Dynamic Flexible Job Shop Scheduling (DFJSS) is an important and challenging problem, and can have multiple conflicting objectives. Genetic Programming Hyper-Heuristic (GPHH) is a promising approach to fast respond to the dynamic and unpredictable events in DFJSS. A GPHH algorithm evolves dispatching rules (DRs) that are used to make decisions during the scheduling process (i.e. the so-called heuristic template). In DFJSS, there are two kinds of scheduling decisions: the routing decision that allocates each operation to a machine to process it, and the sequencing decision that selects the next job to be processed by each idle machine. The traditional heuristic template makes both routing and sequencing decisions in a non-delay manner, which may have limitations in handling the dynamic environment. In this paper, we propose a novel heuristic template that delays the routing decisions rather than making them immediately. This way, all the decisions can be made under the latest and more accurate information. We propose three different delayed routing strategies, and automatically evolve the rules in the heuristic template by GPHH. We evaluate the newly proposed GPHH with Delayed Routing (GPHH-DR) on a multi-objective DFJSS that optimises the energy efficiency and mean tardiness. The experimental results show that GPHH-DR significantly outperformed the state-of-the-art GPHH methods. We further demonstrated the efficacy of the proposed heuristic template with delayed routing, which suggests the importance of delaying the routing decisions.

This paper addresses the tracking control problem of nonstrict-feedback systems with unknown control gains. The dynamic surface control method, Nussbaum gain function control technique, and radial basis function neural network are applied for the design of virtual control laws, and adaptive control laws. Then, an adaptive neural tracking control law is proposed in the last step. By using the dynamic surface control method, the “explosion of complexity” problem of conventional backstepping is avoided. Based on the application of the Nussbaum gain function control technique, the unknown control gain problem is well solved. With the help of the radial basis function neural network, the unknown nonlinear dynamics are approximated. Furthermore, through Lyapunov stability analysis, it is proved that the proposed control law can guarantee that all signals in the closed-loop system are bounded and the tracking error can converge to an arbitrarily small domain of zero by adjusting the design parameters. Finally, two examples are provided to illustrate the effectiveness of the proposed control law.

Dynamic Flexible Job Shop Scheduling (DFJSS) is an important and challenging problem, and can have multiple conflicting objectives. Genetic Programming Hyper-Heuristic (GPHH) is a promising approach to fast respond to the dynamic and unpredictable events in DFJSS. A GPHH algorithm evolves dispatching rules (DRs) that are used to make decisions during the scheduling process (i.e. the so-called heuristic template). In DFJSS, there are two kinds of scheduling decisions: the routing decision that allocates each operation to a machine to process it, and the sequencing decision that selects the next job to be processed by each idle machine. The traditional heuristic template makes both routing and sequencing decisions in a non-delay manner, which may have limitations in handling the dynamic environment. In this paper, we propose a novel heuristic template that delays the routing decisions rather than making them immediately. This way, all the decisions can be made under the latest and more accurate information. We propose three different delayed routing strategies, and automatically evolve the rules in the heuristic template by GPHH. We evaluate the newly proposed GPHH with Delayed Routing (GPHH-DR) on a multi-objective DFJSS that optimises the energy efficiency and mean tardiness. The experimental results show that GPHH-DR significantly outperformed the state-of-the-art GPHH methods. We further demonstrated the efficacy of the proposed heuristic template with delayed routing, which suggests the importance of delaying the routing decisions.

In this work, the position and attitude tracking finite-time adaptive control problem of a type of vertical take-off and landing (VTOL) aircraft system is studied. Here, the dynamic of the VTOL aircraft is subjected to external disturbances and unknown nonlinearities. Firstly, radial basis function neural networks are introduced to approximate these unknown nonlinearities, and adaptive weight update laws are proposed to replace unknown ideal weights. Secondly, for the errors generated in the approximation process and the external disturbances of the aircraft system, adaptive parameter update laws are presented. After that, based on the designed global fast terminal sliding mode control functions and adaptive update laws, we present the position tracking control laws and the roll angle control law. Then, based on this, the adaptive global fast terminal sliding control laws for the given aircraft system are finally obtained. Meanwhile, the stability of the aircraft control system is proven by using Lyapunov stability theory and designed adaptive control laws. It is not only ensured that the outputs of the aircraft system can track the given trajectories, but also ensured that the tracking errors can converge to approximately zero within a finite time. Finally, the validity of the designed adaptive control laws is verified through three numerical examples. It can be obtained that the finite-time tracking problems of the given aircraft system can be achieved at 18.8766 s and 14.6340 s under the given parameters. The results are consistent with the theoretical analysis. In addition, under the control laws proposed in this work, the aircraft system can achieve tracking after 9.443 s and 9.674 s and the tracking errors are basically close to zero, which is significantly superior to other control methods considered in this work.