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Venkatraman Renganathan

Publications and source records attributed to Venkatraman Renganathan.

At least 19 recordsLinked to original sources
arXiv2026

HJ-Gauss: A Monte-Carlo HJ Reachability Scheme

Backward reachable sets or tubes (BRS/Ts), evaluated with grid-based level-set methods over viscous Hamilton-Jacobi (HJ) equations, furnish principled reachability certificates for learning-enabled control. However, these methods incur an $O(M^n)$ memory cost, where $M$ is the number of grid points for every $n$-state dimension, which has precluded their applications in high-dimensional physical phenomena. Towards scalable reachability analysis, we propose a frozen-coefficient Picard iterative Gaussian sampling scheme: with a Cole-Hopf-type transformation, the HJ PDE effectively reduces to a sequence of linear heat equations, whose values are then iteratively recovered via Gaussian heat-kernel expectations. In this sentiment, Monte Carlo roll-outs over Gaussian densities ultimately recover the (approximate) HJ value and its spatial gradient. Ours is a storage- and discretization-free algorithm whose memory footprint scales (for \textit{i.i.d} samples, $N$) as $N\cdot n$; we show that sampling is a polynomial power law in $N$ and provide a conditional linear convergence analysis to the \textit{consistent} viscosity solution. Furthermore, we provide a quasilinearization defect per iteration between frozen coefficient samples to make our HJ sampling scheme tight. Our theoretical machinery is rigorously benchmarked on rocket launch and Dubins pursuit-evasion (P-E) games over Holm-Bonferroni-informed experiments: for a $45D$-multi-rocket launch P-E game, we find an \textit{almost zero} Picard residual floor. Certifying the safety of \textbf{$100,000$} European starlings (\textit{sturnus vulgaris}) in murmurations over their collective value functions reveals vacuole nucleation, cordon formation, and flock splitting on the resulting BRT zero-levelset phase topology as predator attacks evolve , demonstrating the scalability of our approach to large-scale multi-agent systems.

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arXiv2025

Distance Between Stochastic Linear Systems

While the existing stochastic control theory is well equipped to handle dynamical systems with stochastic uncertainties, a paradigm shift using distance measure based decision making is required for the effective further exploration of the field. As a first step, a distance measure between two stochastic linear time invariant systems is proposed here, extending the existing distance metrics between deterministic linear dynamical systems. In the frequency domain, the proposed distance measure corresponds to the worst-case point-wise in frequency Wasserstein distance between distributions characterising the uncertainties using inverse stereographic projection on the Riemann sphere. For the time domain setting, the proposed distance corresponds to the gap metric induced type-q Wasserstein distance between the distributions characterising the uncertainty of plant models. Apart from providing lower and upper bounds for the proposed distance measures in both frequency and time domain settings, it is proved that the former never exceeds the latter. The proposed distance measures will facilitate the provision of probabilistic guarantees on system robustness and controller performances.

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arXiv2025

Probabilistic Robustness in the Gap Metric

Uncertainties influencing the dynamical systems pose a significant challenge in estimating the achievable performance of a controller aiming to control such uncertain systems. When the uncertainties are of stochastic nature, obtaining hard guarantees for the robustness of a controller aiming to hedge against the uncertainty is not possible. This issue set the platform for the development of probabilistic robust control approaches. In this work, we utilise the gap metric between the known nominal model and the unknown perturbed model of the uncertain system as a tool to gauge the robustness of a controller and formulate the gap as a random variable in the setting with stochastic uncertainties. The main results of this paper include giving a probabilistic bound on the gap exceeding a known threshold, followed by bounds on the expected gap value and probabilistic robust stability and performance guarantees in terms of the gap metric. We also provide a probabilistic controller performance certification under gap uncertainty and probabilistic guarantee on the achievable $\mathcal{H}_{\infty}$ robustness. Numerical simulations are provided to demonstrate the proposed approach.

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arXiv2025

Predictive & Trust-based Multi-Agent Coordination

This paper presents a trust-based predictive multi-agent consensus protocol that analyses neighbours' anticipation data and makes coordination decisions. Agents in the network share their future predicted data over a finite look-ahead horizon with their neighbours and update their predictions in a rolling-horizon fashion. The prediction data is then used by agents to learn both the trust and the commitment traits exhibited by their neighbours over time. The proposed protocol is named as the Anticipatory Distributed Coordination (ADC) protocol. Lyapunov theory-based agreement convergence between agents is provided, followed by demonstrations using numerical simulations.

