New methods are introduced in this paper for nonlinear discrete time control systems design. The methods are based on optimization and they use either approximate linearization or the original nonlinear equations to obtain the solution in a unified manner. The finite horizon optimum control problem is solved through a sequence of two-stage optimization and iteration. The infinite horizon control is derived with two-stage optimization and limit value calculation from the linearized model, without iteration. Solution of the stochastic control problem is also based on linearization. Both state space and input-output control problems are treated.