This paper introduces an observer-based neural quadratic sliding mode control strategy for interconnected Markov jump systems faced with unknown interconnections, regardless of the high dimensionality of the systems. Firstly, a dynamic event-triggered scheme is constructed in the communication channel to the Lebesgue state observer, with which an integral quadratic sliding mode hyperplane is put forward; Secondly, a neural-based control method is put forward to make sure that predefined sliding hyperplane is attractive; In addition, the occurrence of Zeno phenomenon is also verified to be avoided with the implementation of the controller; Thirdly, linear matrix inequality technique and Lyapunov stochastic stability theory are proposed to check the stochastic stability of closed-loop systems, including sliding mode dynamics and error dynamics; Finally, simulation results on single-link robot arms are given to reveal the validity of the obtained results.

A recent trend of fair machine learning is to build a decision model subjected to causality-based fairness requirements, which concern with the causality between sensitive attributes and decisions. Almost all (if not all) solutions focus on a single fair decision model and assume no hidden confounder to model causal effects in a too simplified way. However, multiple interdependent decision models are actually used and discrimination may transmit among them. The hidden confounder is another inescapable fact and causal effects cannot be computed from observational data in the unidentifiable situation. To address these problems, we propose a method called CMFL (Causality-based Multiple Fairness Learning). CMFL parameterizes the causal model by response-function variables, whose distributions capture the randomness of causal models. CMFL treats each classifier as a soft intervention to infer the post-intervention distribution, and combines the fairness constraints with the classification loss to train multiple decision classifiers. In this way, all classifiers can make approximately fair decisions. Experiments on synthetic and benchmark datasets confirm its effectiveness, the response-function variables can deal with the unidentifiable issue and hidden confounders.

The paper proposes an adaptive controller design for Markov jump systems with mixed mode transition information through a reduced-order sliding mode approach. The stability criteria and mode-dependent adaptive control law are achieved using linear matrix inequality technique. Firstly, a linear reduced-order sliding surface function is proposed to achieve the reduced-order sliding mode dynamics. Secondly, a feasible approach is presented to check the stochastic stability of resulting sliding motion corresponding to different mode transition information, and to solve the controller gains from stability criteria. Thirdly, an adaptive sliding mode controller is also designed to ensure the finite-time reachability of the predefined hyperplane even when no mode information is available. Finally, the application of the proposed control strategy to the RLC circuit is provided.