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arXiv2024

Stereographic Projection of Probabilistic Frequency-Domain Uncertainty

This paper investigates the stereographic projection of points along the Nyquist plots of single input single output (SISO) linear time invariant (LTI) systems subject to probabilistic uncertainty. At each frequency, there corresponds a complex-valued random variable with given probability distribution in the complex plane. The chordal distance between the stereographic projections of this complex value and the corresponding value for a nominal model, as per the well-known Nu-Gap metric of Vinnicombe, is also a random quantity. The main result provides the cumulative density function (CDF) of the chordal distance at a given frequency. Such a stochastic distance framework opens up a fresh and a fertile research direction on probabilistic robust control theory.

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arXiv2024

A Cantor-Kantorovich Metric Between Markov Decision Processes with Application to Transfer Learning

We extend the notion of Cantor-Kantorovich distance between Markov chains introduced by (Banse et al., 2023) in the context of Markov Decision Processes (MDPs). The proposed metric is well-defined and can be efficiently approximated given a finite horizon. Then, we provide numerical evidences that the latter metric can lead to interesting applications in the field of reinforcement learning. In particular, we show that it could be used for forecasting the performance of transfer learning algorithms.

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arXiv2024

Regret and Conservatism of Distributionally Robust Constrained Stochastic Model Predictive Control

We analyse the conservatism and regret of distributionally robust (DR) stochastic model predictive control (SMPC) when using moment-based ambiguity sets for modeling unknown uncertainties. To quantify the conservatism, we compare the deterministic constraint tightening while taking a DR approach against the optimal tightening when the exact distributions of the stochastic uncertainties are known. Furthermore, we quantify the regret by comparing the performance when the distributions of the stochastic uncertainties are known and unknown. Analysing the accumulated sub-optimality of SMPC due to the lack of knowledge about the true distributions of the uncertainties marks the novel contribution of this work.

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arXiv2023

Distributed Adaptive Control for Uncertain Networks

Control of network systems with uncertain local dynamics has remained an open problem for a long time. In this paper, a distributed minimax adaptive control algorithm is proposed for such networks whose local dynamics has an uncertain parameter possibly taking finite number of values. To hedge against this uncertainty, each node in the network collects the historical data of its neighboring nodes to decide its control action along its edges by finding the parameter that best describes the observed disturbance trajectory. Our proposed distributed adaptive controller is scalable and we give both lower and upper bounds for its $\ell_{2}$ gain. Numerical simulations demonstrate that once each node has sufficiently estimated its local uncertainty, the distributed minimax adaptive controller behaves like the optimal distributed $\mathcal{H}_{\infty}$ controller in hindsight.

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arXiv2023

An Online Learning Analysis of Minimax Adaptive Control

We present an online learning analysis of minimax adaptive control for the case where the uncertainty includes a finite set of linear dynamical systems. Precisely, for each system inside the uncertainty set, we define the model-based regret by comparing the state and input trajectories from the minimax adaptive controller against that of an optimal controller in hindsight that knows the true dynamics. We then define the total regret as the worst case model-based regret with respect to all models in the considered uncertainty set. We study how the total regret accumulates over time and its effect on the adaptation mechanism employed by the controller. Moreover, we investigate the effect of the disturbance on the growth of the regret over time and draw connections between robustness of the controller and the associated regret rate.

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arXiv2023

Distributionally Robust RRT with Risk Allocation

An integration of distributionally robust risk allocation into sampling-based motion planning algorithms for robots operating in uncertain environments is proposed. We perform non-uniform risk allocation by decomposing the distributionally robust joint risk constraints defined over the entire planning horizon into individual risk constraints given the total risk budget. Specifically, the deterministic tightening defined using the individual risk constraints is leveraged to define our proposed exact risk allocation procedure. Our idea of embedding the risk allocation technique into sampling based motion planning algorithms realises guaranteed conservative, yet increasingly more risk feasible trajectories for efficient state space exploration.

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arXiv2022

Regret Analysis for Risk-aware Linear Quadratic Control

This paper investigates the regret associated with the Distributionally Robust Control (DRC) strategies used to address multistage optimization problems where the involved probability distributions are not known exactly, but rather are assumed to belong to specified ambiguity families. We quantify the price (distributional regret) that one ends up paying for not knowing the exact probability distribution of the stochastic system uncertainty while aiming to control it using the DRC strategies. The conservatism of the DRC strategies for being robust to worst-case uncertainty distribution in the considered ambiguity set comes at the price of lack of knowledge about the true distribution in the set. We use the worst case Conditional Value-at-Risk to define the distributional regret and the regret bound was found to be increasing with tighter risk level. The motive of this paper is to promote the design of new control algorithms aiming to minimize the distributional regret.

