arXiv subjects

Lekan Molu

Publications and source records attributed to Lekan Molu.

17 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.

eess.SY↗

arXiv2026

Kolmogorov Regression for Robust Diffusion Policies

Finite-dimensional (FD) diffusion policies exhibit temporal drift owing to discretization artifacts that degrade long-horizon performance (when deployed on physical systems). We introduce a backward Kolmogorov equation that lifts diffusion policies to a Cameron-Martin space -- a subset of the Hilbert space. Essentially, replacing stochastic score matching with a deterministic boundary-value PDE problem. Our core innovation thrives on Gaussian measure theory whereupon the diffusion noise covariance operator is realized from a colored noise distribution which prescribes a notion of regularity on samples from the model at inference time. We train the diffusion model with a derived precision-weighted Cameron- Martin loss and a Kolmogorov residual is introduced as a PDE diagnostic during inference. These substitutions yield (i) convergence guarantees where the bound's constants depend on the effective rank of the kernel rather than action dimension, (ii) improved trajectory regularity via spectral weighting, and (iii) a deterministic failure detector without reward signals. Validation across two application domains demonstrates substantial improvements: on the PushT manipulation benchmark, the Cameron-Martin loss achieves a 17% improvement in maximum episode reward (0.95 vs. 0.78 for MSE) and 67.6% reduction in inter-step drifts during inference via the introduced residual magnitude. Similarly, on a 6-station manufacturing line with constant work-in-process (CONWIP) flow control, we achieve 28.4% lower RMSE than classical LSTM baselines; a high starvation-event recall (1.0 in test cycles), and effective bottleneck identification (Precision@1 = 1.0 in test set, 13x signal-to-noise ratio). We then certify the dispatch policies with Hamilton-Jacobi reachability theory which reduces deadlock events by 96% compared to uncontrolled dispatch over 100 simulated runs (351 events prevented).

cs.LG↗

arXiv2026

A Generalized Nash Equilibrium-Seeking Scheme for Trauma Resuscitation

Trauma resuscitation is a clinical process for treating life-threatening physiological disorders in safety-critical environments, driven by the experience of healthcare workers (HCWs). Designing and optimizing quantifiable metrics that accurately capture HCW decisions may augment current resuscitation procedures with the potential to improve patient outcomes. This motivates our socio-technical formulation of trauma resuscitation as a distributed generalized Nash equilibrium (GNE)-seeking game with coupled inequality constraints. This method is optimized over a time-varying communication graph. We introduce novel insights from clinical experience to model HCWs behavior. This work facilitates the best possible resuscitation outcome given HCWs workloads, schedules, competencies, and limited resources.

cs.MA↗

arXiv2026

AdaFair-MARL: Enforcing Adaptive Fairness Constraints in Multi-Agent Reinforcement Learning

Fair workload enforcement in heterogeneous multi-agent systems that pursue shared objectives remains challenging. Fixed fairness penalties often introduce inefficiencies, training instability, and conflicting agent incentives. Reward-shaping approaches in fair Multi-Agent Reinforcement Learning (MARL) typically incorporate fairness through heuristic penalties or scalar reward modifications and often rely on post-hoc evaluation. However, these methods do not guarantee that a desired fairness level will be satisfied. To address this limitation, we propose the Adaptive Fairness Multi-Agent Reinforcement Learning (AdaFair-MARL) framework, which formulates workload fairness as an explicit constraint so that agents maintain balanced contributions while optimizing team performance. We present AdaFair-MARL, a constrained cooperative MARL framework whose core algorithmic component is a primal-dual update that enforces workload fairness via adaptive Lagrange multiplier updates. Grounding the framework in a cooperative Markov game, we derive the fairness constraint from Jain's Fairness Index (JFI) geometry and show that the resulting feasible set admits a second-order cone representation, enabling principled Lagrangian dual-ascent updates without manual penalty tuning. Experiments in a simulated hospital coordination environment (MARLHospital) demonstrate the effectiveness of AdaFair-MARL compared to reward-shaping and fixed-penalty fairness methods, improving workload balance while maintaining team performance. We found that AdaFair-MARL achieves nearly perfect constraint satisfaction (0.99-1.00) while significantly improving workload fairness compared to fixed-penalty baselines.

cs.LG↗

arXiv2025

LevelSetPy: A GPU-Accelerated Package for Hyperbolic Hamilton-Jacobi Partial Differential Equations

