arXiv subjects

Soon-Jo Chung

Publications and source records attributed to Soon-Jo Chung.

At least 55 records · Page 3Linked to original sources

arXiv2023

Predictive Control of Linear Discrete-Time Markovian Jump Systems by Learning Recurrent Patterns

Incorporating pattern-learning for prediction (PLP) in many discrete-time or discrete-event systems allows for computation-efficient controller design by memorizing patterns to schedule control policies based on their future occurrences. In this paper, we demonstrate the effect of PLP by designing a controller architecture for a class of linear Markovian jump systems (MJS) where the aforementioned ``patterns'' correspond to finite-length sequences of modes. In our analysis of recurrent patterns, we use martingale theory to derive closed-form solutions to quantities pertaining to the occurrence of patterns: 1) the expected minimum occurrence time of any pattern from some predefined collection, 2) the probability of a pattern being the first to occur among the collection. Our method is applicable to real-world dynamics because we make two extensions to common assumptions in prior pattern-occurrence literature. First, the distribution of the mode process is unknown, and second, the true realization of the mode process is not observable. As demonstration, we consider fault-tolerant control of a dynamic topology-switching network, and empirically compare PLP to two controllers without PLP: a baseline based on the novel System Level Synthesis (SLS) approach and a topology-robust extension of the SLS baseline. We show that PLP is able to reject disturbances as effectively as the topology-robust controller at reduced computation time and control effort. We discuss several important tradeoffs, such as the size of the pattern collection and the system scale versus the accuracy of the mode predictions, which show how different PLP implementations affect stabilization and runtime performance.

eess.SY↗

arXiv2022

Unsupervised RGB-to-Thermal Domain Adaptation via Multi-Domain Attention Network

This work presents a new method for unsupervised thermal image classification and semantic segmentation by transferring knowledge from the RGB domain using a multi-domain attention network. Our method does not require any thermal annotations or co-registered RGB-thermal pairs, enabling robots to perform visual tasks at night and in adverse weather conditions without incurring additional costs of data labeling and registration. Current unsupervised domain adaptation methods look to align global images or features across domains. However, when the domain shift is significantly larger for cross-modal data, not all features can be transferred. We solve this problem by using a shared backbone network that promotes generalization, and domain-specific attention that reduces negative transfer by attending to domain-invariant and easily-transferable features. Our approach outperforms the state-of-the-art RGB-to-thermal adaptation method in classification benchmarks, and is successfully applied to thermal river scene segmentation using only synthetic RGB images. Our code is made publicly available at https://github.com/ganlumomo/thermal-uda-attention.

cs.CV↗

arXiv2022

Incremental Nonlinear Stability Analysis of Stochastic Systems Perturbed by Lévy Noise

We present a theoretical framework for characterizing incremental stability of nonlinear stochastic systems perturbed by compound Poisson shot noise and finite-measure Lévy noise. For each noise type, we compare trajectories of the perturbed system with distinct noise sample paths against trajectories of the nominal, unperturbed system. We show that for a finite number of jumps arising from the noise process, the mean-squared error between the trajectories exponentially converge towards a bounded error ball across a finite interval of time under practical boundedness assumptions. The convergence rate for shot noise systems is the same as the exponentially-stable nominal system, but with a tradeoff between the parameters of the shot noise process and the size of the error ball. The convergence rate and the error ball for the Lévy noise system are shown to be nearly direct sums of the respective quantities for the shot and white noise systems separately, a result which is analogous to the Lévy-Khintchine theorem. We demonstrate our results using several numerical case studies.

eess.SY↗

arXiv2022

Meta-Learning-Based Robust Adaptive Flight Control Under Uncertain Wind Conditions

