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This paper investigates an adaptive cooperative fault-tolerant supervisory control problem for nonlinear strict-feedback leader-following systems with unknown control coefficients and actuator faults under the fixed directed graph. Radial basis function neural networks are used to approximate system uncertainties. The Nussbaum gain technique is introduced to address unknown signs of control gains. Then, based on the dynamic surface control method, a distributed adaptive fault-tolerant control scheme is presented to compensate for the actuator faults of followers. For neural networks approximation theory, the unknown smooth function can only be approximated on a compact set due to the approximation errors. By theoretic analysis, the supervisory-based adaptive controllers are proposed to guarantee that system state signals can converge to compact sets and the leader-following systems can achieve the practical output consensus. Finally, the simulation results are provided to show the validity of the proposed consensus scheme. [ABSTRACT FROM AUTHOR]

This paper is devoted to analysing the actuator characterisations for the fractional sub-diffusion equation under consideration to become approximately controllable. Two different cases are considered, where the control inputs emerge in the differential equation as distributed inputs and as boundary inputs in the boundary conditions. The dual system for fractional sub-diffusion equation is solved and the necessary and sufficient conditions for the approximate controllability of the system are established. Several examples are worked out in the end to illustrate our results. [ABSTRACT FROM AUTHOR]

In this paper, through an evaluation process conducted on several designs of mini-LIPCA (Lightweight Piezo-Composite curved Actuator), an optimal design of a mini-LIPCA has been proposed. Comparing with the LIPCA-C2, the design of the mini-LIPCA comes with reduced overall size and a thinner active layer. Since a variation in the number and lay-up of fiber composite layers may strongly affect the performance of the device, one is able to configure several designs of mini-LIPCA. The evaluation process is then followed in order to determine a configuration which characterizes the possibly optimal performance. That is, a design of a mini-LIPCA is said to be optimal if it is capable of producing a maximum out-of-plane displacement. The size of the LIPCA to be investigated was selected to be 10 mm × 20 mm in which the thickness of PZT plate is about 0.1 mm. The thickness of glass/epoxy and carbon/epoxy are about 0.09 mm and 0.1 mm, respectively. The evaluation process has been conducted thoroughly, i.e., analytical estimation, numerical approximation and the experimental measurement are all involved. Firstly, the design equation was used to calculate essential parameters of proposed lay-up configurations. Secondly, ANSYS, a commercial FEA package, was utilized to estimate displacement outputs of the actuators upon being excited. Finally, experimental measurements were able to verify the predicted results. [ABSTRACT FROM AUTHOR]