Adaptive Fault-Tolerant Tracking Control for Uncertain Nonlinear Systems With Unknown Control Directions and Limited Resolution

Adaptive state feedback control of output‐constrained stochastic nonlinear systems with stochastic integral input‐to‐state stability inverse dynamics

“…Proof (i) The proof is divided into three parts. Part I: By the same proof procedure of Reference 25, there exists a nondecreasing positive function $$$ \varrho (s) $$$ such that $$$$ \frac{1}{4}\varrho \left({V}_0\left({z}_0\right)\right)\alpha \left(|{z}_0|\right)\ge \frac{1}{2}{\varrho}^{\prime}\left({V}_0\left({z}_0\right)\right){\psi}_z^2\left(|{z}_0|\right){\psi}_0^2\left(|{z}_0|\right)+\Psi \left(|{z}_0|\right){\left|{z}_0\right|}^{4\varsigma \lambda}.\kern0.5em $$$$ Next, we can design the Lyapunov function $$$$ {V}_{z_0}\left({z}_0\right)={\int}_0^{V_0\left({z}_0\right)}\varrho (s)\mathrm{d}s.\kern0.5em $$$$ From the definition of tangent function, it follows that …”

“…Reference 23 solved the adaptive control problem for output constrained nonstrict‐feedback nonlinear stochastic systems with input delay, and Reference 24 proposed a novel control scheme for stochastic nonlinear systems with output constraint and unknown control coefficients. In the newest Reference 25, the authors discussed the fault‐tolerant control for nonstrict‐feedback stochastic nonlinear systems with actuator faults and output constraints. Nevertheless, all of these results exist an obvious drawback that stochastic inverse dynamics are neglected.…”

Reinforcement learning-based adaptive motion control for autonomous vehicles via actor-critic structure

“…More recently, a Luenberger disturbances observer was established to estimate the prediction term of the load torque in real time for the PMSM servo system in [21]. Both partial loss-of-effectiveness and lockin-place faults of actuators of nonlinear systems were studied in [7]. For this reason, robust terms are added to the adaptive control law to compensate for noise and uncertainty.…”