In this study, an adaptive neuro-observer-based optimal control (ANOPC) policy is introduced for unknown nonaffine nonlinear systems with control input constraints. Hamilton–Jacobi–Bellman (HJB) framework is employed to minimize a non-quadratic cost function corresponding to the constrained control input. ANOPC consists of both analytical and algebraic parts. In the analytical part, first, an observer-based neural network (NN) approximates uncertain system dynamics, and then another NN structure solves the HJB equation. In the algebraic part, the optimal control input that does not exceed the saturation bounds is generated. The weights of two NNs associated with observer and controller are simultaneously updated in an online manner. The ultimately uniformly boundedness (UUB) of all signals of the whole closed-loop system is ensured through Lyapunov’s direct method. Finally, two numerical examples are provided to confirm the effectiveness of the proposed control strategy.

The paper presents a novel control design, which is based on the idea of active disturbance rejection control (ADRC), for a kind of flexible aerocraft whose controlled variable cannot be measured directly. Since the original frame of ADRC cannot be directly applied, the paper puts forward a new extended state observer (ESO) and the corresponding ADRC law. In order to assign the poles of the closed-loop system to ideal positions such that the vibration can be quickly suppressed, an elastic damping term is added into feedback law. The advantages of the new ESO for effectively estimating both the rigid mode and elastic mode from the measurements are discussed. Moreover, the analysis on the stability, the relative stability and the steady state of the closed-loop system is given. Finally, the effectiveness and robustness of the proposed ADRC are verified by simulations.

A finite-time consensus protocol is proposed for multi-dimensional multi-agent systems, using direction-preserving signum controls. Filippov solutions and nonsmooth analysis techniques are adopted to handle discontinuities. Sufficient and necessary conditions are provided to guarantee infinite-time convergence and boundedness of the solutions. It turns out that the number of agents which have continuous control law plays an essential role in finite-time convergence. In addition, it is shown that the unit balls introduced by $$\ell _p$$ norms, where $$p\in [1,\infty ]$$ , are invariant for the closed loop.