Sriram Sankaranarayanan

selected publications

1. Cone-Based Abstract Interpretation for Nonlinear Positive Invariant Synthesis

   Guillaume O. Berger, Masoumeh Ghanbarpour, and Sriram Sankaranarayanan

   In Hybrid Systems: Computation and Control (HSCC), pp. 12:1-12:16, 2024.

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   We present an abstract interpretation approach for synthesizing nonlinear (semi-algebraic) positive invariants for systems of polynomial ordinary differential equations (ODEs) and switched systems. The key behind our approach is to connect the system under study to a positive nonlinear system through a “change of variables”. The positive invariance of the first orthant (R+) for a positive system guarantees, in turn, that the functions involved in the change of variables define a positive invariant for the original system. The challenge lies in discovering such functions for a given system. To this end, we characterize positive invariants as fixed points under an operator that is defined using the Lie derivative. Next, we use abstract-interpretation approaches to systematically compute this fixed point. Whereas abstract interpretation has been applied to the static analysis of programs, and invariant synthesis for hybrid systems to a limited extent, we show how these approaches can compute fixed points over cones generated by polynomials using sum-of-squares optimization and its relaxations. Our approach is shown to be promising over a set of small but hard-to-analyze nonlinear models, wherein it is able to generate positive invariants to place useful bounds on their reachable sets.

           @inproceedings{ Berger+Ghanbarpour+Sankaranarayanan/2024/Cone,
           title = { Cone-Based Abstract Interpretation for Nonlinear Positive Invariant Synthesis },
           author = {   Berger, Guillaume O.  and    Ghanbarpour, Masoumeh  and    Sankaranarayanan, Sriram   },
           booktitle= { Hybrid Systems: Computation and Control (HSCC) },  
           year = { 2024 },  
           publisher = { ACM }, 
           pages = { 12:1-12:16 }, 
           
           
           
           
           
           }
           

2. Counterexample-guided computation of polyhedral Lyapunov functions for piecewise linear systems

   Guillaume O. Berger, and Sriram Sankaranarayanan

   Automatica, 155 pp. 111165, 2023.

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   This paper presents a counterexample-guided iterative algorithm to compute convex, piecewise linear (polyhedral) Lyapunov functions for continuous-time piecewise linear systems. Polyhedral Lyapunov functions provide an alternative to commonly used polynomial Lyapunov functions. Our approach first characterizes intrinsic properties of a polyhedral Lyapunov function including its “eccentricity” and “robustness” to perturbations. We then derive an algorithm that either computes a polyhedral Lyapunov function proving that the system is asymptotically stable, or concludes that no polyhedral Lyapunov function exists whose eccentricity and robustness parameters satisfy some user-provided limits. Significantly, our approach places no a-priori bound on the number of linear pieces that make up the desired polyhedral Lyapunov function. The algorithm alternates between a learning step and a verification step, always maintaining a finite set of witness states. The learning step solves a linear program to compute a candidate Lyapunov function compatible with a finite set of witness states. In the verification step, our approach verifies whether the candidate Lyapunov function is a valid Lyapunov function for the system. If verification fails, we obtain a new witness. We prove a theoretical bound on the maximum number of iterations needed by our algorithm. We demonstrate the applicability of the algorithm on numerical examples.

           @article{ Berger+Sankaranarayanan/2023/Counterexample,
           title = { Counterexample-guided computation of polyhedral Lyapunov functions for piecewise linear systems },
           author = {   Berger, Guillaume O.  and    Sankaranarayanan, Sriram   },
           journal = { Automatica },  
           year = { 2023 },  
           
           pages = { 111165 }, 
           
           
           volume = { 155 },  
           
           
           }
           

3. Temporal Logic-Based Intent Monitoring for Mobile Robots

   Hansol Yoon, and Sriram Sankaranarayanan

   In IROS, pp. 8643–8650, 2023.

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   We propose a framework that uses temporal logic specifications to predict and monitor the intent of a robotic agent through passive observations of its actions over time. Our approach uses a set of possible hypothesized intents specified as Buchi automata, obtained from translating temporal logic formulae. Based on observing the actions of the robot, we update the probabilities of each hypothesis using Bayes rule. Observations of robot actions provide strong evidence for its "immediate" short-term goals, whereas temporal logic specifications describe behaviors over a "never-ending" infinite time horizon. To bridge this gap, we use a two-level hierarchical monitoring approach. At the lower level, we track the immediate short-term goals of the robot which are modeled as atomic propositions in the temporal logic formalism. We apply our approach to predicting intent of human workers and thus their movements in an indoor space based on the publicly available THOR dataset. We show how our approach correctly labels each agent with their appropriate intents after relatively few observations while predicting their future actions accurately over longer time horizons.

           @inproceedings{ Yoon+Sankaranarayanan/2023/Temporal,
           title = { Temporal Logic-Based Intent Monitoring for Mobile Robots },
           author = {   Yoon, Hansol  and    Sankaranarayanan, Sriram   },
           booktitle= { IROS },  
           year = { 2023 },  
           
           pages = { 8643–8650 }, 
           
           
           
           
           
           }