This article introduces a software package release for geometrically reasoning about the \textit{safety} desiderata of (complex) dynamical systems via level set methods. In emphasis, safety is analyzed with Hamilton-Jacobi equations. In scope, we provide implementations of numerical algorithms for the resolution of Hamilton-Jacobi-Isaacs equations: the spatial derivatives of the associated value function via upwinding, the Hamiltonian via Lax-Friedrichs schemes, and the integration of the Hamilton-Jacobi equation altogether via total variation diminishing Runge-Kutta schemes. Since computational speed and interoperability with other modern scientific computing libraries (typically written in the Python language) is of essence, we capitalize on modern computational frameworks such as \texttt{CUPY} and \texttt{NUMPY} and move heavy computations to GPU devices to aid parallelization and improve bring-up time in safety analysis. We hope that this package can aid users to quickly iterate on ideas and evaluate all possible safety desiderata of a system via geometrical simulation in modern engineering problems.

cs.MS↗

arXiv2025

Fast Whole-Body Strain Regulation in Continuum Robots

We propose reaching steps towards the real-time strain control of multiphysics, multiscale continuum soft robots. To study this problem fundamentally, we ground ourselves in a model-based control setting enabled by mathematically precise dynamics of a soft robot prototype. Poised to integrate, rather than reject, inherent mechanical nonlinearities for embodied compliance, we first separate the original robot dynamics into separate subdynamics -- aided by a perturbing time-scale separation parameter. Second, we prescribe a set of stabilizing nonlinear backstepping controllers for regulating the resulting subsystems' strain dynamics. Third, we study the interconnected singularly perturbed system by analyzing and establishing its stability. Fourth, our theories are backed up by fast numerical results on a single arm of the Octopus robot arm. We demonstrate strain regulation to equilibrium, in a significantly reduced time, of the whole-body reduced-order dynamics of an infinite degrees-of-freedom soft robot. This paper communicates our thinking within the backdrop of embodied intelligence: it informs our conceptualization, formulation, computational setup, and yields improved control performance for infinite degrees-of-freedom soft robots.

eess.SY↗

arXiv2025

Is Bellman Equation Enough for Learning Control?

The Bellman equation and its continuous-time counterpart, the Hamilton-Jacobi-Bellman (HJB) equation, serve as necessary conditions for optimality in reinforcement learning and optimal control. While the value function is known to be the unique solution to the Bellman equation in tabular settings, we demonstrate that this uniqueness fails to hold in continuous state spaces. Specifically, for linear dynamical systems, we prove the Bellman equation admits at least $\binom{2n}{n}$ solutions, where $n$ is the state dimension. Crucially, only one of these solutions yields both an optimal policy and a stable closed-loop system. We then demonstrate a common failure mode in value-based methods: convergence to unstable solutions due to the exponential imbalance between admissible and inadmissible solutions. Finally, we introduce a positive-definite neural architecture that guarantees convergence to the stable solution by construction to address this issue.

cs.LG↗

arXiv2024

The Python LevelSet Toolbox (LevelSetPy)

This paper describes open-source scientific contributions in python surrounding the numerical solutions to hyperbolic Hamilton-Jacobi (HJ) partial differential equations viz., their implicit representation on co-dimension one surfaces; dynamics evolution with levelsets; spatial derivatives; total variation diminishing Runge-Kutta integration schemes; and their applications to the theory of reachable sets. They are increasingly finding applications in multiple research domains such as reinforcement learning, robotics, control engineering and automation. We describe the library components, illustrate usage with an example, and provide comparisons with existing implementations. This GPU-accelerated package allows for easy portability to many modern libraries for the numerical analyses of the HJ equations. We also provide a CPU implementation in python that is significantly faster than existing alternatives.

cs.MS↗

arXiv2024

PcLast: Discovering Plannable Continuous Latent States

Goal-conditioned planning benefits from learned low-dimensional representations of rich observations. While compact latent representations typically learned from variational autoencoders or inverse dynamics enable goal-conditioned decision making, they ignore state reachability, hampering their performance. In this paper, we learn a representation that associates reachable states together for effective planning and goal-conditioned policy learning. We first learn a latent representation with multi-step inverse dynamics (to remove distracting information), and then transform this representation to associate reachable states together in $\ell_2$ space. Our proposals are rigorously tested in various simulation testbeds. Numerical results in reward-based settings show significant improvements in sampling efficiency. Further, in reward-free settings this approach yields layered state abstractions that enable computationally efficient hierarchical planning for reaching ad hoc goals with zero additional samples.

