Sayak Mukherjee

Sayak Mukherjee, Ján Drgoňa, Aaron Tuor et al.

We present a learning-based predictive control methodology using the differentiable programming framework with probabilistic Lyapunov-based stability guarantees. The neural Lyapunov differentiable predictive control (NLDPC) learns the policy by constructing a computational graph encompassing the system dynamics, state and input constraints, and the necessary Lyapunov certification constraints, and thereafter using the automatic differentiation to update the neural policy parameters. In conjunction, our approach jointly learns a Lyapunov function that certifies the regions of state-space with stable dynamics. We also provide a sampling-based statistical guarantee for the training of NLDPC from the distribution of initial conditions. Our offline training approach provides a computationally efficient and scalable alternative to classical explicit model predictive control solutions. We substantiate the advantages of the proposed approach with simulations to stabilize the double integrator model and on an example of controlling an aircraft model.

Ján Drgoňa, Sayak Mukherjee, Aaron Tuor et al.

The problem of synthesizing stochastic explicit model predictive control policies is known to be quickly intractable even for systems of modest complexity when using classical control-theoretic methods. To address this challenge, we present a scalable alternative called stochastic parametric differentiable predictive control (SP-DPC) for unsupervised learning of neural control policies governing stochastic linear systems subject to nonlinear chance constraints. SP-DPC is formulated as a deterministic approximation to the stochastic parametric constrained optimal control problem. This formulation allows us to directly compute the policy gradients via automatic differentiation of the problem's value function, evaluated over sampled parameters and uncertainties. In particular, the computed expectation of the SP-DPC problem's value function is backpropagated through the closed-loop system rollouts parametrized by a known nominal system dynamics model and neural control policy which allows for direct model-based policy optimization. We provide theoretical probabilistic guarantees for policies learned via the SP-DPC method on closed-loop stability and chance constraints satisfaction. Furthermore, we demonstrate the computational efficiency and scalability of the proposed policy optimization algorithm in three numerical examples, including systems with a large number of states or subject to nonlinear constraints.

Sayak Mukherjee, Ramij R. Hossain, Yuan Liu et al.

This paper presents a novel federated reinforcement learning (Fed-RL) methodology to enhance the cyber resiliency of networked microgrids. We formulate a resilient reinforcement learning (RL) training setup which (a) generates episodic trajectories injecting adversarial actions at primary control reference signals of the grid forming (GFM) inverters and (b) trains the RL agents (or controllers) to alleviate the impact of the injected adversaries. To circumvent data-sharing issues and concerns for proprietary privacy in multi-party-owned networked grids, we bring in the aspects of federated machine learning and propose a novel Fed-RL algorithm to train the RL agents. To this end, the conventional horizontal Fed-RL approaches using decoupled independent environments fail to capture the coupled dynamics in a networked microgrid, which leads us to propose a multi-agent vertically federated variation of actor-critic algorithms, namely federated soft actor-critic (FedSAC) algorithm. We created a customized simulation setup encapsulating microgrid dynamics in the GridLAB-D/HELICS co-simulation platform compatible with the OpenAI Gym interface for training RL agents. Finally, the proposed methodology is validated with numerical examples of modified IEEE 123-bus benchmark test systems consisting of three coupled microgrids.

Sayak Mukherjee, Ramij R. Hossain, Sheik M. Mohiuddin et al.

