arXiv subjects

S. Sivaranjani

Publications and source records attributed to S. Sivaranjani.

At least 19 recordsLinked to original sources

arXiv2026

SafePG: Safe and Globally Optimal Reinforcement Learning with Hard Constraints

We present an optimal and convergent model-free policy gradient (PG) reinforcement learning (RL) framework for controlling nonlinear dynamical systems under hard safety constraints. We first construct a class of stochastic wrapper policies centered around a deterministic controller, thereby enabling exploration in unknown environments while preserving the underlying deterministic control structure. We then define a class of parameterized safe-by-construction control policies by truncating these stochastic policies onto hard safety constraints. We next establish, via measure-theoretic arguments, that the potentially nonconvex RL objective under the truncated policy class, as well as its policy gradients, are well-defined. We then develop a model-free PG algorithm based on stochastic gradient ascent that directly searches over these truncated policies and leverage gradient dominance to establish convergence and optimality guarantees. Finally, we validate this framework through simulations on a safe quadrotor navigation problem.

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arXiv2026

Control-Oriented System Identification: Classical, Learning, and Physics-Informed Approaches

We survey classical, machine learning, and data-driven system identification approaches to learn control-relevant and physics-informed models of dynamical systems. Recently, machine learning approaches have enabled system identification from noisy, high-dimensional, and complex data. However, their utility is limited by their ability to provide provable guarantees on control-relevant properties. Meanwhile, control theory has identified several properties that are useful in analysis and control synthesis, such as dissipativity, monotonicity, energy conservation, and symmetry-preserving structures. We posit that merging system identification with such control-relevant or physics-informed properties can provide useful inductive bias, enhance explainability, enable control synthesis with provable guarantees, and improve sample complexity. We formulate system identification as an optimization problem where control-relevant properties can be enforced through direct parameterization (constraining the model structure to satisfy a desired property by construction), soft constraints (encouraging control-relevant properties through regularization or penalty terms), and hard constraints (imposing control-relevant properties as constraints in the optimization problem). Through this lens, we survey methods to learn physics-informed and control-relevant models spanning classical linear and nonlinear system identification, machine learning approaches, and direct identification through data-driven and behavioral representations. We also provide several expository examples that are accompanied by code and brief tutorials on a public Github repository. We also describe challenging directions for future research, including identification in networked, switched, and time-varying systems, experiment design, and bridging the gaps between data-driven, learning-based, and control-oriented approaches.

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arXiv2026

Demystifying Lipschitz verification: positive matrices, negative results

The global Lipschitz constant of a neural network is related to robustness and generalization, yet unlike in many classical models, it is not plainly legible from the parameters. This has motivated sophisticated verification algorithms, especially semidefinite programming (SDP) based on incremental quadratic constraints on the activation functions, to improve on the fast but often loose product of layerwise Lipschitz constants (the trivial bound). We ask why Lipschitz verification is a problem in the first place. Our answer is that the difficulty is structural: estimating a network's Lipschitz constant requires knowing which hidden states are reachable, and reachability is NP-hard. If P!=NP, then reachability is a barrier to any polynomial-time algorithm. Through explicit constructions, we show that this blindness can force SDP-based bounds to inherit the same qualitative failures as the trivial bound, including but not limited to polynomial per-layer conservatism. We show that the difficulties of NP-hard questions are not isolated to worst-case computational reductions, but actually afflict every instance of the verification problem. Thus SDP is not sufficient for Lipschitz verification. We also argue that it is not necessary: several apparent failures of the trivial bound arise from removable parameterization pathologies, and can be mitigated by optimizing or regularizing the trivial bound itself. We demonstrate this claim via a "spherical cow" linear model and numerical proofs of concept. While the main contribution is theoretical and negative, we finally motivate a novel form of trigonometric layers that do not need biases for universal approximation. Combined with trivial bound regularization, they make the trivial bound provably and practically tight.

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arXiv2026

ECLipsE-Gen-Local: Efficient Compositional Local Lipschitz Estimates for Deep Neural Networks

