The objective of this research is to check correct functioning of cyber-physical systems during their operation. The approach is to continuously monitor the system and raise an alarm when the system seems to exhibit an erroneous behavior. Correct functioning of cyber-physical systems is of critical importance. This is more so in safety critical systems like medical, automotive and other applications. The approach employs hybrid automata for specifying the property to be monitored and for modeling the system behavior. The system behavior is probabilistic in nature due to noise and other factors. Monitoring such systems is challenging since the monitor can only observe system outputs, but not it's state. Fundamental research, on defining and detecting whether a system is monitorable, is the focus of the work. The project proposes accuracy measures and cost based metrics for optimal monitoring. The project is developing efficient and effective monitoring techniques, based on product automata and Partially Observable Markov Decision Processes. The results of the project are expected to be transformative in ensuring correct operation of systems. The results will have impact in many areas of societal importance and utility for daily life, such as health care, nursing/rehabilitation, automotive systems, home appliances, and more. The benefits in nursing/rehabilitation emanate from the deployment of advanced technologies to assist caregivers. This can lead to improved health and quality of life of older patients at reduced costs. The project includes education and outreach in the form of K-12 outreach and involvement of undergraduate and graduate students in research. The project is committed to involving women and minorities in education and research.