Improving system-level resiliency of networked microgrids is an important aspect with increased population of inverter-based resources (IBRs). This paper (1) presents resilient control design in presence of adversarial cyber-events, and proposes a novel federated reinforcement learning (Fed-RL) approach to tackle (a) model complexities, unknown dynamical behaviors of IBR devices, (b) privacy issues regarding data sharing in multi-party-owned networked grids, and (2) transfers learned controls from simulation to hardware-in-the-loop test-bed, thereby bridging the gap between simulation and real world. With these multi-prong objectives, first, we formulate a reinforcement learning (RL) training setup generating episodic trajectories with adversaries (attack signal) injected at the primary controllers of the grid forming (GFM) inverters where RL agents (or controllers) are being trained to mitigate the injected attacks. For networked microgrids, the horizontal Fed-RL method involving distinct independent environments is not appropriate, leading us to develop vertical variant Federated Soft Actor-Critic (FedSAC) algorithm to grasp the interconnected dynamics of networked microgrid. Next, utilizing OpenAI Gym interface, we built a custom simulation set-up in GridLAB-D/HELICS co-simulation platform, named Resilient RL Co-simulation (ResRLCoSIM), to train the RL agents with IEEE 123-bus benchmark test systems comprising 3 interconnected microgrids. Finally, the learned policies in simulation world are transferred to the real-time hardware-in-the-loop test-bed set-up developed using high-fidelity Hypersim platform. Experiments show that the simulator-trained RL controllers produce convincing results with the real-time test-bed set-up, validating the minimization of sim-to-real gap.

Aowabin Rahman, Arnab Bhattacharya, Thiagarajan Ramachandran et al.

Search and Rescue (SAR) missions in remote environments often employ autonomous multi-robot systems that learn, plan, and execute a combination of local single-robot control actions, group primitives, and global mission-oriented coordination and collaboration. Often, SAR coordination strategies are manually designed by human experts who can remotely control the multi-robot system and enable semi-autonomous operations. However, in remote environments where connectivity is limited and human intervention is often not possible, decentralized collaboration strategies are needed for fully-autonomous operations. Nevertheless, decentralized coordination may be ineffective in adversarial environments due to sensor noise, actuation faults, or manipulation of inter-agent communication data. In this paper, we propose an algorithmic approach based on adversarial multi-agent reinforcement learning (MARL) that allows robots to efficiently coordinate their strategies in the presence of adversarial inter-agent communications. In our setup, the objective of the multi-robot team is to discover targets strategically in an obstacle-strewn geographical area by minimizing the average time needed to find the targets. It is assumed that the robots have no prior knowledge of the target locations, and they can interact with only a subset of neighboring robots at any time. Based on the centralized training with decentralized execution (CTDE) paradigm in MARL, we utilize a hierarchical meta-learning framework to learn dynamic team-coordination modalities and discover emergent team behavior under complex cooperative-competitive scenarios. The effectiveness of our approach is demonstrated on a collection of prototype grid-world environments with different specifications of benign and adversarial agents, target locations, and agent rewards.

Anuj Singh, Sayak Mukherjee, Ahmad Beirami et al.

Aligning diffusion models to downstream tasks often requires finetuning new models or gradient-based guidance at inference time to enable sampling from the reward-tilted posterior. In this work, we explore a simple inference-time gradient-free guidance approach, called controlled denoising (CoDe), that circumvents the need for differentiable guidance functions and model finetuning. CoDe is a blockwise sampling method applied during intermediate denoising steps, allowing for alignment with downstream rewards. Our experiments demonstrate that, despite its simplicity, CoDe offers a favorable trade-off between reward alignment, prompt instruction following, and inference cost, achieving a competitive performance against the state-of-the-art baselines. Our code is available at: https://github.com/anujinho/code.

Kyung-Bin Kwon, Min Gyung Yu, Sayak Mukherjee et al.

Grid-forming (GFM) inverters are essential for enhancing stability in modern power systems with high penetration of inverter-based resources (IBRs). However, their performance highly depends on control parameters tuning, particularly the active power-frequency droop coefficient. This parameter presents a trade-off among competing objectives, including damping, settling time, rate of change of frequencies (RoCoF) and frequency nadirs. This paper proposes a real-time, adaptive optimization framework based on Extremum Seeking Control (ESC) to dynamically tune the GFM droop gain. A multi-objective cost function balances conflicting performance goals such as oscillation energy, frequency nadir, RoCoF, and post-disturbance settling performance. The approach is validated through numerical simulations on a modified IEEE 68-bus system. Results demonstrate that the cost function is convex with respect to the droop parameter, justifying gradient-based optimization. Furthermore, the ESC algorithm successfully tracks the time-varying optimal droop coefficient in real-time as network conditions change, thereby ensuring robust and near-optimal system performance without requiring an analytical grid model.

