During the operation of complex
cyber-physical systems, operation planning and control need to be performed
using limited available information. There are two reasons for this limitation.
First, privacy issues may limit what information can be shared. Second, in a
complex cyber-physical systems, not all state information can be measured, and
the communication between subsystems may be limited.

These limitations give rise to a
number of fundamental research questions as follows. Question 1: Can the right
inference be made using the available state information, for the purposes of
fault diagnosis and state estimation? Question 2: What state measurement or
observation can be made available to facilitate the answer to Question 1
without violating privacy constraints? Question 3: When the information is
transmitted through a non-ideal communication network, resulting in
transmission delay or limited bandwidth, how does it affect Questions 1 and 2
above?

In this project we develop a
framework that provides us with provably correct answers to all of the
questions above. Our framework is a model-based approach to obtain provably
correct methods for designing state measurement/observation that meets the need
for fault diagnosis and state estimation while meeting privacy and network
constraints. This is a hard problem especially for complex systems that are
marked by hybrid behavior (i.e. involving both discrete and continuous
dynamics), high dimensional state space, and nonlinear dynamics.

Our approach is based on
approximating the behavior of the system, i.e. the set of all possible
execution trajectories, with a behavior with finitely many trajectories that
are obtained from numerical simulations. This approximation can be done with
controllable precision, resulting in a trade-off between the complexity of
generating the approximation and its precision. In this framework, state
measurement/observation are performed by online monitors that implement dense
time temporal logic formulae. The formulae are defined over measured variables
(provided by sensors) and logical predicates over these variables (provided by
software-defined sensors). We also develop a framework with which state
observers will be designed on top of the online monitors.

In case the computation for creating the finite approximate behavior is prohibitively costly, we will also explore the use of randomized algorithms. We propose to develop a method to speed-up known randomized algorithms by exploiting the local properties of the generated samples.

[1] Z. Xu, S. Saha, A. A. Julius,
Provably Correct Design of Observations for Fault Detection with Privacy
Preservation. In *Proc. IEEE Int. Conf. Decision and Control*, Melbourne, Australia, 2017.

[2] M. H. Jahnes, D. J. Glowny,
T. A. Spafford, J. L. Clough, E. S. Herkenham, W. Wu, A. A. Julius. Generating
Enthusiasm for Mathematics Through Robotics. In *Proc. ASEE Annual Conference
and Expositions*, Columbus,
Ohio, 2017.

Fig. 1. Four modes of operation of the HVAC control system in a smart building.

Educational Outreach. This project supported Engineering Ambassadors, who created and presented STEM modules to K-12 students in the Capital Region of NY State. This year, we wrote and presented a paper at the 2017 ASEE Annual Conference in Columbus, OH. The paper presents data collected from our outreach activities at Berlin Junior/Senior High School in Berlin, NY and Lansingburgh High School in Troy, NY. The outreach activity was focused on generating enthusiasm for mathematics through robotics. Participants of these programs were asked to fill out a questionnaire before and after they take part in the program. The questionnaire consists of seven questions:

1. I enjoy doing activities within the area of robotics.

2. I enjoy doing activities within the subject of engineering.

3. I enjoy the subject of mathematics.

4. I enjoy the subject of science.

5. I enjoy doing activities like coding or computer science.

6. Mathematics is important when learning robotics.

7. The Engineering Design Process is an important tool for solving challenges.

The responses to the questionnaires are summarized in Fig. 2. To summarize, there is a statistically significant (p<0.05 in a paired t-test) increase in the participants' responses to the questions is all cases, except in the cases of Questions 3 and 4 in Lansingburgh High School. For these cases, however, we still observe a slight increase in the responses (p=0.06 and p=0.22, respectively).

Fig. 2. Survey results from our educational outreach activities showing statistically significant positive impacts on the participants.

Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.