In this paper, the optimal adaptive leader-follower consensus of linear continuous time multi-agent systems is considered. The error dynamics of each player depends on its neighbors’ information. Detailed analysis of online optimal leader-follower consensus under known and unknown dynamics is presented. The introduced reinforcement learning-based algorithms learn online the approximate solution...

This work addresses the problems of robust exponential stability and stabilization for uncertain linear non-autonomous control systems with discrete and distributed time-varying delays and nonlinear perturbations. Based on the combination of the Riccati differential equation approach and the Lyapunov-Krasovskii functional, new sufficient conditions are derived in terms of the solution of Riccat...

We obtain the global existence and uniqueness result for a one-dimensional backward stochastic Riccati equation, whose generator contains a quadratic term of L (the second unknown component). This solves the one-dimensional case of BismutPeng's problem which was initially proposed by Bismut (1978) in the Springer yellow book LNM 649. We use an approximation technique by constructing a sequence ...

Some preliminaries about the integrable families of Riccati equations and solutions structure of these equations in several cases are presented in this paper, then by using of definitions for fractional derivative, we apply the new extended of tanh method to the perturbed nonlinear fractional Schrodinger equation with the kerr law nonlinearity. Finally by using of this method and solutions of R...

In this paper, we investigate a mean-square stabilizing solution to a modified algebraic Riccati equation (MARE), which arises in our previous work on the linear quadratic optimal control for linear time-invariant discrete systems with random input gains. An explicit necessary and sufficient condition ensuring the existence of a mean-square stabilizing solution is given directly in terms of the...