Sayak Mukherjee, Andrea Simonetto, Hadi Jamali-Rad

Effective collaboration among heterogeneous clients in a decentralized setting is a rather unexplored avenue in the literature. To structurally address this, we introduce Model Agnostic Peer-to-peer Learning (coined as MAPL) a novel approach to simultaneously learn heterogeneous personalized models as well as a collaboration graph through peer-to-peer communication among neighboring clients. MAPL is comprised of two main modules: (i) local-level Personalized Model Learning (PML), leveraging a combination of intra- and inter-client contrastive losses; (ii) network-wide decentralized Collaborative Graph Learning (CGL) dynamically refining collaboration weights in a privacy-preserving manner based on local task similarities. Our extensive experimentation demonstrates the efficacy of MAPL and its competitive (or, in most cases, superior) performance compared to its centralized model-agnostic counterparts, without relying on any central server. Our code is available and can be accessed here: https://github.com/SayakMukherjee/MAPL

Sayak Mukherjee, Ramij R. Hossain, Kaustav Chatterjee et al.

This paper explores the development of learning-based tunable control gains using EMT-in-the-loop simulation framework (e.g., PSCAD interfaced with Python-based learning modules) to address critical sub-synchronous oscillations. Since sub-synchronous control interactions (SSCI) arise from the mis-tuning of control gains under specific grid configurations, effective mitigation strategies require adaptive re-tuning of these gains. Such adaptiveness can be achieved by employing a closed-loop, learning-based framework that considers the grid conditions responsible for such sub-synchronous oscillations. This paper addresses this need by adopting methodologies inspired by Markov decision process (MDP) based reinforcement learning (RL), with a particular emphasis on simpler deep policy gradient methods with additional SSCI-specific signal processing modules such as down-sampling, bandpass filtering, and oscillation energy dependent reward computations. Our experimentation in a real-world event setting demonstrates that the deep policy gradient based trained policy can adaptively compute gain settings in response to varying grid conditions and optimally suppress control interaction-induced oscillations.

Sayak Mukherjee, Samrat Chatterjee, Emilie Purvine et al.

Designing rewards for autonomous cyber attack and defense learning agents in a complex, dynamic environment is a challenging task for subject matter experts. We propose a large language model (LLM)-based reward design approach to generate autonomous cyber defense policies in a deep reinforcement learning (DRL)-driven experimental simulation environment. Multiple attack and defense agent personas were crafted, reflecting heterogeneity in agent actions, to generate LLM-guided reward designs where the LLM was first provided with contextual cyber simulation environment information. These reward structures were then utilized within a DRL-driven attack-defense simulation environment to learn an ensemble of cyber defense policies. Our results suggest that LLM-guided reward designs can lead to effective defense strategies against diverse adversarial behaviors.

Sayak Mukherjee, Ramij R. Hossain, Mahantesh Halappanavar

We analyze offline designs of linear quadratic regulator (LQR) strategies with uncertain disturbances. First, we consider the scenario where the exogenous variable can be estimated in a controlled environment, and subsequently, consider a more practical and challenging scenario where it is unknown in a stochastic setting. Our approach builds on the fundamental learning-based framework of adaptive dynamic programming (ADP), combined with a Lyapunov-based analytical methodology to design the algorithms and derive sample-based approximations motivated from the Markov decision process (MDP)-based approaches. For the scenario involving non-measurable disturbances, we further establish stability and convergence guarantees for the learned control gains under sample-based approximations. The overall methodology emphasizes simplicity while providing rigorous guarantees. Finally, numerical experiments focus on the intricacies and validations for the design of offline continuous-time LQR with exogenous disturbances.

Kyung-Bin Kwon, Sayak Mukherjee, Ramij R. Hossain et al.

