Warren E. Dixon

Hsi-Yuan Chen, Zachary I. Bell, Patryk Deptula et al.

Autonomous agents are often tasked with operating in an area where feedback is unavailable. Inspired by such applications, this paper develops a novel switched systems-based control method for uncertain nonlinear systems with temporary loss of state feedback. To compensate for intermittent feedback, an observer is used while state feedback is available to reduce the estimation error, and a predictor is utilized to propagate the estimates while state feedback is unavailable. Based on the resulting subsystems, maximum and minimum dwell time conditions are developed via a Lyapunov-based switched systems analysis to relax the constraint of maintaining constant feedback. Using the dwell time conditions, a switching trajectory is developed to enter and exit the feedback denied region in a manner that ensures the overall switched system remains stable. A scheme for designing a switching trajectory with a smooth transition function is provided. Simulation and experimental results are presented to demonstrate the performance of control design.

Omkar Sudhir Patil, Emily J. Griffis, Wanjiku A. Makumi et al.

Although deep neural network (DNN)-based controllers are popularly used to control uncertain nonlinear dynamic systems, most results use DNNs that are pretrained offline and the corresponding controller is implemented post-training. Recent advancements in adaptive control have developed controllers with Lyapunov-based update laws (i.e., control and update laws derived from a Lyapunov-based stability analysis) for updating the DNN weights online to ensure the system states track a desired trajectory. However, the update laws are based on the tracking error, and offer guarantees on only the tracking error convergence, without providing any guarantees on system identification. This paper provides the first result on simultaneous online system identification and trajectory tracking control of nonlinear systems using adaptive updates for all layers of the DNN. A combined Lyapunov-based stability analysis is provided, which guarantees that the tracking error, state-derivative estimation error, and DNN weight estimation errors are uniformly ultimately bounded. Under the persistence of excitation (PE) condition, the tracking and weight estimation errors are shown to exponentially converge to a neighborhood of the origin, where the rate of convergence and the size of this neighborhood depends on the gains and a factor quantifying PE, thus achieving system identification and enhanced trajectory tracking performance. As an outcome of the system identification, the DNN model can be propagated forward to predict and compensate for the uncertainty in dynamics under intermittent loss of state feedback. Comparative simulation results are provided on a two-link manipulator system and an unmanned underwater vehicle system with intermittent loss of state feedback, where the developed method yields significant performance improvement compared to baseline methods.

Omkar Sudhir Patil, Brandon C. Fallin, Cristian F. Nino et al.

Deep neural networks (DNNs) have emerged as a powerful tool with a growing body of literature exploring Lyapunov-based approaches for real-time system identification and control. These methods depend on establishing bounds for the second partial derivatives of DNNs with respect to their parameters, a requirement often assumed but rarely addressed explicitly. This paper provides rigorous mathematical formulations of polynomial bounds on both the first and second partial derivatives of DNNs with respect to their parameters. We present lemmas that characterize these bounds for fully-connected DNNs, while accommodating various classes of activation function including sigmoidal and ReLU-like functions. Our analysis yields closed-form expressions that enable precise stability guarantees for Lyapunov-based deep neural networks (Lb-DNNs). Furthermore, we extend our results to bound the higher-order terms in first-order Taylor approximations of DNNs, providing important tools for convergence analysis in gradient-based learning algorithms. The developed theoretical framework develops explicit, computable expressions, for previously assumed bounds, thereby strengthening the mathematical foundation of neural network applications in safety-critical control systems.

Yihui Mao, Tian Tan, Xuehui Shen et al.

Mapping is essential in robotics and autonomous systems because it provides the spatial foundation for path planning. Efficient mapping enables planning algorithms to generate reliable paths while ensuring safety and adapting in real time to complex environments. Fixed-resolution mapping methods often produce overly conservative obstacle representations that lead to suboptimal paths or planning failures in cluttered scenes. To address this issue, we introduce Parallel OctoMapping (POMP), an efficient OctoMap-based mapping technique that maximizes available free space and supports multi-threaded computation. To the best of our knowledge, POMP is the first method that, at a fixed occupancy-grid resolution, refines the representation of free space while preserving map fidelity and compatibility with existing search-based planners. It can therefore be integrated into existing planning pipelines, yielding higher pathfinding success rates and shorter path lengths, especially in cluttered environments, while substantially improving computational efficiency.

