The master's thesis presents the derivation of the numerical algorithm for optimal control of nonlinear multivariable systems with limited state and control vectors. The algorithm derivation is based on the BPTT (backpropagation-through-time) algorithm which is used as a learning algorithm for dynamic neural networks. Presented is also the derivation of the algorithm for time optimal control which is based on the characteristics of penalty functions for constraints of state and control vectors. The derived algorithms are used for various problems concerning optimal robot control with two degrees of freedom. The thesis first deals with the problem of time optimal robot control with control vector constraints. It also considers the same problem with an additional condition - avoidance of obstacles, that is, constraint of state vectors. The thesis further deals with the problem of optimal control of cooperative work of two robots, that is, of joint transfer of solid material from one place to another including control vector constraint and conditions of mutual avoidance of clashes and maintaining of constant distance between the hands of the robot. Derivation of the optimal control algorithm with a feedback for nonlinear multivariable systems with control vector constraint is presented at the end. This derivation is also based on the BPTT algorithm.