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• A novel online mode-free integral reinforcement learning algorithm is proposed to solve the mutiplayer non-zero sum games. • The online learning is used to compute the corresponding N coupled algebraic Riccati equations. • The policy iterative algorithm is applied to solve the coupled algebraic Riccati equations corresponding to the multiplayer nonzero sum games. In this paper, a novel online mode-free integral reinforcement learning algorithm is proposed to solve the multiplayer non-zero sum games. We first collect and learn the subsystems information of states and inputs; then we use the online learning to compute the corresponding N coupled algebraic Riccati equations. The policy iterative algorithm proposed in this paper can solve the coupled algebraic Riccati equations corresponding to the multiplayer non-zero sum games. Finally, the effectiveness and feasibility of the design method of this paper is proved by simulation example with three players. [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]

• A novel numerical approach for solving SIVIE has been proposed first time ever. • Operational matrices are used to transform the SIVIE into a system of algebraic equations. • Resultant system of algebraic equations has been solved by the collocation method. • This technique has the advantage of being simple to implement. • Error estimate, convergence, and stability analysis are also established. In this paper, a numerical method is implemented to solve the stochastic Itô-Volterra integral equations. In this approach, operational matrices have been applied to reduce the stochastic Itô-Volterra integral equations to linear algebraic equations. Then collocation method is applied to solve the algebraic equations. The error, convergence, and stability analysis of the proposed method are discussed. Also, the steps of the proposed method have been presented in the form of an algorithm. Numerical examples are introduced to confirm the efficiency and reliability of the proposed scheme. [ABSTRACT FROM AUTHOR]