Exoskeletons are made to help patients perform repetitive exercises. The role of these systems in passive rehabilitation is to follow predefined trajectories and to completely guide movement. However, dealing with uncertainties, external disturbances, and accounting for the dynamics of the human upper limb remains a major challenge to improving training results. In addition, existing variable-gain control strategies exhibit reduced robustness when the tracking error converges toward zero in the presence of persistent disturbances. To address these issues and the limitations associated with existing variable-gain control strategies, this paper first proposes an improved variable-gain robust integral of the sign of the error (VARISE) control strategy. The proposed strategy introduces an adaptive minimum-gain mechanism in which the lower bound of the variable control gain is dynamically adjusted according to the tracking error, thereby maintaining a sufficient robust gain level even when the tracking error approaches zero in the presence of persistent disturbances and parametric uncertainties. Then, the stability analysis of the closed-loop system is determined using the Lyapunov theory, proving that the tracking errors converge asymptotically to zero. A comparative study is conducted with existing variable-gain control approaches. The proposed method is validated on a model that includes both the robotic system (exoskeleton) and the human upper-limb dynamics. Moreover, the system is subjected to variable external disturbances and parametric uncertainties introduced by increasing the nominal model parameters by 80 % . The performance of the proposed approach is further assessed through the computation of control performance indices.
This paper focuses on Takagi-Sugeno (T-S) fuzzy systems with delayed state feedback and proposes an H_∞ control design framework based on the Chebyshev spectral continuous-time approximation (ChSCTA) method. The design procedure consists of two main steps. First, suitable augmented matrices are formulated to transform the original time-delay system into an approximated delay-free augmented system, thereby facilitating controller synthesis. Second, the nonlinear matrix inequalities arising in the controller design are reformulated as bilinear matrix inequality (BMI) constraints. This reformulation enables the development of an efficient iterative algorithm for computing the required feedback gain matrices. Numerical examples show that the controller synthesized via the proposed ChSCTA method yields favorable disturbance attenuation and lower H_∞ index for the approximated system; simulations on the original delayed T-S fuzzy system illustrate the effectiveness of the resulting controller.
Lower-limb rehabilitation requires intelligent gait trajectory correction methods that preserve biomechanical authenticity and accommodate diverse pathological gait patterns. Existing gait trajectory correction and rehabilitation control methods often rely on predefined control strategies and exhibit limited adaptability to diverse gait impairments. This study proposes a Kinematics-Informed Deep Q-Network (KI-DQN) for offline pathological gait trajectory correction by embedding biomechanically motivated kinematic constraints into the reinforcement learning framework through constraints on tracking error, velocity consistency, control effort, and acceleration consistency within both the reward formulation and the network optimization process. The proposed framework has been tested on the Post-Stroke and Hip Osteoarthritis gait datasets, with healthy gait trajectories used as reference. The performance of the algorithm was compared with the popular trajectory correction methods: Proportional-Derivative, Model Predictive Control, Deep Q-Network and Soft Actor Critic. Convergence of the training process across 10 experiments yielded reliable results, with the mean episode return increasing from −111.61 to −2.56, −76.75 to −1.84, and −69.90 to −1.79 for the hip, knee, and ankle joints, respectively. The proposed KI-DQN achieved competitive or superior gait restoration performance across the evaluated joints and metrics and reduced the mean absolute error to 0.33 ^∘ , 0.33 ^∘ , and 0.54 ^∘ for the Post-Stroke group, and to 0.47 ^∘ , 0.74 ^∘ , and 0.76 ^∘ for the Hip Osteoarthritis group. In addition, the KI-DQN also achieved competitive RMSE, ROM error, and waveform-correlation performance across the evaluated joints. These results demonstrate that incorporating biomechanically motivated kinematic constraints within a reinforcement learning framework can improve pathological gait trajectory restoration while preserving physiologically plausible gait characteristics.
This paper presents a space-fractional PDE-constrained optimal control formulation for nonlocal transport systems with anomalous diffusion and long-range spatial interactions. The state equation is given by a space-fractional advection–diffusion model, which generalizes classical transport dynamics by incorporating nonlocal dispersive effects. The associated control problem seeks to track a prescribed density distribution while penalizing excessive control action through a quadratic objective functional. A monolithic space–time localized radial basis function (ST-LRBF) meshfree collocation scheme is developed for the discretization of the coupled optimality system. By embedding time as an additional coordinate, the method constructs a unified approximation over the full space–time domain and produces a sparse Karush–Kuhn–Tucker (KKT) system involving the state, adjoint, and control variables. This formulation avoids the sequential treatment of forward and backward equations and provides a direct discretization of the coupled optimality conditions for the space-fractional state equation. The proposed approach is assessed using a method of manufactured solutions benchmark and spatial and temporal refinement studies. The results indicate consistent empirical convergence and stable numerical behavior for the tested discretizations. The method is also applied to a macroscopic ride-sourcing fleet-control problem, where the controlled density evolution more closely follows the desired distribution than the uncontrolled dynamics. Additional sensitivity studies with respect to the fractional orders, penalty ratio, and anisotropic dispersion coefficients show that the framework can accommodate different nonlocal transport regimes. The results demonstrate the potential of monolithic ST-LRBF collocation as a computational approach for space-fractional optimal control problems governed by nonlocal transport dynamics.