The Lipschitz constant is a key measure for certifying the robustness of neural networks to input perturbations. However, computing the exact constant is NP-hard, and standard approaches to estimate the Lipschitz constant involve solving a large matrix semidefinite program (SDP) that scales poorly with network size. Further, there is a potential to efficiently leverage local information on the input region to provide tighter Lipschitz estimates. We address this problem here by proposing a compositional framework that yields tight yet scalable Lipschitz estimates for deep feedforward neural networks. Specifically, we begin by developing a generalized SDP framework that is highly flexible, accommodating heterogeneous activation function slope, and allowing Lipschitz estimates with respect to arbitrary input-output pairs and arbitrary choices of sub-networks of consecutive layers. We then decompose this generalized SDP into a sequence of small sub-problems, with computational complexity that scales linearly with respect to the network depth. We also develop a variant that achieves near-instantaneous computation through closed-form solutions to each sub-problem. All our algorithms are accompanied by theoretical guarantees on feasibility and validity. Next, we develop a series of algorithms, termed as ECLipsE-Gen-Local, that effectively incorporate local information on the input. Our experiments demonstrate that our algorithms achieve substantial speedups over a multitude of benchmarks while producing significantly tighter Lipschitz bounds than global approaches. Moreover, we show that our algorithms provide strict upper bounds for the Lipschitz constant with values approaching the exact Jacobian from autodiff when the input region is small enough. Finally, we demonstrate the practical utility of our approach by showing that our Lipschitz estimates closely align with network robustness.

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arXiv2026

Set-Based Value Function Characterization and Neural Approximation of Stabilization Domains for Input-Constrained Discrete-Time Systems

Analyzing nonlinear systems with stabilizable controlled invariant sets (CISs) requires accurate estimation of their domains of stabilization (DOS) together with associated stabilizing controllers. Despite extensive research, estimating DOSs for general nonlinear systems remains challenging due to fundamental theoretical and computational limitations. In this paper, we propose a novel framework for estimating DOSs for controlled input-constrained discrete-time systems. The DOS is characterized via newly introduced value functions defined on metric spaces of compact sets. We establish the fundamental properties of these value functions and derive the associated Bellman-type (Zubov-type) functional equations. Building on this characterization, we develop a physics-informed neural network (NN) framework that learns the value functions by embedding the derived functional equations directly into the training process. The proposed methodology is demonstrated through two numerical examples, illustrating its ability to accurately estimate DOSs and synthesize stabilizing controllers from the learned value functions.

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arXiv2025

Learning Neural Network Safe Tracking Controllers from Backward Reachable Sets

The design of tracking controllers that closely follow a reference trajectory while ensuring safety and robustness against disturbances is a challenging problem in the control of autonomous systems. In this work, we propose a neural network-based safe tracking control framework for nonlinear discrete-time systems with reach-avoid specifications in the presence of disturbances. Our approach begins with generation of a nominal trajectory using standard trajectory synthesis approaches, followed by construction of safe zonotopic backward reachable sets along the nominal trajectory. The states lying within the backward reachable sets are guaranteed to satisfy safe reachability specifications. Then, our key insight is to leverage the computed backward reachable sets to inform the architecture and training of a neural network-based tracking controller such that the neural network drives the system's states through these backward reachable sets, thereby improving the likelihood of safe reachability. We perform formal verification with conformal prediction to achieve statistical safety guarantees on the performance of the learned neural controller. The performance of our approach is illustrated through a numerical example on the discrete-time Dubin's car model.

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arXiv2025

Learning Neural Koopman Operators with Dissipativity Guarantees

We address the problem of learning a neural Koopman operator model that provides dissipativity guarantees for an unknown nonlinear dynamical system that is known to be dissipative. We propose a two-stage approach. First, we learn an unconstrained neural Koopman model that closely approximates the system dynamics. Then, we minimally perturb the parameters to enforce strict dissipativity. Crucially, we establish theoretical guarantees that extend the dissipativity properties of the learned model back to the original nonlinear system. We realize this by deriving an exact relationship between the dissipativity of the learned model and the true system through careful characterization of the identification errors from the noisy data, Koopman operator truncation, and generalization to unseen data. We demonstrate our approach through simulation on a Duffing oscillator model.

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arXiv2024

ECLipsE: Efficient Compositional Lipschitz Constant Estimation for Deep Neural Networks

The Lipschitz constant plays a crucial role in certifying the robustness of neural networks to input perturbations. Since calculating the exact Lipschitz constant is NP-hard, efforts have been made to obtain tight upper bounds on the Lipschitz constant. Typically, this involves solving a large matrix verification problem, the computational cost of which grows significantly for both deeper and wider networks. In this paper, we provide a compositional approach to estimate Lipschitz constants for deep feed-forward neural networks. We first obtain an exact decomposition of the large matrix verification problem into smaller sub-problems. Then, leveraging the underlying cascade structure of the network, we develop two algorithms. The first algorithm explores the geometric features of the problem and enables us to provide Lipschitz estimates that are comparable to existing methods by solving small semidefinite programs (SDPs) that are only as large as the size of each layer. The second algorithm relaxes these sub-problems and provides a closed-form solution to each sub-problem for extremely fast estimation, altogether eliminating the need to solve SDPs. The two algorithms represent different levels of trade-offs between efficiency and accuracy. Finally, we demonstrate that our approach provides a steep reduction in computation time (as much as several thousand times faster, depending on the algorithm for deeper networks) while yielding Lipschitz bounds that are very close to or even better than those achieved by state-of-the-art approaches in a broad range of experiments. In summary, our approach considerably advances the scalability and efficiency of certifying neural network robustness, making it particularly attractive for online learning tasks.

