In this study, an accurate convergence time of the supertwisting algorithm is proposed to build up a framework for nonaffine nonlinear systems’ finite-time control. The convergence time of the STA is provided by calculating the solution of a differential equation instead of constructing Lyapunov function. Therefore, precise convergence time is presented instead of estimation of the upper bound of the algorithm’s reaching time. Regardless of affine or nonaffine nonlinear systems, supertwisting control provides a general solution based on virtual control law (...) skill ensuring the output of the systems converges to the origin point at exact time. Benchmark tests are simulated to demonstrate the effectiveness and efficiency of the algorithm. (shrink)

An adaptive neural network control problem is addressed for a class of nonlinear hydraulic servo-systems with time-varying state constraints. In view of the low precision problem of the traditional hydraulic servo-system which is caused by the tracking errors surpassing appropriate bound, the previous works have shown that the constraint for the system is a good way to solve the low precision problem. Meanwhile, compared with constant constraints, the time-varying state constraints are more general in the actual systems. Therefore, when the (...) states of the system are forced to obey bounded time-varying constraint conditions, the high precision tracking performance of the system can be easily realized. In order to achieve this goal, the time-varying barrier Lyapunov function is used to prevent the states from violating time-varying constraints. By the backstepping design, the adaptive controller will be obtained. A radial basis function neural network is used to estimate the uncertainties. Based on analyzing the stability of the hydraulic servo-system, we show that the error signals are bounded in the compacts sets; the time-varying state constrains are never violated and all singles of the hydraulic servo-system are bounded. The simulation and experimental results show that the tracking accuracy of system is improved and the controller has fast tracking ability and strong robustness. (shrink)