Yixuan Wang, Wenqian Xue, Warren E. Dixon

Generative models based on static scalar energy functions represent an emerging paradigm in which a single time independent potential drives sample generation through its gradient field, eliminating the need for time conditioning entirely. We unify the training and sampling phases of this paradigm, conventionally treated as separate procedures, within a single framework: density transport on the Wasserstein space, cast as a nonlinear control problem in which the Kullback Leibler (KL) divergence serves as a Lyapunov function. Training and sampling are then two instances of this same master dynamics, differing only in initial condition. Within this autonomous framework we develop two analytic results. First, since the Lyapunov certificate is asymptotic, we derive a finite step stopping criterion for Langevin sampling and prove that no Lyapunov certificate exists for the deterministic gradient flow on the same energy landscape. Second, the reformulation brings the toolkit of nonlinear control theory to bear on static scalar energy generative modeling, that is, we show that additive composition of trained scalar energies retains an explicit Gibbs invariant measure and inherits the closed-loop Lyapunov certificate. Beyond these immediate results, this reformulation bridges static scalar energy generative models with the full toolkit of nonlinear control theory, opening the door to barrier functions for constrained generation and contraction metrics for accelerated sampling. Experiments on synthetic distributions validate the theoretical predictions.

Saiedeh Akbari, Emily J. Griffis, Omkar Sudhir Patil et al.

Deep neural network (DNN)-based adaptive controllers can be used to compensate for unstructured uncertainties in nonlinear dynamic systems. However, DNNs are also very susceptible to overfitting and co-adaptation. Dropout regularization is an approach where nodes are randomly dropped during training to alleviate issues such as overfitting and co-adaptation. In this paper, a dropout DNN-based adaptive controller is developed. The developed dropout technique allows the deactivation of weights that are stochastically selected for each individual layer within the DNN. Simultaneously, a Lyapunov-based real-time weight adaptation law is introduced to update the weights of all layers of the DNN for online unsupervised learning. A non-smooth Lyapunov-based stability analysis is performed to ensure asymptotic convergence of the tracking error. Simulation results of the developed dropout DNN-based adaptive controller indicate a 38.32% improvement in the tracking error, a 53.67% improvement in the function approximation error, and 50.44% lower control effort when compared to a baseline adaptive DNN-based controller without dropout regularization.

Yixuan Wang, Omkar Sudhir Patil, Warren E. Dixon

We introduce Riemannian Lyapunov Optimizers (RLOs), a family of optimization algorithms that unifies classic optimizers within one geometric framework. Unlike heuristic improvements to existing optimizers, RLOs are systematically derived from a novel control-theoretic framework that reinterprets optimization as an extended state discrete-time controlled dynamical system on a Riemannian parameter manifold. Central to this framework is the identification of a Normally Attracting Invariant Manifold (NAIM), which organizes training dynamics into two distinct stages: rapid alignment of the speed state to a target graph, followed by controlled evolution within it. We formalize this by constructing a strict Lyapunov function that certifies convergence to a target manifold. This perspective yields a constructive ``optimizer generator" that not only recovers classic algorithms but enables the principled design of RLOs. We validate our theory via geometric diagnostics and demonstrate that grounding optimizer design in control theory yields state-of-the-art performance in large-scale benchmarks. Overall, RLOs bridge control theory and modern machine learning optimization, providing a unified language and a systematic toolkit for designing stable, effective optimizers.

Yixuan Wang, Dan P. Guralnik, Warren E. Dixon

Inferring the eventual goal of a mobile agent from noisy observations of its trajectory is a fundamental estimation problem. We initiate the study of such intent inference using a variant of a Rao-Blackwellized Particle Filter (RBPF), subject to the assumption that the agent's intent manifests through closed-loop behavior with a state-of-the-art provable practical stability property. Leveraging the assumed closed-form agent dynamics, the RBPF analytically marginalizes the linear-Gaussian substructure and updates particle weights only, improving sample efficiency over a standard particle filter. Two difference estimators are introduced: a Gaussian mixture model using the RBPF weights and a reduced version confining the mixture to the effective sample. We quantify how well the adversary can recover the agent's intent using information-theoretic leakage metrics and provide computable lower bounds on the Kullback-Leibler (KL) divergence between the true intent distribution and RBPF estimates via Gaussian-mixture KL bounds. We also provide a bound on the difference in performance between the two estimators, highlighting the fact that the reduced estimator performs almost as well as the complete one. Experiments illustrate fast and accurate intent recovery for compliant agents, motivating future work on designing intent-obfuscating controllers.

Rebecca G. Hart, Omkar Sudhir Patil, Zachary I. Bell et al.

