solving the HJI is developed. A game theoretic differential dynamic programming based algorithm for calculating both minimizing and maximizing inputs based on Taylor series expansion of the associated HJI equation around a nominal trajectory is proposed in [11]. Using a critic neural network with time-varying activation functions, the HJI equation is approximately solved in [9]. An event-triggering function for two-player zero-sum games in the presence of control constraints is designed in [17]. Furthermore, in [13], an iterative procedure to find the stabilizing solution of a set of Riccati equations related to discrete-time \(\mathcal{H}_{\infty}\) control problems for periodic systems is addressed. The randomized algorithm based on the Ray-Shooting Method for \(\mathcal{H}_{\infty}\) optimal synthesis of proportional-integral-derivative (PID) controller for linear systems is proposed in [18]. In the case of the methods and algorithms mentioned above, the application of LMI and solving Riccati equation requires the linearization, and in this case the optimality of solution cannot be guaranteed in all operating states of nonlinear system dynamics. On the other hand, solving the HJI equation can be very complex and therefore difficult to apply in real control tasks. In this paper, the nonlinear state-feedback \(\mathcal{H}_{\infty}\) control problem is formulated as zero-sum differential game, and we approach its solution without the LMI formalism or the need to approximate the solution of the HJI equation. The main idea of the presented approach is in the application of the conjugate gradient method, where the first-order derivatives are calculated by matrix relations backwards in time, which gives a direct numerical calculation of the control and uncertainty variables that explicitly depend on the system states. In contrast to the approaches proposed in [11; 16], which in the case of including a more complex nonlinearity of the dynamic system in the objective function result in a HJI equation so complex that it is practically impossible to solve, in our approach the nonlinear system dynamics is not included in the objective function as an equality constraint, but the state variables, control law and uncertainty are coupled by recursive matrix relations and chain rule for ordered derivatives, which are used to calculate the objective function gradients that appear in conjugate gradient method. Furthermore, in contrast to approaches presented in [10; 12], which can be computationally expensive since the tuning of neural network weights is based on a method of weighted residuals that includes calculation of Lebesgue integrals and estimation of state variables, in our approach, the computational complexity does not depend on the dimension of the state space since procedure proposed for gradient calculation has a backward in time structure similar to the back propagation through time algorithm. Bed sides the conjugate gradient method, which is used for computation of saddle point of zero-sum differential game, the quasi-Newton method for \(\mathcal{L}_{2}\)-gain minimization, line search method with Wolfe conditions, Adams approximation method for time discretization and the complex-step method for calculation of derivatives are also systematically integrated into an efficient mathematical tool in order to achieve numerical robustness and stability. The rest of the paper is organized as follows. In Section 2, the preliminaries of the nonlinear state-feedback \(\mathcal{H}_{\infty}\) control from the concept of dissipativity point of view and also from the zero-sum differential games point of view are presented. Although theories of these concepts are well known, providing basic terms is necessary to understand the contributions contained in the following sections. A complete framework of the derivation of the algorithmic procedure that optimizes the \(\mathcal{L}_{2}\)-gain of nonlinear dynamic systems without solving the HJI partial differential equation is given in Section 3.