This article studies the optimal control for mobile agents, aiming at achieving a tradeoff between the control performance and state unpredictability over a long time horizon. The main challenge lies in incorporating the state unpredictability requirement into the optimization problem and generalizing the algorithm to various models. Utilizing random perturbations to maximize the attackers' prediction errors of future states, we formulate the problem as a multiperiod convex stochastic optimization problem and solve it via dynamic programming. We design the State unPredictable Optimal Control algorithm for both unconstrained and input-constrained systems. Moreover, we extend the algorithm to nonlinear affine systems by linearization. The analytical iterative expressions of the control inputs are further provided. Simulation illustrates that the algorithm increases the prediction errors under Kalman filter while satisfying the control performance requirements successfully.