Jul 2026· International Journal of Robust and Nonlinear Control· 0 citations· 58 references
TL;DR
A novel prescribed‐time optimal (PTO) tracking control scheme for nonlinear strict‐feedback systems with unknown affine terms based on radial basis function (RBF) neural networks is proposed and it is demonstrated for the first time that the critic‐actor weights can converge exponentially to the same values.
Abstract
This article proposes a novel prescribed‐time optimal (PTO) tracking control scheme for nonlinear strict‐feedback systems with unknown affine terms based on radial basis function (RBF) neural networks. First, by combining the barrier Lyapunov function method, a simple coordinate transformation is used to enable the system's tracking performance to be artificially set. Subsequently, at each step of the backstepping method, reinforcement learning algorithms with critic‐actor structures are introduced to design the optimal virtual controllers and the actual controller by finding solutions to Hamilton–Jacobi–Bellman (HJB) equations for the corresponding subsystems. Meantime, the complexity of system stability analysis caused by PT optimal control is overcome by appropriately decomposing ideal virtual controllers and the ideal actual controller. Based on the new HJB equation with PT characteristics, the easy‐to‐implement critic‐actor updating laws are designed by introducing tracking error as a driving term. It is demonstrated for the first time that, under the persistent excitation (PE) condition, the critic‐actor weights can converge exponentially to the same values. Finally, simulation and experimental results illustrate the effectiveness of the proposed control scheme.
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.
Tao Wang, Yuan Sun, Yong Qin et al.· Machines· 0 citations
This paper investigates the problem of adaptive finite‐time optimal control for stochastic nonlinear multi‐agent systems (MASs) subject to input saturation. To address the challenges posed by unknown dynamics and the Hamilton‐Jacobi‐Bellman (HJB) equation, a novel double critic‐actor architecture is developed, enabling efficient approximation of both the value function and system uncertainties. By integrating the command filter technique and function approximation within a backstepping framework, a finite‐time optimal tracking control scheme is constructed. An auxiliary system is further introduced to explicitly handle input saturation. Rigorous analysis based on the finite‐time stochastic Lyapunov theorem ensures that the tracking error remains within a prescribed bound in finite time, and the closed‐loop system achieves semi‐globally finite‐time stability in probability (SGFSP). The effectiveness of the proposed approach is validated through its successful application to a single‐link manipulator system.
Wei-Di Cheng, Shu-Ping He, Hong-Jing Liang· International Journal of Rob...· 0 citations
This work presents an optimal predefined‐time tracking control framework for a nonlinear robot manipulator subject to exogenous disturbances. To guarantee that the tracking errors converge within a user‐specified time bound, regardless of the initial conditions, a predefined‐time sliding mode control (PT‐SMC) technique is devised. This feature guarantees strict temporal performance for safety‐ and mission‐critical applications. An actor‐critic reinforcement learning (RL) architecture is seamlessly integrated with the PT‐SMC technique to achieve optimal torque utilization. A rigorous Lyapunov‐based stability analysis is also provided to establish the predefined‐time convergence and the overall closed‐loop stability. Simulation studies conducted on a 2‐DOF robot manipulator demonstrate superior tracking accuracy, reduced control effort, actuator‐friendly control action, and deterministic convergence time compared with several state‐of‐the‐art controllers. Notably, the proposed controller improves the settling time by more than threefold. Overall, the proposed approach offers a cohesive framework that blends RL‐based optimal tracking control with predefined‐time robustness, making it well‐suited for Industry 5.0: human‐centric robotic systems.
Seema Chaudhary, Vaishnavi Gupta, Dipayan Guha et al.· Optimal control applications...· 0 citations
This paper develops a zero-sum game-based reinforcement learning tracking controller with predefined-time prescribed performance (ZG-RL-PP) for highly flexible aircraft. The disturbed tracking-error dynamics are first transformed into a min–max optimal control problem, where the control input and the disturbance are treated as two players with opposite objectives. To guarantee the prescribed transient and steady-state tracking performance, logarithmic barrier Lyapunov functions are incorporated into the value function and the Hamilton–Jacobi–Isaacs equation. For higher-relative-degree tracking-error channels, recursive auxiliary constraint variables are introduced to preserve the prescribed bounds on the original errors and enable constraint enforcement through the derivative channels in which the control inputs appear. A critic neural network is employed to approximate the value function online, and a predefined-time fractional-power learning law is adopted for critic weight updating. It is shown that the critic weight-estimation error is practically predefined-time convergent and that all closed-loop signals are uniformly ultimately bounded. Simulation results demonstrate the effectiveness and robustness of ZG-RL-PP in terms of tracking accuracy, disturbance attenuation, prescribed-performance satisfaction, and predefined-time learning.
Han-Wen Zhang, Chi Peng, Yu-Xin Zhang et al.· Aerospace· 0 citations
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.
Meng-Jie Wang, Kou Du, Xi-Ming Cai et al.· Symmetry· 0 citations
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.
Xiaozheng Jin· Poster Volume 0008 The 2026...· 0 citations
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