Deep Neural Networks (DNNs) are increasingly used in control applications due to their powerful function approximation capabilities. However, many existing formulations focus primarily on tracking error convergence, often neglecting the challenge of identifying the system dynamics using the DNN. This paper presents the first result on simultaneous trajectory tracking and online system identification using a DNN-based controller, without requiring persistent excitation. Two new concurrent learning adaptation laws are constructed for the weights of all the layers of the DNN, achieving convergence of the DNN's parameter estimates to a neighborhood of their ideal values, provided the DNN's Jacobian satisfies a finite-time excitation condition. A Lyapunov-based stability analysis is conducted to ensure convergence of the tracking error, weight estimation errors, and observer errors to a neighborhood of the origin. Simulations performed on a range of systems and trajectories, with the same initial and operating conditions, demonstrated 40.5% to 73.6% improvement in function approximation performance compared to the baseline, while maintaining a similar tracking error and control effort. Simulations evaluating function approximation capabilities on data points outside of the trajectory resulted in 58.88% and 74.75% improvement in function approximation compared to the baseline.

Zhe Xu, Federico M. Zegers, Bo Wu et al.

This paper investigates the controller synthesis problem for a multi-agent system (MAS) with intermittent communication. We adopt a relay-explorer scheme, where a mobile relay agent with absolute position sensors switches among a set of explorers with relative position sensors to provide intermittent state information. We model the MAS as a switched system where the explorers' dynamics can be either fully-actuated or underactuated. The objective of the explorers is to reach approximate consensus to a predetermined goal region. To guarantee the stability of the switched system and the approximate consensus of the explorers, we derive maximum dwell-time conditions to constrain the length of time each explorer goes without state feedback (from the relay agent). Furthermore, the relay agent needs to satisfy practical constraints such as charging its battery and staying in specific regions of interest. Both the maximum dwell-time conditions and these practical constraints can be expressed by metric temporal logic (MTL) specifications. We iteratively compute the optimal control inputs for the relay agent to satisfy the MTL specifications, while guaranteeing stability and approximate consensus of the explorers. We implement the proposed method on a case study with the CoppeliaSim robot simulator.

Zhe Xu, Federico M. Zegers, Bo Wu et al.

This paper develops a controller synthesis approach for a multi-agent system (MAS) with intermittent communication. We adopt a leader-follower scheme, where a mobile leader with absolute position sensors switches among a set of followers without absolute position sensors to provide each follower with intermittent state information.We model the MAS as a switched system. The followers are to asymptotically reach a predetermined consensus state. To guarantee the stability of the switched system and the consensus of the followers, we derive maximum and minimal dwell-time conditions to constrain the intervals between consecutive time instants at which the leader should provide state information to the same follower. Furthermore, the leader needs to satisfy practical constraints such as charging its battery and staying in specific regions of interest. Both the maximum and minimum dwell-time conditions and these practical constraints can be expressed by metric temporal logic (MTL) specifications. We iteratively compute the optimal control inputs such that the leader satisfies the MTL specifications, while guaranteeing stability and consensus of the followers. We implement the proposed method on a case study with three mobile robots as the followers and one quadrotor as the leader.

Rushikesh Kamalapurkar, Lindsey Andrews, Patrick Walters et al.

This paper provides an approximate online adaptive solution to the infinite-horizon optimal tracking problem for control-affine continuous-time nonlinear systems with unknown drift dynamics. Model-based reinforcement learning is used to relax the persistence of excitation condition. Model-based reinforcement learning is implemented using a concurrent learning-based system identifier to simulate experience by evaluating the Bellman error over unexplored areas of the state space. Tracking of the desired trajectory and convergence of the developed policy to a neighborhood of the optimal policy are established via Lyapunov-based stability analysis. Simulation results demonstrate the effectiveness of the developed technique.

Zhen Kan, Justin Klotz, Eduardo L. Pasiliao et al.

A group of wheeled robots with nonholonomic constraints is considered to rendezvous at a common specified setpoint with a desired orientation while maintaining network connectivity and ensuring collision avoidance within the robots. Given communication and sensing constraints for each robot, only a subset of the robots are aware or informed of the global destination, and the remaining robots must move within the network connectivity constraint so that the informed robots can guide the group to the goal. The mobile robots are also required to avoid collisions with each other outside a neighborhood of the common rendezvous point. To achieve the rendezvous control objective, decentralized time-varying controllers are developed based on a navigation function framework to steer the robots to perform rendezvous while preserving network connectivity and ensuring collision avoidance. Only local sensing feedback, which includes position feedback from immediate neighbors and absolute orientation measurement, is used to navigate the robots and enables radio silence during navigation. Simulation results demonstrate the performance of the developed approach.

Patrick Walters, Warren E. Dixon

Online approximation of an optimal station keeping strategy for a fully actuated six degrees-of-freedom autonomous underwater vehicle is considered. The developed controller is an approximation of the solution to a two player zero-sum game where the controller is the minimizing player and an external disturbance is the maximizing player. The solution is approximated using a reinforcement learning-based actor-critic framework. The result guarantees uniformly ultimately bounded (UUB) convergence of the states and UUB convergence of the approximated policies to the optimal polices without the requirement of persistence of excitation.