## 1 Introduction  
It is ineluctable to contain uncertain parameters and disturbances in practical systems due to modeling errors, external disturbances, and so on [1]. Thus, it is of great practical significance to study robust control of the uncertain systems. In recent years, the control problem of uncertain systems has been extensively studied. The literature on robust control of uncertain systems mainly includes linear systems and nonlinear systems. For the uncertain linear systems, algebraic Riccati equations (ARE) or linear matrix inequalities (LMI) were mostly used to deal with them in the classical research methods [2, 3, 4, 5, 6]. In this literature, both matched and mismatched systems were involved. For nonlinear systems, the early research methods include feedback linearization, fuzzy modeling, nonlinear \(H_{\infty}\) control, and so on [7, 8, 9, 10, 11]. However, in recent decades, neural networks (NN) and PI in RL were used to approximate the robust control law numerically [12, 13, 14]. The PI method in RL was initially utilized to calculate the optimal control law for some deterministic systems. [PERSON] first proposed an idea of approximating the solution in [PERSON]'s equation using approximate dynamic programming (ADP) [15]. There have been many results of using the PI method to calculate the optimal control law for some deterministic systems [16, 17, 18, 19]. There are two major benefits of using the PI algorithm to deal with such optimal problems. On the one hand, it can effectively solve some problems of the \"curse of dimensionality\" in engineering control [20]. On the other hand, it can be utilized to calculate the optimal control law without knowing the system dynamics. In the practice of engineering control, it is difficult to obtain system dynamics accurately. Therefore, it is a good choice to use the PI algorithm to solve unknown model control problems. Within the last ten years, the PI method was also developed to calculate the robust controller for some uncertain systems, which is based on the optimal control method of robust control [21]. For an input constraint nonlinear system with continuous time, a novel RL-based algorithm was prosposed to deal with the robust control problem in [22]. Based on network structure approximation, an online PI algorithm was developed to solve robust control of a class of nonlinear discrete-time uncertain systems in [23]. Using a data-driven RL algorithm, a robust control scheme was developed for a class of completely unknown dynamic systems with uncertainty in [24]. In addition, there are many other examples of literature on robust control based on RL, such as [25; 26; 27]. In all the literature listed above, the solution to the Hamilton Jacobi Bellman (HJB) equation was approximated by neural network. In fact, solving the HJB equation is a key problem in optimal control problem [28]. The HJB equation is difficult to solve because it is a nonlinear partial differential equation. For a nonlinear system, the HJB equation is solved with neural network approximation in many cases. Meanwhile, for the linear system, ARE is used to solve it instead of a neural network. However, for all we know, most of the current studies have not considered the input uncertainty in system. The input uncertainty does exist in the actual control system. In this study, a class of continuous-time nonlinear systems with internal and input uncertainties is considered. The main objective is to establish robust control laws for the uncertain systems. By solving the optimal control problem constructed, the robust control problem is converted into calculating an optimal controller. The online PI algorithms are proposed to calculate robust control by approximating the optimal cost with neural network. The convergence of the proposed algorithms is proved. Numerical examples are given to illustrate the availability of the method. Our main contributions are as follows.