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• It is the first time to investigate the problem of decentralized finite-time tracking control with prescribed settling time for a class of p -normal form stochastic large-scale systems with output interconnections existing in both the drift and diffusion terms. • It is the first time to investigate the connective stability problem for stochastic large-scale systems when the system structure changes. • Differing from the existing results, this paper proposes a new mathematical treatment algorithm to deal with the interconnections of stochastic large-scale systems, such that the decentralized tracking control is achieved. • The proposed control strategy is more convenient for practical application than the general finite-time control. • Due to the complexity of the system mathematics model, this paper can better reflect the application of mathematics. This paper aims to solve the decentralized finite-time connective tracking control problem for p -normal form stochastic large-scale systems with output interconnections existing in both the drift and diffusion terms. By means of the stochastic system theory and a prescribed finite-time performance function (PFTPF), a novel design scheme is presented for the decentralized finite-time connective tracking controllers with an arbitrarily prescribed settling time. The connective stability problem of stochastic large-scale systems is investigated for the first time. In addition, a new solution for the decentralized tracking control problem of stochastic large-scale systems is presented via a novel mathematical treatment algorithm. The proposed controllers can ensure that the tracking errors converge to a predetermined region within an arbitrarily prescribed settling time and the controlled system is connectively bounded stable in probability. Three simulation examples are presented to exhibit the performance and the superiority of the new control strategy. [ABSTRACT FROM AUTHOR]

• For optimal control, the stochastic information with current iterative results is used to solve the stochastic algebraic Riccati equation, which has stochastic characteristics. • Calculate the increment instead of the value itself to improve the calculation accuracy. • Newton's method with line search solve the potentially disastrous problem of the first Newton step. • The convergence and even quadratic convergence of the proposed incremental Newton's iterative algorithm have been discussed. In this paper, a novel incremental Newton's iterative algorithm for investigating the optimal control problem of Itô stochastic systems is presented. Newton's method is employed under the Fréchet derivative framework to iteratively solve a stochastic algebraic Riccati equation. Under moderate conditions, the convergence and even quadratic convergence of the proposed incremental Newton's iterative algorithm are discussed, respectively. In addition, the Newton's method is extended to the one with linear search. In the end, numerical results are given to demonstrate the effectiveness and superiority of the proposed algorithms. [ABSTRACT FROM AUTHOR]