Prescribed-Time Fault-Tolerant Optimal Control of Continuum Surgical Robots via Composite Deep Learning

Fault-tolerant control is essential for surgical continuum robots, where actuator and sensor faults, time-varying delays, input saturation, disturbances, and nonlinearities can rapidly degrade accuracy and safety. This paper proposes a prescribed-time fault-tolerant framework that guarantees convergence within a user-defined settling time, independent of initial conditions, under stated assumptions. A descriptor-form observer simultaneously estimates sensor delays and fault signals, while a deep neural network (DNN) approximates unmodeled dynamics. Adaptive laws compensate for disturbances and approximation errors, and a time-base generator enforces prescribed-time convergence of the estimation errors. Building on these estimates, a resilient near-optimal controller is synthesized, whose residual term is learned online by a DNN via composite learning that combines tracking and observer errors. An auxiliary compensator mitigates input-delay and saturation effects. Lyapunov analysis provides sufficient LMI conditions for prescribed-time closed-loop stabilization. Simulations on a tendon-driven continuum robot under simultaneous actuator and sensor faults, time-varying delays, and saturation demonstrate superior tracking accuracy, faster convergence, and lower control effort compared with a representative robust baseline, highlighting the framework’s strong potential for safe and precise surgical manipulation.