Investigation of the problem of control of nonlinear dynamic systems using the method of piecewise linear approximation

By the method of piecewise-linear approximation the investigation of nonlinear control dynamical systems is modified to the investigation of stage by stage changing linear dynamic systems. For those systems necessary and sufficient conditions of complete controllability are formulated. A constructive method for solving problems of control is proposed and the conditions for existence of program control and motion are formulated. An explicit form of control action and motion are constructed. A method to solve the problem of optimal control is proposed.