Multi-period Optimal Control for Mobile Agents Considering State Unpredictability

The optimal control for mobile agents is an important and challenging issue. Recent work shows that using randomized mechanism in agents' control can make the state unpredictable, and thus improve the security of agents. However, the unpredictable design is only considered in single period, which can lead to intolerable control performance in long time horizon. This paper aims at the trade-off between the control performance and state unpredictability of mobile agents in long time horizon. Utilizing random perturbations consistent with uniform distributions to maximize the attackers' prediction errors of future states, we formulate the problem as a multi-period convex stochastic optimization problem and solve it through dynamic programming. Specifically, we design the optimal control strategy considering both unconstrained and input constrained systems. The analytical iterative expressions of the control are further provided. Simulation illustrates that the algorithm increases the prediction errors under Kalman filter while achieving the control performance requirements successfully.