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arXiv2024

Learning Dissipative Neural Dynamical Systems

Consider an unknown nonlinear dynamical system that is known to be dissipative. The objective of this paper is to learn a neural dynamical model that approximates this system, while preserving the dissipativity property in the model. In general, imposing dissipativity constraints during neural network training is a hard problem for which no known techniques exist. In this work, we address the problem of learning a dissipative neural dynamical system model in two stages. First, we learn an unconstrained neural dynamical model that closely approximates the system dynamics. Next, we derive sufficient conditions to perturb the weights of the neural dynamical model to ensure dissipativity, followed by perturbation of the biases to retain the fit of the model to the trajectories of the nonlinear system. We show that these two perturbation problems can be solved independently to obtain a neural dynamical model that is guaranteed to be dissipative while closely approximating the nonlinear system.

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arXiv2024

Sampling-based Safe Reinforcement Learning for Nonlinear Dynamical Systems

We develop provably safe and convergent reinforcement learning (RL) algorithms for control of nonlinear dynamical systems, bridging the gap between the hard safety guarantees of control theory and the convergence guarantees of RL theory. Recent advances at the intersection of control and RL follow a two-stage, safety filter approach to enforcing hard safety constraints: model-free RL is used to learn a potentially unsafe controller, whose actions are projected onto safe sets prescribed, for example, by a control barrier function. Though safe, such approaches lose any convergence guarantees enjoyed by the underlying RL methods. In this paper, we develop a single-stage, sampling-based approach to hard constraint satisfaction that learns RL controllers enjoying classical convergence guarantees while satisfying hard safety constraints throughout training and deployment. We validate the efficacy of our approach in simulation, including safe control of a quadcopter in a challenging obstacle avoidance problem, and demonstrate that it outperforms existing benchmarks.

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arXiv2023

Safe Control Design through Risk-Tunable Control Barrier Functions

We consider the problem of designing controllers to guarantee safety in a class of nonlinear systems under uncertainties in the system dynamics and/or the environment. We define a class of uncertain control barrier functions (CBFs), and formulate the safe control design problem as a chance-constrained optimization problem with uncertain CBF constraints. We leverage the scenario approach for chance constrained optimization to develop a risk-tunable control design that provably guarantees the satisfaction of CBF safety constraints up to a user-defined probabilistic risk bound, and provides a trade-off between the sample complexity and risk tolerance. We demonstrate the performance of this approach through simulations on a quadcopter navigation problem with obstacle avoidance constraints.

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arXiv2022

Distributed Learning of Neural Lyapunov Functions for Large-Scale Networked Dissipative Systems

This paper considers the problem of characterizing the stability region of a large-scale networked system comprised of dissipative nonlinear subsystems, in a distributed and computationally tractable way. One standard approach to estimate the stability region of a general nonlinear system is to first find a Lyapunov function for the system and characterize its region of attraction as the stability region. However, classical approaches, such as sum-of-squares methods and quadratic approximation, for finding a Lyapunov function either do not scale to large systems or give very conservative estimates for the stability region. In this context, we propose a new distributed learning based approach by exploiting the dissipativity structure of the subsystems. Our approach has two parts: the first part is a distributed approach to learn the storage functions (similar to the Lyapunov functions) for all the subsystems, and the second part is a distributed optimization approach to find the Lyapunov function for the networked system using the learned storage functions of the subsystems. We demonstrate the superior performance of our proposed approach through extensive case studies in microgrid networks.

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arXiv2022

A Multi-scale Time-series Dataset with Benchmark for Machine Learning in Decarbonized Energy Grids

The electric grid is a key enabling infrastructure for the ambitious transition towards carbon neutrality as we grapple with climate change. With deepening penetration of renewable energy resources and electrified transportation, the reliable and secure operation of the electric grid becomes increasingly challenging. In this paper, we present PSML, a first-of-its-kind open-access multi-scale time-series dataset, to aid in the development of data-driven machine learning (ML) based approaches towards reliable operation of future electric grids. The dataset is generated through a novel transmission + distribution (T+D) co-simulation designed to capture the increasingly important interactions and uncertainties of the grid dynamics, containing electric load, renewable generation, weather, voltage and current measurements over multiple spatio-temporal scales. Using PSML, we provide state-of-the-art ML baselines on three challenging use cases of critical importance to achieve: (i) early detection, accurate classification and localization of dynamic disturbance events; (ii) robust hierarchical forecasting of load and renewable energy with the presence of uncertainties and extreme events; and (iii) realistic synthetic generation of physical-law-constrained measurement time series. We envision that this dataset will enable advances for ML in dynamic systems, while simultaneously allowing ML researchers to contribute towards carbon-neutral electricity and mobility.