Realtime model learning proves challenging for complex dynamical systems, such as drones flying in variable wind conditions. Machine learning technique such as deep neural networks have high representation power but is often too slow to update onboard. On the other hand, adaptive control relies on simple linear parameter models can update as fast as the feedback control loop. We propose an online composite adaptation method that treats outputs from a deep neural network as a set of basis functions capable of representing different wind conditions. To help with training, meta-learning techniques are used to optimize the network output useful for adaptation. We validate our approach by flying a drone in an open air wind tunnel under varying wind conditions and along challenging trajectories. We compare the result with other adaptive controller with different basis function sets and show improvement over tracking and prediction errors.

cs.RO↗

arXiv2022

Trajectory Optimization of Chance-Constrained Nonlinear Stochastic Systems for Motion Planning Under Uncertainty

We present gPC-SCP: Generalized Polynomial Chaos-based Sequential Convex Programming to compute a sub-optimal solution for a continuous-time chance-constrained stochastic nonlinear optimal control (SNOC) problem. The approach enables motion planning for robotic systems under uncertainty. The gPC-SCP method involves two steps. The first step is to derive a surrogate problem of \emph{deterministic} nonlinear optimal control (DNOC) with convex constraints by using gPC expansion and the distributionally-robust convex subset of the chance constraints. The second step is to solve the DNOC problem using sequential convex programming for trajectory generation and control. We prove that in the unconstrained case, the optimal value of the DNOC converges to that of SNOC asymptotically and that any feasible solution of the constrained DNOC is a feasible solution of the chance-constrained SNOC. We also present the predictor-corrector extension (gPC-SCP$^\mathrm{PC}$) for real-time motion trajectory generation in the presence of stochastic uncertainty. In the gPC-SCP$^\mathrm{PC}$ method, we first predict the uncertainty using the gPC method and then optimize the motion plan to accommodate the uncertainty. We empirically demonstrate the efficacy of the gPC-SCP and the gPC-SCP$^\mathrm{PC}$ methods for the following two test cases: 1) collision checking under uncertainty in actuation and physical parameters and 2) collision checking with stochastic obstacle model for 3DOF and 6DOF robotic systems. We validate the effectiveness of the gPC-SCP method on the 3DOF robotic spacecraft testbed.

cs.RO↗

arXiv2022

Competitive Control with Delayed Imperfect Information

This paper studies the impact of imperfect information in online control with adversarial disturbances. In particular, we consider both delayed state feedback and inexact predictions of future disturbances. We introduce a greedy, myopic policy that yields a constant competitive ratio against the offline optimal policy. We also analyze the fundamental limits of online control with limited information by showing that our competitive ratio bounds for the greedy, myopic policy in the adversarial setting match (up to lower-order terms) lower bounds in the stochastic setting.

math.OC↗

arXiv2021

Learning-based methods to model small body gravity fields for proximity operations: Safety and Robustness

Accurate gravity field models are essential for safe proximity operations around small bodies. State-of-the-art techniques use spherical harmonics or high-fidelity polyhedron shape models. Unfortunately, these techniques can become inaccurate near the surface of the small body or have high computational costs, especially for binary or heterogeneous small bodies. New learning-based techniques do not encode a predefined structure and are more versatile. In exchange for versatility, learning-based techniques can be less robust outside the training data domain. In deployment, the spacecraft trajectory is the primary source of dynamics data. Therefore, the training data domain should include spacecraft trajectories to accurately evaluate the learned model's safety and robustness. We have developed a novel method for learning-based gravity models that directly uses the spacecraft's past trajectories. We further introduce a method to evaluate the safety and robustness of learning-based techniques via comparing accuracy within and outside of the training domain. We demonstrate this safety and robustness method for two learning-based frameworks: Gaussian processes and neural networks. Along with the detailed analysis provided, we empirically establish the need for robustness verification of learned gravity models when used for proximity operations.

