Decentralized adaptive neural fixed‐time tracking control of constrained interconnected nonlinear systems with partially unmeasurable states

Abstract

This article devises a new adaptive fixed-time tracking control strategy for interconnected nonlinear systems containing partially unmeasurable states and time-varying output constraints. Radial basis function neural networks, as function approximators, are utilized to model the unknown functions, and the partially unmeasurable states of the systems are estimated by a reduced-order observer. By constructing a transferred function, system outputs are directly constrained in a time-varying constraint bound. Meanwhile, the first-order sliding mode differentiators are utilized to reduce the computational burden caused by the repeated differentiations of virtual controllers. Under the Lyapunov function and the fixed-time theory, the decentralized adaptive fixed-time controllers are constructed. It is proved that the closed-loop systems are fixed-time stable and the output signals are restricted in the bounded compact set. Finally, two simulation examples demonstrate the validity of the proposed control scheme.

Adaptive dynamic surface control of MIMO nonlinear systems: A hybrid event triggering mechanism

“…Utilizing the Young's inequality 35 yields $$$$ 2\left\Vert {e}_j\right\Vert \left\Vert {P}_j\right\Vert \left\Vert {l}_{\psi_j}\right\Vert \left|{y}_j\right|\left\Vert {\theta}_j\right\Vert \kern0.5em \le {\left\Vert {P}_j\right\Vert}^2{\left\Vert {l}_{\psi_j}\right\Vert}^2{\left\Vert {e}_j\right\Vert}^2+{\left|{y}_j\right|}^2{\Theta}_j $$$$ …”

“…Theorem 1. Considering the closed-loop MIMO nonlinear system (1) satisfies Assumption 1, the state observer given in (4), the first-order filter designed in (15), the virtual controllers proposed in (22), (35), and the hybrid ETM with event detectors (2), ( 46), ( 47) and (50). For any bounded initial conditions, all the closed-loop variables are bounded under the help of Lyapunov stability theory, 39,40 and the Zeno behavior can be avoided.…”