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International audience; This paper proposes the design of an event-triggered control strategy for consensus of interconnected two-time scales systems with structured uncertainty. The control design under consideration ensures also that consensus is achieved with an overall guaranteed cost. Since each system involves processes evolving on both fast and slow time scales, two Zeno-free event-triggered mechanisms are designed to independently decide the sampling and transmission instants for the slow and fast states respectively. As the first step, we design an event-triggering consensus protocol in the ideal/nominal case when the interconnected systems are not affected by uncertainties and the interactions happen over a fixed interaction network. Next, the results are extended in order to take into account structured uncertainties affecting the systems dynamics. At this step, we go further and we provide sufficient conditions for event-triggering consensus with a guaranteed overall cost. Finally, two numerical examples are provided to demonstrate the effectiveness of the proposed theoretical results.

International audience; The paper proposes several fault-tolerant control (FTC) laws for singularly perturbed systems (SPS) with actuator faults and disturbances. On of the main challenges in this context is that the fast-slow decomposition is not available for actuator faults and disturbances. In view of this, some conditions for the asymptotic stability of the closed-loop dynamics are investigated by amending the composite Lyapunov approach. On top of this, a closed-form expression of the upper-bound of singular perturbation parameter (SPP) is provided. Moreover, we design several SPP-independent composite FTC laws which can be applied when this parameter is unknown. Finally, the chattering phenomenon is eliminated by using the continuous approximation technique. We also emphasize that, for linear SPSs, the FTC design can be formulated as a set of linear matrix inequalities while the SPP upper-bound can be obtained by solving a convex optimization problem. Two numerical examples are given to illustrate the effectiveness of the proposed methodology.

In this paper, we study the exponential stability problem for singularly perturbed switched systems(SPSSs), in which subsystems with two-time-scale property are all unstable, and both the destabilizing and stabilizing switching behaviors coexist. To estimate the state divergence during each two consecutive switching instants, the general property of a two-dimensional matrix involving singular perturbation parameter is explored. The switching sequence is properly reordered to provide an appropriate way to describe different switching behaviors. In addition, multiple composite Lyapunov functions(MCLFs) are employed to derive some stability criteria for the nonlinear SPSSs. Furthermore, by using switching-time-dependent MCLFs and dwell time method, some computable stability condition is given for the linear case. The obtained results show the relationship between the ratio of the stabilizing switching behavior and the singular perturbation parameter. Besides, the obtained results are free of ill-conditioning and stiffness problems. This work is supported by the National Natural Science Foundation of China under Grants 61773172, 61903147, and 51537003, the Natural Science Foundation of Hubei Province of China (2017CFA035), the Fundamental Research Funds for the Central Universities, China (2018KFYYXJJ119) and the Postdoctoral Science Foundation of China under Grant 2019M652644.

During vertebrate early embryogenesis, the ventral development is directed by the ventral-to-dorsal activity gradient of the bone morphogenetic protein (BMP) signaling. As secreted ligands, the extracellular traffic of BMP has been extensively studied. However, it remains poorly understood that how BMP ligands are secreted from BMP-producing cells. In this work, we show the dominant role of Marcksb controlling the secretory process of Bmp2b via interaction with Hsp70 in vivo. We firstly carefully characterized the role of Marcksb in promoting BMP signaling during dorsoventral axis formation through knockdown approach. We then showed that Marcksb cell autonomously regulates the trafficking of Bmp2b from producing cell to the extracellular space and both the total and the extracellular Bmp2b was decreased in Marcksb-deficient embryos. However, neither the zygotic mutant of marcksb (Zmarcksb) nor the maternal zygotic mutant of marcksb (MZmarcksb) showed any defects of dorsalization. In contrast, the MZmarcksb embryos even showed increased BMP signaling activity as measured by expression of BMP targets, phosphorylated Smad1/5/9 levels and imaging of Bmp2b, suggesting that a phenomenon of “genetic over-compensation” arose. Finally, we revealed that the over-compensation effects of BMP signaling in MZmarcksb was achieved through a sequential up-regulation of MARCKS-family members Marcksa, Marcksl1a and Marcksl1b, and MARCKS-interacting protein Hsp70.3. We concluded that the Marcksb modulates BMP signaling through regulating the secretory pathway of Bmp2b., Author summary Bone morphogenetic proteins (BMPs) are extracellular proteins which belong to the transforming growth factor-β (TGF-β) superfamily. BMP signaling is essential for embryonic development, organogenesis, and tissue regeneration and homeostasis, and tightly linked to various diseases and tumorigenesis. However, as secreted proteins, how BMPs are transported and secreted from BMP-producing cells remains poorly understood. In this study, we showed that Marcksb interacts with a molecular chaperon–Hsp70.3 to mediate the secretory pathway of BMP ligands during early development of zebrafish. Moreover, we discovered a novel phenomenon of “genetic over-compensation” in the genetic knock-out mutants of marcksb. To our knowledge, this is the first report that reveals the molecules and their related trafficking system mediating the secretion of BMPs. Considering the wide distribution of BMP and MARCKS within the human body, our work may shed light on the studies of BMPs secretion in organogenesis and adult tissue homeostasis. The finding of MARCKS in controlling BMP secretion may provide potential therapeutic targets for modulating the activity of BMP signaling and thus will be of interest to clinical research.