cs.RO↗

arXiv2021

Meta-Adaptive Nonlinear Control: Theory and Algorithms

We present an online multi-task learning approach for adaptive nonlinear control, which we call Online Meta-Adaptive Control (OMAC). The goal is to control a nonlinear system subject to adversarial disturbance and unknown $\textit{environment-dependent}$ nonlinear dynamics, under the assumption that the environment-dependent dynamics can be well captured with some shared representation. Our approach is motivated by robot control, where a robotic system encounters a sequence of new environmental conditions that it must quickly adapt to. A key emphasis is to integrate online representation learning with established methods from control theory, in order to arrive at a unified framework that yields both control-theoretic and learning-theoretic guarantees. We provide instantiations of our approach under varying conditions, leading to the first non-asymptotic end-to-end convergence guarantee for multi-task nonlinear control. OMAC can also be integrated with deep representation learning. Experiments show that OMAC significantly outperforms conventional adaptive control approaches which do not learn the shared representation, in inverted pendulum and 6-DoF drone control tasks under varying wind conditions.

cs.LG↗

arXiv2021

Learning-based Adaptive Control using Contraction Theory

Adaptive control is subject to stability and performance issues when a learned model is used to enhance its performance. This paper thus presents a deep learning-based adaptive control framework for nonlinear systems with multiplicatively-separable parametrization, called adaptive Neural Contraction Metric (aNCM). The aNCM approximates real-time optimization for computing a differential Lyapunov function and a corresponding stabilizing adaptive control law by using a Deep Neural Network (DNN). The use of DNNs permits real-time implementation of the control law and broad applicability to a variety of nonlinear systems with parametric and nonparametric uncertainties. We show using contraction theory that the aNCM ensures exponential boundedness of the distance between the target and controlled trajectories in the presence of parametric uncertainties of the model, learning errors caused by aNCM approximation, and external disturbances. Its superiority to the existing robust and adaptive control methods is demonstrated using a cart-pole balancing model.

cs.LG↗

arXiv2021

A Theoretical Overview of Neural Contraction Metrics for Learning-based Control with Guaranteed Stability

This paper presents a theoretical overview of a Neural Contraction Metric (NCM): a neural network model of an optimal contraction metric and corresponding differential Lyapunov function, the existence of which is a necessary and sufficient condition for incremental exponential stability of non-autonomous nonlinear system trajectories. Its innovation lies in providing formal robustness guarantees for learning-based control frameworks, utilizing contraction theory as an analytical tool to study the nonlinear stability of learned systems via convex optimization. In particular, we rigorously show in this paper that, by regarding modeling errors of the learning schemes as external disturbances, the NCM control is capable of obtaining an explicit bound on the distance between a time-varying target trajectory and perturbed solution trajectories, which exponentially decreases with time even under the presence of deterministic and stochastic perturbation. These useful features permit simultaneous synthesis of a contraction metric and associated control law by a neural network, thereby enabling real-time computable and probably robust learning-based control for general control-affine nonlinear systems.

cs.LG↗

arXiv2021

Learning-based Robust Motion Planning with Guaranteed Stability: A Contraction Theory Approach

This paper presents Learning-based Autonomous Guidance with RObustness and Stability guarantees (LAG-ROS), which provides machine learning-based nonlinear motion planners with formal robustness and stability guarantees, by designing a differential Lyapunov function using contraction theory. LAG-ROS utilizes a neural network to model a robust tracking controller independently of a target trajectory, for which we show that the Euclidean distance between the target and controlled trajectories is exponentially bounded linearly in the learning error, even under the existence of bounded external disturbances. We also present a convex optimization approach that minimizes the steady-state bound of the tracking error to construct the robust control law for neural network training. In numerical simulations, it is demonstrated that the proposed method indeed possesses superior properties of robustness and nonlinear stability resulting from contraction theory, whilst retaining the computational efficiency of existing learning-based motion planners.

cs.RO↗

arXiv2021

A Two-Part Controller Synthesis Approach for Nonlinear Stochastic Systems Perturbed by Lévy Noise Using Renewal Theory and HJB-Based Impulse Control