This letter develops a novel physics-informed neural ordinary differential equations-based framework to emulate the proprietary dynamics of the inverters -- essential for improved accuracy in grid dynamic simulations. In current industry practice, the original equipment manufacturers (OEMs) often do not disclose the exact internal controls and parameters of the inverters, posing significant challenges in performing accurate dynamic simulations and other relevant studies, such as gain tunings for stability analysis and controls. To address this, we propose a Physics-Informed Latent Neural ODE Model (PI-LNM) that integrates system physics with neural learning layers to capture the unmodeled behaviors of proprietary units. The proposed method is validated using a grid-forming inverter (GFM) case study, demonstrating improved dynamic simulation accuracy over approaches that rely solely on data-driven learning without physics-based guidance.

Thanh Long Vu, Sayak Mukherjee, Renke Huang et al.

Under voltage load shedding has been considered as a standard approach to recover the voltage stability of the electric power grid under emergency conditions, yet this scheme usually trips a massive amount of load inefficiently. Reinforcement learning (RL) has been adopted as a promising approach to circumvent the issues; however, RL approach usually cannot guarantee the safety of the systems under control. In this paper, we discuss a couple of novel safe RL approaches, namely constrained optimization approach and Barrier function-based approach, that can safely recover voltage under emergency events. This method is general and can be applied to other safety-critical control problems. Numerical simulations on the 39-bus IEEE benchmark are performed to demonstrate the effectiveness of the proposed safe RL emergency control.

Ján Drgoňa, Sayak Mukherjee, Jiaxin Zhang et al.

Deep Markov models (DMM) are generative models that are scalable and expressive generalization of Markov models for representation, learning, and inference problems. However, the fundamental stochastic stability guarantees of such models have not been thoroughly investigated. In this paper, we provide sufficient conditions of DMM's stochastic stability as defined in the context of dynamical systems and propose a stability analysis method based on the contraction of probabilistic maps modeled by deep neural networks. We make connections between the spectral properties of neural network's weights and different types of used activation functions on the stability and overall dynamic behavior of DMMs with Gaussian distributions. Based on the theory, we propose a few practical methods for designing constrained DMMs with guaranteed stability. We empirically substantiate our theoretical results via intuitive numerical experiments using the proposed stability constraints.

Sayak Mukherjee, Veronica Adetola

This paper presents a secure reinforcement learning (RL) based control method for unknown linear time-invariant cyber-physical systems (CPSs) that are subjected to compositional attacks such as eavesdropping and covert attack. We consider the attack scenario where the attacker learns about the dynamic model during the exploration phase of the learning conducted by the designer to learn a linear quadratic regulator (LQR), and thereafter, use such information to conduct a covert attack on the dynamic system, which we refer to as doubly learning-based control and attack (DLCA) framework. We propose a dynamic camouflaging based attack-resilient reinforcement learning (ARRL) algorithm which can learn the desired optimal controller for the dynamic system, and at the same time, can inject sufficient misinformation in the estimation of system dynamics by the attacker. The algorithm is accompanied by theoretical guarantees and extensive numerical experiments on a consensus multi-agent system and on a benchmark power grid model.

Sayak Mukherjee, Renke Huang, Qiuhua Huang et al.

This paper presents a novel hierarchical deep reinforcement learning (DRL) based design for the voltage control of power grids. DRL agents are trained for fast, and adaptive selection of control actions such that the voltage recovery criterion can be met following disturbances. Existing voltage control techniques suffer from the issues of speed of operation, optimal coordination between different locations, and scalability. We exploit the area-wise division structure of the power system to propose a hierarchical DRL design that can be scaled to the larger grid models. We employ an enhanced augmented random search algorithm that is tailored for the voltage control problem in a two-level architecture. We train area-wise decentralized RL agents to compute lower-level policies for the individual areas, and concurrently train a higher-level DRL agent that uses the updates of the lower-level policies to efficiently coordinate the control actions taken by the lower-level agents. Numerical experiments on the IEEE benchmark 39-bus model with 3 areas demonstrate the advantages and various intricacies of the proposed hierarchical approach.

