Sriram Sankaranarayanan

selected publications

1. An Algorithm for Learning Switched Linear Dynamics from Data

   Guillaume O. Berger, Monal Narasimhamurthy, Kandai Watanabe, Morteza Lahijanian, and Sriram Sankaranarayanan

   In Neural Information Processing Systems (NeurIPS’22), pp. TBA, 2022.

   Note: To Appear.

   Abs Bib URL Supp

   We present an algorithm for learning switched linear dynamical systems in discrete time from noisy observations of the system’s full state or output. Switched linear systems use multiple linear dynamical modes to fit the data within some desired tolerance. They arise quite naturally in applications to robotics and cyber-physical systems. Learning switched systems from data is a NP-hard problem that is nearly identical to the k-linear regression problem of fitting k > 1 linear models to the data. A direct mixed-integer linear programming (MILP) approach yields time complexity that is exponential in the number of data points. In this paper, we modify the problem formulation to yield an algorithm that is linear in the size of the data while remaining exponential in the number of state variables and the desired number of modes. To do so, we combine classic ideas from the ellipsoidal method for solving convex optimization problems, and well-known oracle separation results in non-smooth optimization. We demonstrate our approach on a set of microbenchmarks and a few interesting real-world problems. Our evaluation suggests that the benefits of this algorithm can be made practical even against highly optimized off-the-shelf MILP solvers.

           @inproceedings{ Berger+Others/2022/Algorithm,
           title = { An Algorithm for Learning Switched Linear Dynamics from Data },
           author = {   Berger, Guillaume O.  and    Narasimhamurthy, Monal  and    Watanabe, Kandai  and    Lahijanian, Morteza  and    Sankaranarayanan, Sriram   },
           booktitle= { Neural Information Processing Systems (NeurIPS’22) },  
           year = { 2022 },  
           
           pages = { TBA }, 
           
           
           
           
           
           }
           

   Poster

2. Using Artificial Potential Fields to Model Driver Situational Awareness

   Emily Jensen, Maya Luster, Brandon Pitts, and Sriram Sankaranarayanan

   In Workshop on Cyber-Physical Human Systems (CPHS), pp. TBA, 2022.

   Note: To Appear.

   Abs Bib URL

   Recently, the use of artificial potential fields, known as risk fields, has been proposed for modeling human driver decision making. Such potential fields map from vehicle states and control inputs to a numerical risk measure such that the probability of choosing a control decreases as the risk associated increases. In this paper, we show that such a model can be used in a natural manner to also capture aspects of the driver’s situational awareness, assuming that the risk fields govern their underlying behavior. We demonstrate our ideas on a specific obstacle avoidance scenario wherein obstacles to be avoided are placed in front of a driver at predicable intervals. Using data collected on a pilot experiment involving six different drivers using a high-fidelity driving simulator, we demonstrate the ability of our approach to capture the likelihood that the driver has perceived/reacted to the obstacle. Our approach works for scenarios when the driver collides with the obstacle as well as scenarios involving successful collision avoidance.

           @inproceedings{ Jensen+Others/2022/Situational,
           title = { Using Artificial Potential Fields to Model Driver Situational Awareness },
           author = {   Jensen, Emily  and    Luster, Maya  and    Pitts, Brandon  and    Sankaranarayanan, Sriram   },
           booktitle= { Workshop on Cyber-Physical Human Systems (CPHS) },  
           year = { 2022 },  
           
           pages = { TBA }, 
           
           
           
           
           
           }
           

3. Mathematical Models of Human Drivers using Artificial Risk Fields

   Emily Jensen, Maya Luster, Hansol Yoon, Brandon Pitts, and Sriram Sankaranarayanan

   In IEEE Intelligent Transportation Systems Symposium (ITSC), pp. TBA, 2022.

   Note: To Appear.

   Abs Bib URL

   In this paper, we use the concept of artificial risk fields to predict how human operators control a vehicle in response to upcoming road situations. A risk field assigns a non-negative risk measure to the state of the system in order to model how close that state is to violating a safety property, such as hitting an obstacle or exiting the road. Using risk fields, we construct a stochastic model of the operator that maps from states to likely actions. We demonstrate our approach on a driving task wherein human subjects are asked to drive a car inside a realistic driving simulator while avoiding obstacles placed on the road. We show that the most likely risk field given the driving data is obtained by solving a convex optimization problem. Next, we apply the inferred risk fields to generate distinct driving behaviors while comparing predicted trajectories against ground truth measurements. We observe that the risk fields are excellent at predicting future trajectory distributions with high prediction accuracy for up to twenty seconds prediction horizons. At the same time, we observe some challenges such as the inability to account for how drivers choose to accelerate/decelerate based on the road conditions.

           @inproceedings{ Jensen+Others/2022/Mathematical,
           title = { Mathematical Models of Human Drivers using Artificial Risk Fields },
           author = {   Jensen, Emily  and    Luster, Maya  and    Yoon, Hansol  and    Pitts, Brandon  and    Sankaranarayanan, Sriram   },
           booktitle= {  IEEE Intelligent Transportation Systems Symposium (ITSC) },  
           year = { 2022 },  
           
           pages = { TBA }, 
           
           
           
           
           
           }
           

4. Decoding Output Sequences for Discrete-Time Linear Hybrid Systems

   Monal Narasimhamurthy, and Sriram Sankaranarayanan

   In ACM International Conference on Hybrid Systems: Computation and Control (HSCC), pp. 6:1–6:7, 2022.

   Abs Bib URL

   In this paper, we study the "decoding" problem for discrete-time, stochastic hybrid systems with linear dynamics in each mode. Given an output trace of the system, the decoding problem seeks to construct a sequence of modes and states that yield a trace "as close as possible" to the original output trace. The decoding problem generalizes the state estimation problem, and is applicable to hybrid systems with non-determinism. The decoding problem is NP-complete, and can be reduced to solving a mixed-integer linear program (MILP). In this paper, we decompose the decoding problem into two parts: (a) finding a sequence of discrete modes and transitions; and (b) finding corresponding continuous states for the mode/transition sequence. In particular, once a sequence of modes/transitions is fixed, the problem of "filling in" the continuous states is performed by a linear programming problem. In order to support the decomposition, we "cover" the set of all possible mode/transition sequences by a finite subset. We use well-known probabilistic arguments to justify a choice of cover with high confidence and design randomized algorithms for finding such covers. Our approach is demonstrated on a series of benchmarks, wherein we observe that relatively tiny fraction of the possible mode/transition sequences can be used as a cover. Furthermore, we show that the resulting linear programs can be solved rapidly by exploiting the tree structure of the set cover.

           @inproceedings{ Narasimhamurthy+Sankaranarayanan/2022/Decoding,
           title = { Decoding Output Sequences for Discrete-Time Linear Hybrid Systems },
           author = {   Narasimhamurthy, Monal  and    Sankaranarayanan, Sriram   },
           booktitle= {  ACM International Conference on Hybrid Systems:
                  Computation and Control (HSCC) },  
           year = { 2022 },  
           publisher = { ACM }, 
           pages = { 6:1–6:7 }, 
           
           
           
           
           
           }