Human ability to coordinate one's actions with other individuals to perform a task together is fascinating. For example, we coordinate our action with others when we carry a heavy object or when we construct a piece of furniture. Capabilities such as (1) force/compliance adaptation, (2) intention recognition, and (3) action/motion prediction enables us to assist others and fulfill the task. For instance, by adapting the compliance, we not only reject undesirable perturbations that undermine the task but also incorporate others' motions into the interaction. Complying with partners' motions allows us to recognize their intention and consequently predict their actions. With the growth of factories involving humans and robots working side by side, designing controllers and algorithms with such capacities is a crucial step toward assistive robotics. The challenge, however, is to attain a unified control strategy with predictive/adaptive capacities at the task, motion, and force-level which ensures a stable and safe interaction. To this aim, this thesis proposes a state-dependent dynamical system-based approach for prediction and control in physical human-robot interactions. In the first part of this dissertation, we focus on the human capacity to predict their partners' motion. More specifically, we investigate mechanisms of spatio-temporal coordination between two partners. We employ a simple scenario called “the mirror game” where two individuals (human, robot, or avatar) imitate each other's motions. Our empirical assessment reveal that the intention-based prediction of the leader's motions allows the follower to compensate for perception-action delays and to improve the tracking performance in terms of temporal coordination and confidence. In the second part of this dissertation, we propose an adaptive mechanism that enables the robot to recognize the intention of a human user. We utilize state-dependent dynamical systems for motion planning and impedance control to deliver safe and compliant human-robot interaction. We consider a series of tasks (possible human intentions) encoded by dynamical system. Applying a similarity metric between the real velocities (induced by the human) and desired velocities generated by the dynamical systems, the robot is thus able to recognize the human's intention and switch to the intended task. We provide a rigorous experimental and analytical evaluation of our method yielding an interaction behavior that is safe and intuitive for the human. Finally, we tackle the compliance adaptation capability. We propose an admittance controller that reacts only when human-intentional forces are detected. Intentional and accidental forces are distinguished by measuring the persistency of the external forces, through a computation of the autocorrelation/energy of the force patterns. The overall controller exhibits variable stiffness where high stiffness allows the robot to reject the external disturbances and execute the task autonomously whereas low stiffness enables the robot to comply with human intentional forces. We demonstrate that our control architecture is effective in delivering satisfactory tracking and compliant behavior through a series of robotic experimentations.