Sayak Mukherjee, Thanh Long Vu

This paper discusses learning a structured feedback control to obtain sufficient robustness to exogenous inputs for linear dynamic systems with unknown state matrix. The structural constraint on the controller is necessary for many cyber-physical systems, and our approach presents a design for any generic structure, paving the way for distributed learning control. The ideas from reinforcement learning (RL) in conjunction with control-theoretic sufficient stability and performance guarantees are used to develop the methodology. First, a model-based framework is formulated using dynamic programming to embed the structural constraint in the linear quadratic regulator (LQR) setting along with sufficient robustness conditions. Thereafter, we translate these conditions to a data-driven learning-based framework - robust structured reinforcement learning (RSRL) that enjoys the control-theoretic guarantees on stability and convergence. We validate our theoretical results with a simulation on a multi-agent network with 6 agents.

Sayak Mukherjee, Thanh Long Vu

This paper delves into designing stabilizing feedback control gains for continuous linear systems with unknown state matrix, in which the control is subject to a general structural constraint. We bring forth the ideas from reinforcement learning (RL) in conjunction with sufficient stability and performance guarantees in order to design these structured gains using the trajectory measurements of states and controls. We first formulate a model-based framework using dynamic programming (DP) to embed the structural constraint to the Linear Quadratic Regulator (LQR) gain computation in the continuous-time setting. Subsequently, we transform this LQR formulation into a policy iteration RL algorithm that can alleviate the requirement of known state matrix in conjunction with maintaining the feedback gain structure. Theoretical guarantees are provided for stability and convergence of the structured RL (SRL) algorithm. The introduced RL framework is general and can be applied to any control structure. A special control structure enabled by this RL framework is distributed learning control which is necessary for many large-scale cyber-physical systems. As such, we validate our theoretical results with numerical simulations on a multi-agent networked linear time-invariant (LTI) dynamic system.

Sayak Mukherjee, He Bai, Aranya Chakrabortty

We present a set of model-free, reduced-dimensional reinforcement learning (RL) based optimal control designs for linear time-invariant singularly perturbed (SP) systems. We first present a state-feedback and output-feedback based RL control design for a generic SP system with unknown state and input matrices. We take advantage of the underlying time-scale separation property of the plant to learn a linear quadratic regulator (LQR) for only its slow dynamics, thereby saving a significant amount of learning time compared to the conventional full-dimensional RL controller. We analyze the sub-optimality of the design using SP approximation theorems and provide sufficient conditions for closed-loop stability. Thereafter, we extend both designs to clustered multi-agent consensus networks, where the SP property reflects through clustering. We develop both centralized and cluster-wise block-decentralized RL controllers for such networks, in reduced dimensions. We demonstrate the details of the implementation of these controllers using simulations of relevant numerical examples and compare them with conventional RL designs to show the computational benefits of our approach.

Sayak Mukherjee, David Stewart, William Stewart et al.

Single cell responses are shaped by the geometry of signaling kinetic trajectories carved in a multidimensional space spanned by signaling protein abundances. It is however challenging to assay large number (>3) of signaling species in live-cell imaging which makes it difficult to probe single cell signaling kinetic trajectories in large dimensions. Flow and mass cytometry techniques can measure a large number (4 - >40) of signaling species but are unable to track single cells. Thus cytometry experiments provide detailed time stamped snapshots of single cell signaling kinetics. Is it possible to use the time stamped cytometry data to reconstruct single cell signaling trajectories? Borrowing concepts of conserved and slow variables from non-equilibrium statistical physics we develop an approach to reconstruct signaling trajectories using snapshot data by creating new variables that remain invariant or vary slowly during the signaling kinetics. We apply this approach to reconstruct trajectories using snapshot data obtained from in silico simulations and live-cell imaging measurements. The use of invariants and slow variables to reconstruct trajectories provides a radically different way to track object using snapshot data. The approach is likely to have implications for solving matching problems in a wide range of disciplines.