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arXiv2022

The Impact of Heavy-Duty Vehicle Electrification on Large Power Grids: a Synthetic Texas Case Study

The electrification of heavy-duty vehicles (HDEVs) is a nascent and rapidly emerging avenue for decarbonization of the transportation sector. In this paper, we examine the impacts of increased vehicle electrification on the power grid infrastructure, with particular focus on HDEVs. We utilize a synthetic representation of the 2000-bus Texas transmission grid, and realistic representations of multiple distribution grids in Travis county, Texas, as well as transit data pertaining to HDEVs, to uncover the consequences of HDEV electrification, and expose the limitations imposed by existing electric grid infrastructure. Our analysis reveals that grid-wide voltage problems that are spatiotemporally correlated with the mobility of HDEVs may occur even at modest penetration levels. In fact, we find that as little as 11% of heavy duty vehicles in Texas charging simultaneously can lead to significant voltage violations on the transmission network that compromise grid reliability. Furthermore, we find that just a few dozen EVs charging simultaneously can lead to voltage violations at the distribution level.

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arXiv2021

Safety during Transient Response in Direct Current Microgrids using Control Barrier Functions

We consider the problem of guaranteeing that the transient voltages and currents stay within prescribed bounds in Direct Current (DC) microgrids, when the controller does not have access to accurate system dynamics due to the load being unknown and/or time-varying. To achieve this, we propose an optimization based controller design using control barrier functions. We show that the proposed controller has a decentralized structure and is robust with respect to the uncertainty in the precise values of the system parameters, such as the load.

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arXiv2020

Reinforcement Learning based Distributed Control of Dissipative Networked Systems

We consider the problem of designing distributed controllers to stabilize a class of networked systems, where each subsystem is dissipative and designs a reinforcement learning based local controller to maximize an individual cumulative reward function. We develop an approach that enforces dissipativity conditions on these local controllers at each subsystem to guarantee stability of the entire networked system. The proposed approach is illustrated on a DC microgrid example, where the objective is maintain voltage stability of the network using local distributed controllers at each generation unit.

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arXiv2020

A Cross-Domain Approach to Analyzing the Short-Run Impact of COVID-19 on the U.S. Electricity Sector

The novel coronavirus disease (COVID-19) has rapidly spread around the globe in 2020, with the U.S. becoming the epicenter of COVID-19 cases since late March. As the U.S. begins to gradually resume economic activity, it is imperative for policymakers and power system operators to take a scientific approach to understanding and predicting the impact on the electricity sector. Here, we release a first-of-its-kind cross-domain open-access data hub, integrating data from across all existing U.S. wholesale electricity markets with COVID-19 case, weather, cellular location, and satellite imaging data. Leveraging cross-domain insights from public health and mobility data, we uncover a significant reduction in electricity consumption across that is strongly correlated with the rise in the number of COVID-19 cases, degree of social distancing, and level of commercial activity.

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arXiv2020

Distributed Synthesis of Local Controllers for Networked Systems with Arbitrary Interconnection Topologies

We consider the problem of designing distributed controllers to guarantee dissipativity of a networked system comprised of dynamically coupled subsystems. We require that the control synthesis is carried out locally at the subsystem-level, without explicit knowledge of the dynamics of other subsystems in the network. We solve this problem in two steps. First, we provide distributed subsystem-level dissipativity analysis conditions whose feasibility is sufficient to guarantee dissipativity of the networked system. We then use these conditions to synthesize controllers locally at the subsystem-level, using only the knowledge of the dynamics of that subsystem, and limited information about the dissipativity of the subsystems to which it is dynamically coupled. We show that the subsystem-level controllers synthesized in this manner are sufficient to guarantee dissipativity of the networked dynamical system. We also provide an approach to make this synthesis compositional, that is, when a new subsystem is added to an existing network, only the dynamics of the new subsystem, and information about the dissipativity of the subsystems in the existing network to which it is coupled are used to design a controller for the new subsystem, while guaranteeing dissipativity of the networked system including the new subsystem. Finally, we demonstrate the application of this synthesis in enabling plug-and-play operations of generators in a microgrid by extending our results to networked switched systems.

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