Much recently, an internal model approach from output regulation theory has been adopted to solve the speed tracking control problem of permanent magnet synchronous motor (PMSM) system on simulation level. A striking advantage of this approach is that it can achieve multiple goals including trajectory tracking, disturbance rejection and robustness simultaneously. This paper further studies a position tracking control problem of PMSM system under nonlinear load torque disturbance. A nonlinear internal model based output feedback controller is proposed, which can achieve exact position tracking and allow certain parameter uncertainties. Besides simulation results, a real-time experimental setup is built and experimental results are provided to illustrate the effectiveness of the proposed controller. It is worth mentioning that the proposed controller can lead to a high precision position tracking performance under nonlinear load torque disturbance.

This article addresses the issue of adaptive memory event triggered output feedback finite-time lane keeping control for autonomous heavy truck with roll prevention subject to nonlinear corning stiffness, time-varying driving speed and trace curvature. A novel adaptive memory event triggered scheme is developed to slow down control command update under unexpected system dynamic fluctuation excited by abrupt trace disturbances by releasing less triggered times, as well as speed up update under large amplitude response but gentle variation around critical crest/trough situation by releasing more triggering times. In order to overcome the shortcomings of slower convergence and longer response time resulted from designed scheme for control command update, finite-time lane keeping control with prescribed H∞ performance is employed to achieve expected convergence properties. Additionally, better tracking control quality requirements for designed control strategy are specifically achieved with considered roll prevention control for sprung mass and front/rear solid axle by eliminating negative effects on yaw motion and decreasing dynamic load transfer rate. Furthermore, sufficient conditions are established to guarantee finite-time boundedness with prescribed H∞ performance, gain matrices for controller and trigger are co-designed and obtained by solving certain matrix inequalities. Benefiting from regulated control command update and roll prevention under adaptive memory event triggered scheme, the obtained results illustrating reasonable triggered times, less tracking error, smoother centroid trajectory, smaller roll angle and decreased dynamic load transfer rate demonstrate effectiveness of the proposed control strategy.

The finite-time synchronization (FTS) is studied for a class of fractional-order delayed fuzzy cellular neural networks (FODFCNNs) with parameter uncertainties. A linear fractional-order finite time inequality (FOFTI) ${}^{c}_{t_{0}}D^{p}_{t} V(t)\le -a V(t)-b$ is extended to the nonlinear case ${}^{c}_{t_{0}}D^{p}_{t} V(t)\le -a V^{-\eta }(t)-b$ , $\eta \ge 1$ , which plays a vital role in the FTS of fractional-order systems. However, for the case of $0< \eta < 1$ , a theoretical cornerstone justifying its use is still missing. To fill this research gap, on the basis of the $C_{p}$ inequality and the rule for fractional-order derivative of composite function, a nonlinear FOFTI ${}^{c}_{t_{0}}D^{p}_{t} V(t)\le -a V^{-\eta }(t)-b$ , $0< \eta < 1$ is developed. Furthermore, a nonlinear FOFTI ${}^{c}_{t_{0}}D^{p}_{t} V(t)\le -bV^{-\xi }(t)-a V^{-\eta }(t)$ is also established. These two novel inequalities provide the new tools for the research on the finite time stability and synchronization of fractional-order systems and can greatly extend the pioneer ones. Next, on the basis of these novel inequalities, the feedback controller is designed and two novel FTS criteria of FODFCNNs with parameter uncertainties are obtained. Finally, two examples are presented to verify the effectiveness of the derived results.

In this article, the finite-time stability (FTS) of fractional-order Hopfield neural networks with time delays (FHNNTDs) is studied. A widely used inequality in investigating the stability of the fractional-order neural networks is fractional-order Gronwall inequality related to the Mittag-Leffler function, which cannot be directly used to study the stability of the factional-order neural networks with time delays. In the existing works related to fractional-order Gronwall inequality with time delays, the order λ>0 was divided into two cases: λ∈(0,0.5] and λ∈(0.5,+∞). In this article, a new fractional-order Gronwall integral inequality with time delay and the unified form for all the fractional order λ>0 is developed, which can be widely applied to investigate FTS of various fractional-order systems with time delays. Based on this new inequality, a new criterion for the FTS of FHNNTDs is derived. Compared with the existing criteria, in which fractional order λ∈(0,1) was divided into two cases, λ∈(0,0.5] and λ∈(0.5,1), the obtained results in this article are presented in the unified form of fractional order λ∈(0,1) and convenient to verify. More importantly, the criteria in this article are less conservative than some existing ones. Finally, two numerical examples are given to demonstrate the validity of the proposed results.