This project is to develop a dynamical systems model of distributed computation motivated from recent work on the distributed computation of averages. The key idea is that static optimization problems (particularly convex optimization problems) can be solved by designing a dynamic system that stabilizes around the optimal solution of the problem. Moreover, when the optimization problem is separable, then the designed dynamic system decomposes into a set of locally-interacting dynamic systems. This is expected to open a door to a host of new computational approaches that take advantage of recent developments in control engineering including robust control (providing a mechanism for errors introduced by discretization), Markovian Jump Linear Systems (providing a mechanism for random discretization time), event-driven control (providing a mechanism for assured asynchronous execution), control over networks (providing a mechanism for improved performance of distributed computational systems in general). The new approach is essential in emerging applications, where the optimization runs on physically separated agents, operating in a noisy environment and communicating over unreliable channels. As a test bed, the project will make use of a two-vehicle robotic system developed by the PI designed to monitor a crop of corn plants, where the dynamic systems perspective of this grant will, for example, allow for distributed optimal estimation toward the goal of optimal station-keeping. By studying how natural systems can collectively compute and optimize, this research has potential to impact many disciplines involving networked systems, from controlling the electric power grid, to modeling the behavior of social, biological or economic systems. It is directly applicable to cooperative networked multi-agent systems like robotic search and rescue missions and disaster-relief operations, distributed machine learning problems, and intelligent systems. An intriguing mix of motivating applications and theoretical problems offer a unique multidisciplinary educational opportunity to students who will be involved in the project, and provide exciting innovative material for courses and labs. Software developed will be distributed as open source via the CPS Virtual Organization.

Autonomous navigation in unknown and dynamic environments has been a major challenge for synthetic mobile robotic agents. On the other hand, insects can easily solve such complex navigational problems and demonstrate remarkably stable and optimized locomotion skills in almost any environment. This project aims to develop a mobile sensor network where insects are used as mobile biological-robotic (biobotic) nodes. Insects, in fact, build a "natural" sensor network through the use of their biological sensing organs and release of chemical, mechanical and optical cues to communicate the information to the rest of the group. In the scope of this project, a novel cyber-physical communication network will be established among the individual insect in addition to the aforementioned natural one. For this, insects will be equipped with synthetic electronic sensors to sense additional cues, neuromuscular stimulation systems to direct the control of the insect and microcontrollers with radios to establish an RF link between the insects. This novel network will enable operation of insect biobots in complicated and uncertain dynamic environments for applications such as environmental sensing and search-and-rescue operations after natural disasters. The unique interdisciplinary nature of this project will help engineers to reach to younger generations and train them to be able to look at engineering problems from a cyberphysical systems point of view. Planned activities include development of lab modules and demos by undergraduate and graduate students to teach K-12 students and their teachers through our on-going collaborations with educational partners. These demos will also be instrumental during nation level efforts to promote graduate education to underrepresented minority students.