Adaptive Compensation and Adaptive Optimal Control of a Single Link Manipulator

Adaptive Trajectory Tracking Control for Manipulators Based on Receding Horizon Optimization and Sliding Mode Robust Compensation

With the rapid development of modern industry, robotic manipulators are required to achieve increasingly high trajectory-tracking accuracy and robustness in practical applications. To enhance tracking performance under complex operating conditions, this paper proposes an Adaptive Model Predictive Control with Sliding-Mode Robust Compensation (AMPC–SMC) scheme that integrates an adaptive mechanism with sliding-mode control theory. First, a dynamic model of the manipulator is established, and parameter linearization is employed to transform the nonlinear dynamics into a linearly parameterized form with unknown parameters. Second, an adaptive law is derived based on Lyapunov stability theory to update the model parameters online, thereby mitigating the adverse effects of parametric perturbations and external disturbances on tracking accuracy. Building on this, a receding-horizon optimization strategy is introduced by formulating a quadratic cost function that penalizes both tracking errors and control effort, and the optimal control input is obtained by solving the resulting optimization problem. Meanwhile, a sliding-mode term is incorporated as a robust compensator to eliminate residual tracking errors. Finally, the desired trajectory is generated via point-to-point path planning in Cartesian space, and the proposed method is validated on a real six-degree-of-freedom robotic manipulator. Comparative experiments against conventional model predictive control (MPC) and traditional sliding-mode control (SMC) demonstrate that the proposed AMPC-SMC controller achieves remarkably superior tracking performance compared with the conventional MPC and SMC controllers. In terms of tracking accuracy, the mean absolute errors (MAE) of Joint 2, Joint 4 and Joint 5 under AMPC-SMC are reduced by 91.7%, 92.1% and 86.1% respectively relative to MPC, and decreased by 76.1%, 77.3% and 85.1% compared with the standalone SMC controller.

Optimal Parallel Tracking Control of Unknown Time-Varying Nonlinear Systems Based on Adaptive Dynamic Programming

This article investigates an optimal parallel tracking control problem for a class of nonaffine time-varying nonlinear systems (NATVNSs) under the unknown-model adaptive dynamic programming (UMADP) framework. First, a parallel control strategy is developed to address the tracking problem, which directly decouples the nonaffine characteristics by constructing an affine augmented system (AAS) and an augmented performance index (API). Second, to cope with the lack of an accurate system model, integral reinforcement learning (IRL) is extended to the constructed augmented system with completely unknown dynamics, thereby eliminating the reliance on model reconstruction. Third, an online learning strategy within the UMADP framework is proposed to achieve real-time optimal tracking control without assuming bounded input dynamics. Furthermore, rigorous theoretical analysis is carried out to prove that all closed-loop signals are uniformly ultimately bounded (UUB). Finally, the simulation results demonstrate that our proposed theoretical framework ensures effective attitude tracking of a morphing vehicle (MV), even under sweep-angle variations and unknown system dynamics.

Actor–Critic Predefined-Time Adaptive Tracking Control for Partially Unknown Euler–Lagrange Systems

This paper studies predefined-time trajectory tracking for Euler–Lagrange systems with composite uncertainties encompassing partially known dynamics, parametric variations, and bounded disturbances. A two-step backstepping architecture is developed. In Step 1, a predefined-time virtual control law is constructed for the position subsystem. In Step 2, an energy-based torque controller is designed for the velocity subsystem using nominal model compensation, adaptive parameter estimation, actor neural network approximation of residual dynamics, a critic network for performance-oriented learning, and a continuous robust term. A rigorous Lyapunov analysis shows that all closed-loop signals are uniformly ultimately bounded and that the tracking errors converge to a computable residual set within a predefined time for all initial conditions contained in the selected compact set. Comparative simulations on a 2-DOF planar manipulator demonstrate that the proposed method provides faster convergence and improved steady-state tracking accuracy than both a PID baseline and a classical Slotine–Li adaptive baseline, while respecting the predefined-time bound.

Robust Adaptive Neural Network-Based Backstepping Tracking for Second-Order Euler-Lagrange Systems with Unknown Parameters

A continuous adaptive control law is developed that eliminates chattering typically caused by discontinuous robust terms and proves that all closed-loop signals are uniformly ultimately bounded, achieving asymptotic trajectory tracking with smooth control inputs.

Inverse optimal control of general nonlinear systems based on adaptive dynamic programming

Adaptive Prescribed-Time Tracking Control for Output-Constrained Hydraulic Servo Systems with Time-Varying Parameters

This paper proposes an adaptive prescribed-time tracking control strategy based on the dynamic surface technique for hydraulic servo systems subject to time-varying parameters, external disturbances, and output constraints. First, a state-constrained transformation function is introduced to convert the strict output constraint condition into an error boundedness problem. Meanwhile, the dynamic surface control (DSC) technique is employed to effectively avoid the “explosion of complexity” inherent in traditional backstepping design. Second, to tackle complex uncertainties, prescribed-time-driven adaptive update and disturbance estimation laws are separately formulated for precise parameter learning and active disturbance feedforward compensation. Furthermore, a smooth nonlinear robust term is specifically integrated to suppress the residual errors induced by parameter adaptation. Based on the transformed system, a novel control framework integrating error constraints, adaptive parameter estimation, and prescribed-time performance is developed. Rigorous Lyapunov stability analysis proves that the proposed controller not only strictly prevents the system output from violating the constraint boundaries throughout the entire operation, but also ensures that the tracking error converges rapidly and smoothly to a small bounded region near the origin within a time that can be independently predetermined by the designer. Finally, the effectiveness and superiority of the proposed control strategy are fully validated through simulations.