Abstract. The issues of synthesis of optimal terminal control of a nonlinear dynamic system are considered when the control is not on the boundaries of the maximum allowable set of values and linearly enters the mathematical model of the system. In this case, equating to zero the partial derivatives of the Hamiltonian with respect to the control leads to the requirement of zeroing the corresponding Lagrange multipliers. But then, on the formal side, any control satisfies the optimum condition, that is, the optimal control cannot be found in the traditional way. The problem of finding a special control arises. A method for finding a special optimal control is known, but its implementation is associated with the features of solving a nonlinear boundary value problem. Therefore, another method of determining a special optimal control is proposed, based on the sequential differentiation of the condition of the first row of the singularity. The result obtained must satisfy both necessary and sufficient optimality conditions. Illustrative examples are presented.

Keywords: optimal special control, terminal functional, nonlinear mathematical model, order of singularity

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