Sriram Sankaranarayanan

selected publications

1. Successive Control Barrier Functions for Nonlinear Systems

   Rameez Wajid, and Sriram Sankaranarayanan

   In Hybrid Systems: Computation and Control (HSCC), pp. TBA, 2025.

   Note: To Appear.

   Abs Bib URL

   We present the idea of successive control barrier functions for nonlinear (polynomial) control systems. Control Barrier Functions (CBFs) can be used to maintain safety properties for a system through the online modification of control inputs to ensure that the state remains inside a controlled invariant set that excludes a set of unsafe states. However, the synthesis of CBFs is quite difficult in practice, especially for nonlinear dynamical systems. Computationally inexpensive approaches employ relaxed control barrier conditions that result in relatively small control invariant sets. In turn, this can result in unnecessary modification of the nominal control input to keep the dynamics inside this set. In this paper, we propose the concept of “successive” CBFs. Rather than rely on a single CBF, our approach uses a hierarchy of functions wherein functions at one level of a hierarchy become active only if the functions at the previous levels have “failed”. Using a well-known approach to finding barrier functions for polynomial dynamical systems using sum of squares optimization, we show how to adapt it to synthesize successive barrier functions. We also provide “transit time” guarantees to construct a “chattering-free” runtime enforcement scheme that avoids collisions with fixed obstacles. We demonstrate our approach on a set of interesting nonlinear benchmarks, while comparing it with state of the art approaches for synthesizing CBFs.

           @inproceedings{ Wajid+Sankaranarayanan/2025/Successive,
           title = { Successive Control Barrier Functions for Nonlinear Systems },
           author = {   Wajid, Rameez  and    Sankaranarayanan, Sriram   },
           booktitle= { Hybrid Systems: Computation and Control (HSCC) },  
           year = { 2025 },  
           
           pages = { TBA }, 
           
           
           
           
           
           }
           

2. Polyhedral Control Lyapunov Functions for Switched Affine Systems

   Sara Kamali, Guillaume O. Berger, and Sriram Sankaranarayanan

   In Hybrid Systems: Computation and Control (HSCC), pp. TBA, 2025.

   Note: To Appear.

   Abs Bib URL

   We present a counterexample-guided approach for synthesizing convex piecewise affine control Lyapunov functions, obtained as the maximum over a finite number of affine functions, for stabilizing switched linear systems. Our approach considers systems whose dynamics are defined by a set of affine ODEs over different regions of the state-space. The goal is to synthesize a control feedback function that uses state-based switching by assigning a dynamical mode to each state from the set of available dynamics. This is achieved by synthesizing a piecewise affine control Lyapunov function that guarantees that for each state variable, the appropriate choice of a control input can cause an instantaneous decrease in the value of the Lyapunov function. Since piecewise affine functions are not smooth, we use a non-smooth analytic characterization of piecewise affine Lyapunov functions. The key contribution of our approach is a counterexample driven algorithm that alternates between verification that a given convex PWA function is a control Lyapunov function or generating a counterexample point where the Lyapunov conditions fail, and synthesis from a finite set of counterexamples generated in the past. We demonstrate that the two steps can be performed using mixed integer linear programming problems (MILP) although no termination guarantees are possible. We show that the branch and cut approach used inside a MILP solver can be adapted to yield a termination guarantee. Although the resulting approach is computationally expensive, it has the advantage of not requiring a “demonstrator” or a pre-existing controller. We provide an empirical evaluation that explores the results of this approach over a set of numerical examples.

           @inproceedings{ Kamali+Berger+Sankaranarayanan/2025/Piecewise,
           title = { Polyhedral Control Lyapunov Functions for Switched Affine Systems },
           author = {   Kamali, Sara  and    Berger, Guillaume O.  and    Sankaranarayanan, Sriram   },
           booktitle= { Hybrid Systems: Computation and Control (HSCC) },  
           year = { 2025 },  
           
           pages = { TBA }, 
           
           
           
           
           
           }
           

3. Anticipating Oblivious Opponents in Stochastic Games

   Shadi Tasdighi Kalat, Sriram Sankaranarayanan, and Ashutosh Trivedi

   In Workshop on Algorithmic Foundations of Robotics (WAFR), pp. TBA, 2024.

   Note: To Appear.

   Abs Bib URL

   We present an approach for systematically anticipating the actions and policies employed by oblivious environments in concurrent stochastic games, while maximizing a reward function. Our main contribution lies in the synthesis of a finite information state machine (ISM) whose alphabet ranges over the actions of the environment. Each state of the ISM is mapped to a belief state about the policy used by the environment. We introduce a notion of consistency that guarantees that the belief states tracked by the ISM stays within a fixed distance of the precise belief state obtained by knowledge of the full history. We provide methods for checking consistency of an automaton and a synthesis approach which, upon successful termination, yields an ISM. We construct a Markov Decision Process (MDP) that serves as the starting point for computing optimal policies for maximizing a reward function defined over plays. We present an experimental evaluation over benchmark examples including human activity data for tasks such as cataract surgery and furniture assembly, wherein our approach successfully anticipates the policies and actions of the environment in order to maximize the reward.

           @inproceedings{ Kalat+Others/2024/Anticipating,
           title = { Anticipating Oblivious Opponents in Stochastic Games },
           author = {   Kalat, Shadi Tasdighi  and    Sankaranarayanan, Sriram  and    Trivedi, Ashutosh   },
           booktitle= { Workshop on Algorithmic Foundations of Robotics (WAFR) },  
           year = { 2024 },  
           
           pages = { TBA }, 
           
           
           
           
           
           }