This paper is related to nonzero-sum stochastic differential games in the Markovian framework. We show existence of a Nash equilibrium point for the game when the drift is no longer bounded and only satisfies a linear growth condition. The main tool is the notion of backward stochastic differential equations which, in our case, are multidimensional with continuous coefficient and stochastic linear growth.

The blood-brain barrier (BBB) severely blocks the intracranial accumulation of most systemic drugs. Inspired by the contribution of the bacterial outer membrane to Escherichia coli K1 (EC-K1) binding to and invasion of BBB endothelial cells in bacterial meningitis, utilization of the BBB invasion ability of the EC-K1 outer membrane for brain-targeted drug delivery and construction of a biomimetic self-assembled nanoparticle with a surface featuring a lipopolysaccharide-free EC-K1 outer membrane are proposed. BBB penetration of biomimetic nanoparticles is demonstrated to occur through the transcellular vesicle transport pathway, which is at least partially dependent on internalization, endosomal escape, and transcytosis mediated by the interactions between outer membrane protein A and gp96 on BBB endothelial cells. This biomimetic nanoengineering strategy endows the loaded drugs with prolonged circulation, intracranial interstitial distribution, and extremely high biocompatibility. Based on the critical roles of gp96 in cancer biology, this strategy reveals enormous potential for delivering therapeutics to treat gp96-overexpressing intracranial malignancies.

In this paper, we study a nonzero-sum stochastic differential game of bang-bang type in the Markovian framework. We show the existence of a Nash equilibrium point for this game. The main tool is the notion of backward stochastic differential equations which, in our case, are multidimensional with discontinuous generators with respect to z component.where B := (B s ) s≤T is a Brownian motion. Next with each player π i , i = 1, 2, is associated a payoff J i (u, v), i = 1, 2, given by:The objective is to find a pair (u * , v * ) which satisfy (1.

In this article, the leader-follower consensus problem is considered for a class of nonlinear multiagent systems with event-triggered inputs. A novel time-varying gain compensator is designed for each follower by only utilizing the output information of the follower and its neighbors. Based on a time-varying threshold strategy and a directed communication topology, a distributed event-triggered output feedback controller is designed for each follower. It is proved by the Lyapunov theory that the leader-follower consensus of the multiagent systems is achieved and the Zeno-behavior is avoided. Compared with the existing results, it is the first time that a time-varying gain control algorithm is proposed for the multiagent systems subject to event-triggered inputs. The effectiveness of the proposed consensus protocol is validated by the chemical reactor systems.

In this paper, the leader–follower consensus problem is investigated for multi‐agent systems subject to external disturbances generated by heterogeneous nonlinear exosystems. First, the disturbance observers are developed for each follower to effectively estimate the nonlinear disturbances. Then, based on the presented observers, the distributed state and output feedback consensus protocols are proposed to guarantee that the consensus tracking errors converge to zero asymptotically, and meanwhile to reject the nonlinear disturbances. Particularly, the output feedback protocol can be designed and implemented without any global information about the whole network, which means it is fully distributed. Finally, two numerical examples are given to illustrate the effectiveness of the results.

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