in which carefully designed fictitious states are embedded into a standard distributed formation control protocol. Then, a sufficient criterion for successful directional induced eviction is established, which introduces a fictitious formation center function and derives its corresponding feasibility constraint. In particular, the derived eviction criterion is intrinsically linked to the smallest eigenvalue of the defined eviction relationship matrix. Furthermore, an explicit analytical expression for the trajectory of the compromised quadrotor is derived, where it is revealed that the original formation structure of an autonomous quadrotor swarm may be destroyed and be divided into two independent parts. Finally, both flight experiments and numerical simulations are carried out to validate the effectiveness and practical feasibility of the proposed theoretical results.
This paper presents a bilateral control strategy for a leader–follower system of quadrotors collaboratively transporting a cable-suspended payload. The suspended payload introduces time-varying swing-induced disturbances, which are estimated via a fixed-time extended state observer (ESO). Leveraging the fixed-time ESO, a fixed-time fast terminal sliding mode controller is developed for the attitude loop of each quadrotor to enhance transient performance and robustness. For the position loop, an integral sliding mode controller is employed to achieve high-precision trajectory tracking within the leader–follower framework. Rigorous stability analysis demonstrates that both observation and tracking errors converge to zero in a fixed time despite bounded disturbances. Simulation results validate the effectiveness of the proposed bilateral control approach, demonstrating desired swing suppression and accurate motion coordination in a dual-quadrotor transport system.
This paper presents a reinforcement learning-based practically predefined-time optimal consensus control scheme with an improved prescribed performance function for multirobot systems in the presence of dynamic uncertainties, input saturation and external disturbance. By integrating a backstepping control strategy into the actor–critic–identifier framework, an adaptive optimal tracking controller is developed to avoid directly solving the Hamilton–Jacobi–Bellman equation and to effectively approximate unknown nonlinear dynamics via neural networks. A saturation compensation mechanism and the improved prescribed performance function are incorporated to achieve higher tracking error accuracy under input saturation than traditional constraint-based methods do, with the precision adjustable via preset factors. On the basis of the barrier Lyapunov stability criterion and predefined-time theory, the proposed scheme is proven to ensure that all closed-loop signals are practically predefined-time stable with a preassignable settling-time upper bound. Finally, the effectiveness of the approach is validated through simulation results on multiple two-link manipulator systems.
This paper investigates a robust Takagi–Sugeno (T–S) fuzzy controller for flapping-wing micro aerial vehicles (FWMAVs) subject to actuator saturation and external disturbances. To this end, we first construct a state-scheduled T–S fuzzy model to represent the longitudinal dynamics of FWMAVs, explicitly accounting for state-dependent nonlinearities. Based on this model, we propose a two-loop control architecture: an inner-loop T–S fuzzy controller that regulates the vertical position and pitch angle, and an outer-loop PD controller that achieves full position-tracking by generating a pitch reference from the desired longitudinal position. Then, we formulate the T–S fuzzy stabilization conditions as linear matrix inequalities (LMIs) that guarantee closed-loop stability. Specifically, by exploiting the mismatch between the current and subsequent fuzzy basis functions (FBFs), we introduce a relaxation method that incorporates additional slack variables into the stabilization conditions, thereby reducing conservatism. Finally, numerical comparisons and simulations for FWMAVs are presented to verify the reduced conservatism and effectiveness of the proposed method.
This paper presents a simplified control strategy to stabilize the model of the planar vertical take-off and landing (PVTOL) nonlinear system. The stability analysis is based on a Lyapunov function and therefore exponential stability is ensured when the initial conditions belong to a domain of attraction which is also specified. A robustness analysis is presented based on the Lyapunov function. Numerical simulations illustrate the performance of the proposed control algorithm.
This paper studies distributed learning in two-network zero-sum games, where agents in each network obtain local information from their neighbors including their own network and opposing network, and the agents’ payoffs are characterized by time-varying cost functions. An online distributed dual-averaging algorithm, termed ODDA-TN, is proposed for each agent to search the Nash equilibrium of the zero-sum game. The upper bound of the static regret of the proposed algorithm is given, which is shown to be sublinear with the time horizon T. Finally, the effectiveness of the proposed algorithm is further demonstrated through numerical experiments.
To mitigate vehicle instability caused by lateral collisions and reduce the likelihood of subsequent secondary crashes, a phased pre-steering cooperative control framework is developed. The proposed strategy enables the vehicle to execute a pre-steering maneuver before impact and adopts a stage-based control scheme after the collision event. During the first stage, a hierarchical stability control architecture is established. The upper-level controller employs a two-degree-of-freedom vehicle dynamics model and sliding mode control to calculate the required corrective yaw moment, while the lower-level controller performs adaptive allocation of four-wheel driving torques according to the tire load distribution ratio. Vehicle stability is evaluated using phase-plane analysis. In the second stage, a three-degree-of-freedom vehicle dynamics model integrated with a trajectory tracking controller is introduced to restore vehicle motion and achieve accurate path following. Two typical scenarios, including an intersection crossing case and a parallel lane driving case, are constructed based on a Matlab/Simulink and CarSim co-simulation platform. In the intersection scenario, the robustness of the proposed pre-steering cooperative control strategy is investigated under different collision impact forces and road adhesion conditions. The simulation results demonstrate that the proposed method maintains satisfactory vehicle stability under various operating conditions. Moreover, it effectively suppresses external disturbances, improves trajectory tracking performance, and avoids potential secondary collisions, confirming the effectiveness and robustness of the proposed control framework.