cs.LG↗

arXiv2024

Verification-Aided Learning of Neural Network Barrier Functions with Termination Guarantees

Barrier functions are a general framework for establishing a safety guarantee for a system. However, there is no general method for finding these functions. To address this shortcoming, recent approaches use self-supervised learning techniques to learn these functions using training data that are periodically generated by a verification procedure, leading to a verification-aided learning framework. Despite its immense potential in automating barrier function synthesis, the verification-aided learning framework does not have termination guarantees and may suffer from a low success rate of finding a valid barrier function in practice. In this paper, we propose a holistic approach to address these drawbacks. With a convex formulation of the barrier function synthesis, we propose to first learn an empirically well-behaved NN basis function and then apply a fine-tuning algorithm that exploits the convexity and counterexamples from the verification failure to find a valid barrier function with finite-step termination guarantees: if there exist valid barrier functions, the fine-tuning algorithm is guaranteed to find one in a finite number of iterations. We demonstrate that our fine-tuning method can significantly boost the performance of the verification-aided learning framework on examples of different scales and using various neural network verifiers.

cs.LG↗

arXiv2023

Lagrangian Properties and Control of Soft Robots Modeled with Discrete Cosserat Rods

The characteristic ``in-plane" bending associated with soft robots' deformation make them preferred over rigid robots in sophisticated manipulation and movement tasks. Executing such motion strategies to precision in soft deformable robots and structures is however fraught with modeling and control challenges given their infinite degrees-of-freedom. Imposing \textit{piecewise constant strains} (PCS) across (discretized) Cosserat microsolids on the continuum material however, their dynamics become amenable to tractable mathematical analysis. While this PCS model handles the characteristic difficult-to-model ``in-plane" bending well, its Lagrangian properties are not exploited for control in literature neither is there a rigorous study on the dynamic performance of multisection deformable materials for ``in-plane" bending that guarantees steady-state convergence. In this sentiment, we first establish the PCS model's structural Lagrangian properties. Second, we exploit these for control on various strain goal states. Third, we benchmark our hypotheses against an Octopus-inspired robot arm under different constant tip loads. These induce non-constant ``in-plane" deformation and we regulate strain states throughout the continuum in these configurations. Our numerical results establish convergence to desired equilibrium throughout the continuum in all of our tests. Within the bounds here set, we conjecture that our methods can find wide adoption in the control of cable- and fluid-driven multisection soft robotic arms; and may be extensible to the (learning-based) control of deformable agents employed in simulated, mixed, or augmented reality.

cs.RO↗

arXiv2023

Robust Policy Optimization in Continuous-time Mixed $\mathcal{H}_2/\mathcal{H}_\infty$ Stochastic Control

Following the recent resurgence in establishing linear control theoretic benchmarks for reinforcement leaning (RL)-based policy optimization (PO) for complex dynamical systems with continuous state and action spaces, an optimal control problem for a continuous-time infinite-dimensional linear stochastic system possessing additive Brownian motion is optimized on a cost that is an exponent of the quadratic form of the state, input, and disturbance terms. We lay out a model-based and model-free algorithm for RL-based stochastic PO. For the model-based algorithm, we establish rigorous convergence guarantees. For the sampling-based algorithm, over trajectory arcs that emanate from the phase space, we find that the Hamilton-Jacobi Bellman equation parameterizes trajectory costs -- resulting in a discrete-time (input and state-based) sampling scheme accompanied by unknown nonlinear dynamics with continuous-time policy iterates. The need for known dynamics operators is circumvented and we arrive at a reinforced PO algorithm (via policy iteration) where an upper bound on the $\mathcal{H}_2$ norm is minimized (to guarantee stability) and a robustness metric is enforced by maximizing the cost with respect to a controller that includes the level of noise attenuation specified by the system's $H_\infty$ norm. Rigorous robustness analyses is prescribed in an input-to-state stability formalism. Our analyses and contributions are distinguished by many natural systems characterized by additive Wiener process, amenable to Îto's stochastic differential calculus in dynamic game settings.

