This paper proposes an adaptive finite time command filtered backstepping control scheme for single‐input and single‐output (SISO) uncertain strict-feedback nonlinear systems. The problem of the explosion of complexity existing in the adaptive backstepping control design and the singularity problem are solved by using the proposed adaptive finite time control method. In addition, the compensating signals are introduced to deal with the effect of the known filtering errors caused by the command filters. By using the finite time Lyapunov stability theory, the proposed adaptive finite time control strategy guarantees that all the signals in the closed-loop system are practical finite time stable, and the tracking errors converge to an arbitrarily small neighbourhood of the origin in finite time. Simulation and experimental results of the DC-DC buck converter are given to illustrate the effectiveness of the proposed adaptive finite time control scheme.
This paper introduces an algorithm for estimating the invariant set of closed-loop controlled dynamical systems identified using single-hidden layer Rectified linear units (ReLU) neural networks or piecewise affine () functions, particularly addressing the challenge of providing safety guarantees for single-hidden layer ReLU networks commonly used in safety–critical applications. The invariant set of dynamical system is estimated using single-hidden layer ReLU networks or its equivalent function. This method entails formulating the barrier function as a function and converting the search process into a linear optimization problem using vertices. We incorporate a domain refinement strategy to increase flexibility in case the optimization does not find a valid barrier function. Moreover, the objective of the optimization is to find a less conservative invariant set based on the current partition. Our experimental results demonstrate the effectiveness and efficiency of our approach, demonstrating its potential for ensuring the safety of dynamical systems.