Motivated by the limitations of the current reinforcement learning and optimal control techniques, this dissertation proposes quantum theory inspired algorithms for learning and control of both single-agent and multi-agent stochastic systems.

A common problem encountered in traditional reinforcement learning techniques is the exploration-exploitation trade-off. To address the above issue an action selection procedure inspired by a quantum search algorithm called Grover's iteration is developed. This procedure does not require an explicit design parameter to specify the relative frequency of explorative/exploitative actions.

The second part of this dissertation extends the powerful adaptive critic design methodology to solve finite horizon stochastic optimal control problems. To numerically solve the stochastic Hamilton Jacobi Bellman equation, which characterizes the optimal expected cost function, large number of trajectory samples are required. The proposed methodology overcomes the above difficulty by using the path integral control formulation to adaptively sample trajectories of importance.

The third part of this dissertation presents two quantum inspired coordination models to dynamically assign targets to agents operating in a stochastic environment. The first approach uses a quantum decision theory model that explains irrational action choices in human decision making. The second approach uses a quantum game theory model that exploits the quantum mechanical phenomena "entanglement" to increase individual pay-off in multi-player games. The efficiency and scalability of the proposed coordination models are demonstrated through simulations of a large scale multi-agent system.