Highly dynamic legged locomotion is essential for deploying robots in complex unstructured environments, where rapid disturbance recovery and smooth, physically feasible contact-force generation are both required. However, standard model predictive path integral control often faces a trade-off between responsiveness and smoothness when applied to legged systems with high-dimensional dynamics and intermittent contacts. This paper proposes an enhanced model predictive path integral control framework that coordinates adaptive nominal-sequence update and perturbation generation within the standard control loop. A sampling-informed adaptive update mechanism scales the warm-start nominal sequence according to sample concentration and tracking deviation, while a Kullback–Leibler divergence bound limits excessive proposal-distribution shifts. A mixed perturbation-generation strategy further combines a small fraction of time-correlated rollouts with standard temporally uncorrelated samples, providing smoother candidate trajectories while preserving exploration diversity. The framework is evaluated in high-fidelity MuJoCo simulations, including high-speed walking, lateral disturbance rejection, and terrain-induced contact uncertainty tests. In high-speed walking, the forward position root-mean-square error is reduced from 2.235 to 0.931 m, corresponding to a 58.3
This paper explores the issue of formation tracking for multiple autonomous surface vehicle (ASV) systems, focusing on achieving prescribed performance while accounting for model uncertainties. A hierarchical fuzzy adaptive control scheme is introduced, where the estimator problem about the state of leader and formation control problem of the multiple ASVs are addressed in different layers. Utilizing fuzzy logic systems, a set of adaptive laws is developed to estimate lumped uncertainties and velocity information. The controller leverages outputs from the fuzzy observer to mitigate input saturation, ensuring compliance with the prescribed performance of tracking errors. Through rigorous analysis, the estimation problem about leader states can be solved within predefined-time, and it is shown that all variables in the closed-loop systems remain bounded. Finally, simulations are conducted to validate the effectiveness of the proposed algorithm.
This large cast iron pipes produced by centrifugal casting require post-processing operations, such as washing, grinding, and cutting, all of which are currently performed manually. In this study, a mechanical system for a post-processing automation system for centrifugal cast pipes was newly modeled and designed using SolidWorks software. The structural analysis results showed that the maximum equivalent stress was 94.89 MPa, the safety factor was 3.64, and the maximum displacement was 0.45 mm. The system was manufactured based on the design results. The characteristics of the automation system were experimentally evaluated, and it was confirmed that the system operates as a platform for washing, circumferential surface grinding, and cutting of large pipes. Therefore, the proposed automation system is expected to be useful for the post-processing of large pipes.
This study proposes a novel homing guidance law for intercepting speed-superior maneuvering targets, formulated in a relative virtual frame using exact nonlinear kinematics. The law employs a nonlinear zero-effort miss (ZEM) distance regulated by a prescribed performance controller (PPC), which confines the ZEM dynamics within a range-contracted performance envelope and guarantees a prescribed terminal miss-distance accuracy. The PPC is constructed using a rigorously defined range-parameterized performance function. To compensate for unknown target maneuvers, the target acceleration is estimated in real time using a nonlinear disturbance observer. The simulation results validate that the proposed method achieves accurate interception with bounded acceleration while maintaining a robust performance across diverse maneuvering scenarios.
This paper provides a comprehensive survey of the convergence properties of temporal-difference (TD) learning and Q-learning, which are two fundamental algorithms in reinforcement learning (RL). We systematically categorize the existing literature into the tabular setting and two function approximation regimes: linear and nonlinear (deep neural networks). In the tabular setting, we review the foundational stochastic-approximation theory that ensures asymptotic convergence and discuss recent non-asymptotic results that provide explicit sample-complexity bounds under various coverage and sampling conditions. For linear function approximation, we address the stability challenges inherent in off-policy learning and examine stabilization mechanisms, such as gradient-based methods, regularization, and target networks. Furthermore, we explore the recent theoretical advancements in deep RL, focusing on finite-time analysis within the overparameterized regime. By synthesizing these diverse perspectives, this survey highlights the theoretical evolution from asymptotic stability to non-asymptotic efficiency and identifies the remaining gaps and provides a coherent roadmap for future research toward a unified theoretical understanding of RL dynamics.
In the probe-and-drogue refueling (PDR) docking phase, the probe with slow dynamics attempts to track the drogue with fast dynamics. Therefore, during this phase, it is crucial for the receiver to obtain the drogue position information and respond rapidly to control commands to guarantee successful docking. This paper considers the input delay caused by complex factors in PDR systems, such as sensors and controllers, and designs a control framework based on additive state decomposition (ASD). The ASD-based framework decomposes the PDR docking system with input delay into a primary system with disturbances and a secondary system with input delay. By combining classical control methods, the docking task of the primary system is completed using proportional-integral (PI) control, while the input-delay stabilization task of the secondary system is achieved through model predictive control. Simulation results show that the proposed comprehensive control method can effectively improve docking speed and enhance the system’s robustness against input delays, compared to the traditional PI control methods.