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arXiv2022

Leveraging second-order information for tuning of inverse optimal controllers

We leverage second-order information for tuning of inverse optimal controllers for a class of discrete-time nonlinear input-affine systems. For this, we select the input penalty matrix, representing a tuning knob, to yield the Hessian of the Lyapunov function of the closed-loop dynamics. This draws a link between second-order methods known for their high speed of convergence and the tuning of inverse optimal stabilizing controllers to achieve a fast decay of the closed-loop trajectories towards a steady state. In particular, we ensure quadratic convergence, a feat that is otherwise not achieved with a constant input penalty matrix. To balance trade-offs, we suggest a practical implementation of the Hessian and validate this numerically on a network of phase-coupled oscillators that represent voltage source controlled power inverters.

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arXiv2022

Distributionally Robust Covariance Steering with Optimal Risk Allocation

This article extends the optimal covariance steering (CS) problem for discrete time linear stochastic systems modeled using moment-based ambiguity sets. To hedge against the uncertainty in the state distributions while performing covariance steering, distributionally robust risk constraints are employed during the optimal allocation of the risk. Specifically, a distributionally robust iterative risk allocation (DR-IRA) formalism is used to solve the optimal risk allocation problem for the CS problem using a two-stage approach. The upper-stage of DR-IRA is a convex problem that optimizes the risk, while the lower-stage optimizes the controller with the new distributionally robust risk constraints. The proposed framework results in solutions that are robust against arbitrary distributions in the considered ambiguity set. Finally, we demonstrate our proposed approach using numerical simulations. Addressing the covariance steering problem through the lens of distributional robustness marks the novel contribution of this article.

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arXiv2022

Path Planning Using Wassertein Distributionally Robust Deep Q-learning

We investigate the problem of risk averse robot path planning using the deep reinforcement learning and distributionally robust optimization perspectives. Our problem formulation involves modelling the robot as a stochastic linear dynamical system, assuming that a collection of process noise samples is available. We cast the risk averse motion planning problem as a Markov decision process and propose a continuous reward function design that explicitly takes into account the risk of collision with obstacles while encouraging the robot's motion towards the goal. We learn the risk-averse robot control actions through Lipschitz approximated Wasserstein distributionally robust deep Q-learning to hedge against the noise uncertainty. The learned control actions result in a safe and risk averse trajectory from the source to the goal, avoiding all the obstacles. Various supporting numerical simulations are presented to demonstrate our proposed approach.

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arXiv2022

Distributed Implementation of Minimax Adaptive Controller For Finite Set of Linear Systems

This paper deals with a distributed implementation of minimax adaptive control algorithm for networked dynamical systems modeled by a finite set of linear models. To hedge against the uncertainty arising out of finite number of possible dynamics in each node in the network, it collects only the historical data of its neighboring nodes to decide its control action along its edges. This makes our proposed distributed approach scalable. Numerical simulations demonstrate that once each node has sufficiently estimated the uncertain parameters, the distributed minimax adaptive controller behaves like the optimal distributed H-infinity controller in hindsight.

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arXiv2022

History Data Driven Distributed Consensus in Networks

The association of weights in a distributed consensus protocol quantify the trust that an agent has on its neighbors in a network. An important problem in such networked systems is the uncertainty in the estimation of trust between neighboring agents, coupled with the losses arising from mistakenly associating wrong amounts of trust with different neighboring agents. We introduce a probabilistic approach which uses the historical data collected in the network, to determine the level of trust between each agent. Specifically, using the finite history of the shared data between neighbors, we obtain a configuration which represents the confidence estimate of every neighboring agent's trustworthiness. Finally, we propose a History-Data-Driven (HDD) distributed consensus protocol which translates the computed configuration data into weights to be used in the consensus update. The approach using the historical data in the context of a distributed consensus setting marks the novel contribution of our paper.

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arXiv2022

Risk Bounded Nonlinear Robot Motion Planning With Integrated Perception & Control

Robust autonomy stacks require tight integration of perception, motion planning, and control layers, but these layers often inadequately incorporate inherent perception and prediction uncertainties, either ignoring them altogether or making questionable assumptions of Gaussianity. Robots with nonlinear dynamics and complex sensing modalities operating in an uncertain environment demand more careful consideration of how uncertainties propagate across stack layers. We propose a framework to integrate perception, motion planning, and control by explicitly incorporating perception and prediction uncertainties into planning so that risks of constraint violation can be mitigated. Specifically, we use a nonlinear model predictive control based steering law coupled with a decorrelation scheme based Unscented Kalman Filter for state and environment estimation to propagate the robot state and environment uncertainties. Subsequently, we use distributionally robust risk constraints to limit the risk in the presence of these uncertainties. Finally, we present a layered autonomy stack consisting of a nonlinear steering-based distributionally robust motion planning module and a reference trajectory tracking module. Our numerical experiments with nonlinear robot models and an urban driving simulator show the effectiveness of our proposed approaches.

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