In this study, a framework for processing gradient algorithms is proposed in accordance with nabla fractional-order system theory. Unlike most of the literature, the gradient algorithm is initially recast into a nabla fractional-order dynamic system. To be specific, the algorithm is designed using control theory and analyzed using the Lyapunov theory, which is a more general and effective way to render high-performance algorithm. Three types of algorithms are built in this study, i.e., the asymptotic convergence case, the finite-time convergence case, and the fixed-time convergence case. Finally, a comprehensive simulation study is conducted verifying the correctness, usefulness, and practicality of the framework.

Deep learning (DL) is becoming increasingly popular in many domains, including computer vision, speech recognition, self-driving automobiles, etc. GPU can train DL models efficiently but is expensive, which motivates users to share GPU resource to reduce money costs in practice. To ensure efficient sharing among multiple users, it is necessary to develop efficient GPU resource management and scheduling solutions. However, existing ones have several shortcomings. First, they require the users to specify the job resource requirement which is usually quite inaccurate and leads to cluster resource underutilization. Second, when scheduling DL jobs, they rarely take the cluster network characteristics into consideration, resulting in low job execution performance. To overcome the above issues, we propose Liquid, an efficient GPU resource management platform for DL jobs with intelligent resource requirement estimation and scheduling. First, we propose a regression model based method for job resource requirement estimation to avoid users over-allocating computing resources. Second, we propose intelligent cluster network-efficient scheduling methods in both immediate and batch modes based on the above resource requirement estimation techniques. Third, we further propose three system-level optimizations, including pre-scheduling data transmission, fine-grained GPU sharing, and event-driven communication. Experimental results show that our Liquid can accelerate the job execution speed by 18% on average and shorten the average job completion time (JCT) by 21% compared with cutting-edge solutions. Moreover, the proposed optimization methods are effective in various scenarios.

The well-known generalized Kalman–Yakubovich–Popov lemma is widely used in system analysis and synthesis. However, the corresponding theory for singular systems, especially singular fractional-order systems (SFOSs), is lacking. Therefore, many control problems for this type of systems cannot be optimized in limited frequency ranges. In this article, a universal framework of the finite frequency band generalized Kalman–Yakubovich–Popov lemma for SFOSs is established, the bounded real lemma in the sense of the${L_{\infty }}$-norm is derived for different frequency ranges, and the corresponding controller is designed to improve the${L_{\infty } }$performance index of SFOSs. Three illustrative examples are given to demonstrate the correctness and effectiveness of the theoretical results.

This paper focus on developing a flexible biomimetic sensor, which is embedded in a soft earthworm-like crawling mini-robot and mimics exteroceptive and proprioceptive functions of invertebrates, such as its biological counterpart-earthworm. A polyvinylidene fluoride (PVDF) film is selected as the sensing element because it is flexible, highly sensitive and easy to be integrated in different shapes. Thin and narrow PVDF strips are embedded with an innovative molding-embedding-remolding fabrication procedure in a segmented compliant silicone shell which serves as skin and passive actuation of a crawling earthworm-like mini-robot with the ability to elongate and contract. Several experiments were performed by using a purposely developed test-bench in order to test sensor behaviour. The results show that the biomimetic flexible PVDF-based sensor can detect both the external contact and the internal actions, thus imitating the exteroceptive and proprioceptive sensing capabilities of real earthworms. The developed biomimetic sensors are promising in order to achieve an useful sensor feedback for the earthworm-like minirobot motion control