eess.SY↗

arXiv2023

Mixed $\mathcal{H}_2/\mathcal{H}_\infty$-Policy Learning Synthesis

A robustly stabilizing optimal control policy in a model-free mixed $\mathcal{H}_2/\mathcal{H}_\infty$-control setting is here put forward for counterbalancing the slow convergence and non-robustness of traditional high-variance policy optimization (and by extension policy gradient) algorithms. Leveraging Itô's stochastic differential calculus, we iteratively solve the system's continuous-time closed-loop generalized algebraic Riccati equation whilst updating its admissible controllers in a two-player, zero-sum differential game setting. Our new results are illustrated by learning-enabled control systems which gather previously disseminated results in this field in one holistic data-driven presentation with greater simplification, improvement, and clarity.

math.OC↗

arXiv2022

Guaranteed Discovery of Control-Endogenous Latent States with Multi-Step Inverse Models

In many sequential decision-making tasks, the agent is not able to model the full complexity of the world, which consists of multitudes of relevant and irrelevant information. For example, a person walking along a city street who tries to model all aspects of the world would quickly be overwhelmed by a multitude of shops, cars, and people moving in and out of view, each following their own complex and inscrutable dynamics. Is it possible to turn the agent's firehose of sensory information into a minimal latent state that is both necessary and sufficient for an agent to successfully act in the world? We formulate this question concretely, and propose the Agent Control-Endogenous State Discovery algorithm (AC-State), which has theoretical guarantees and is practically demonstrated to discover the minimal control-endogenous latent state which contains all of the information necessary for controlling the agent, while fully discarding all irrelevant information. This algorithm consists of a multi-step inverse model (predicting actions from distant observations) with an information bottleneck. AC-State enables localization, exploration, and navigation without reward or demonstrations. We demonstrate the discovery of the control-endogenous latent state in three domains: localizing a robot arm with distractions (e.g., changing lighting conditions and background), exploring a maze alongside other agents, and navigating in the Matterport house simulator.

cs.LG↗

arXiv2022

Interaction-Grounded Learning with Action-inclusive Feedback

Consider the problem setting of Interaction-Grounded Learning (IGL), in which a learner's goal is to optimally interact with the environment with no explicit reward to ground its policies. The agent observes a context vector, takes an action, and receives a feedback vector, using this information to effectively optimize a policy with respect to a latent reward function. Prior analyzed approaches fail when the feedback vector contains the action, which significantly limits IGL's success in many potential scenarios such as Brain-computer interface (BCI) or Human-computer interface (HCI) applications. We address this by creating an algorithm and analysis which allows IGL to work even when the feedback vector contains the action, encoded in any fashion. We provide theoretical guarantees and large-scale experiments based on supervised datasets to demonstrate the effectiveness of the new approach.

cs.LG↗

arXiv2022

Comments on "Time-Varying Lyapunov Functions for Tracking Control of Mechanical Systems With and Without Frictions"

In the article$^a$, the authors introduced a time-varying Lyapunov function for the stability analysis of nonlinear systems whose motion is governed by standard Newton-Euler equations. The authors established asymptotic stability with the choice of two symmetric positive definite matrices restricted by certain eigenvalue bounds in the control law. Exponential stability in the sense of Lyapunov using integrator backstepping and Lyapunov redesign is established in this note using just one matrix in the derived controller. We do not impose minimum eigenvalue bound requirements on the symmetric positive definite matrix introduced in our analysis to guarantee stability. Reducing the parameters needed in the control law, our analysis improves the stability and convergence rates of tracking errors reported in the article$^a$. $^a$Ren, W., Zhang, B, Li, H, and Yan L. IEEE Access. vol. 8. pp. 51510-51517. 2020.

eess.SY↗

arXiv2022

A Second-Order Reachable Sets Computation Scheme via a Cauchy-Type Variational Hamilton-Jacobi-Isaacs Equation

Motivated by the scalability limitations of Eulerian methods for variational Hamilton-Jacobi-Isaacs (HJI) formulations that provide a least restrictive controller in problems that involve state or input constraints under a worst-possible disturbance, we introduce a second-order, successive sweep algorithm for computing the zero sublevel sets of a popular reachability value functional. Under sufficient HJI partial differential equation regularity and continuity assumption throughout the state space, we show that with state feedback control under the worst-possible disturbance, we can compute the state set that are reachable within a prescribed verification time bound.

eess.SY↗