  This paper formulates a stochastic optimal control problem for linear
networked control systems featuring stochastic packet disordering with a unique
stabilizing solution certified. The problem is solved by proposing
reinforcement learning algorithms. A measurement method is first presented to
deal with PD and calculate the newest control input. The NCSs with stochastic
PD are modeled as stochastic NCSs. Then, given a cost function, a modified
algebraic Riccati equation is derived within the formulation. We propose
offline policy iteration and value iteration algorithms to solve the MARE
associated with provable convergence. These two algorithms require knowledge of
NCS dynamics and PD probabilities. To release that, we further design online
model-free off-policy and Q-learning algorithms with an online estimation
method for PD probability. Both model-free algorithms solve the optimal control
problem using real-time system states, control inputs, and PD probability
estimates. Simulation results verify the proposed formulation and algorithms at
last.