We are motivated by the lack of discussion surrounding methodological control design procedures for nonlinear shot and Lévy noise stochastic systems to propose a hierarchical controller synthesis method with two parts. The first part is a primitive pattern-learning component which recognizes specific state sequences and stores in memory the corresponding control action that needs to be taken when the sequence has occurred. The second part is a modulation control component which computes the optimal control action for a pattern when it has occurred for the first time. Throughout our presentation of both components, we provide a self-contained discussion of theoretical concepts from Poisson processes theory, renewal theory, and impulse control, all of which are necessary as background. We demonstrate application of this controller to the simplified, concrete case studies of fault-tolerance and vehicle congestion control.

eess.SY↗

arXiv2021

Neural-Swarm2: Planning and Control of Heterogeneous Multirotor Swarms using Learned Interactions

We present Neural-Swarm2, a learning-based method for motion planning and control that allows heterogeneous multirotors in a swarm to safely fly in close proximity. Such operation for drones is challenging due to complex aerodynamic interaction forces, such as downwash generated by nearby drones and ground effect. Conventional planning and control methods neglect capturing these interaction forces, resulting in sparse swarm configuration during flight. Our approach combines a physics-based nominal dynamics model with learned Deep Neural Networks (DNNs) with strong Lipschitz properties. We make use of two techniques to accurately predict the aerodynamic interactions between heterogeneous multirotors: i) spectral normalization for stability and generalization guarantees of unseen data and ii) heterogeneous deep sets for supporting any number of heterogeneous neighbors in a permutation-invariant manner without reducing expressiveness. The learned residual dynamics benefit both the proposed interaction-aware multi-robot motion planning and the nonlinear tracking control design because the learned interaction forces reduce the modelling errors. Experimental results demonstrate that Neural-Swarm2 is able to generalize to larger swarms beyond training cases and significantly outperforms a baseline nonlinear tracking controller with up to three times reduction in worst-case tracking errors.

cs.RO↗

arXiv2021

Neural Tree Expansion for Multi-Robot Planning in Non-Cooperative Environments

We present a self-improving, Neural Tree Expansion (NTE) method for multi-robot online planning in non-cooperative environments, where each robot attempts to maximize its cumulative reward while interacting with other self-interested robots. Our algorithm adapts the centralized, perfect information, discrete-action space method from AlphaZero to a decentralized, partial information, continuous action space setting for multi-robot applications. Our method has three interacting components: (i) a centralized, perfect-information "expert" Monte Carlo Tree Search (MCTS) with large computation resources that provides expert demonstrations, (ii) a decentralized, partial-information "learner" MCTS with small computation resources that runs in real-time and provides self-play examples, and (iii) policy & value neural networks that are trained with the expert demonstrations and bias both the expert and the learner tree growth. Our numerical experiments demonstrate Neural Tree Expansion's computational advantage by finding better solutions than a MCTS with 20 times more resources. The resulting policies are dynamically sophisticated, demonstrate coordination between robots, and play the Reach-Target-Avoid differential game significantly better than the state-of-the-art control-theoretic baseline for multi-robot, double-integrator systems. Our hardware experiments on an aerial swarm demonstrate the computational advantage of Neural Tree Expansion, enabling online planning at 20Hz with effective policies in complex scenarios.

cs.RO↗

arXiv2021

H-TD2: Hybrid Temporal Difference Learning for Adaptive Urban Taxi Dispatch

We present H-TD2: Hybrid Temporal Difference Learning for Taxi Dispatch, a model-free, adaptive decision-making algorithm to coordinate a large fleet of automated taxis in a dynamic urban environment to minimize expected customer waiting times. Our scalable algorithm exploits the natural transportation network company topology by switching between two behaviors: distributed temporal-difference learning computed locally at each taxi and infrequent centralized Bellman updates computed at the dispatch center. We derive a regret bound and design the trigger condition between the two behaviors to explicitly control the trade-off between computational complexity and the individual taxi policy's bounded sub-optimality; this advances the state of the art by enabling distributed operation with bounded-suboptimality. Additionally, unlike recent reinforcement learning dispatch methods, this policy estimation is adaptive and robust to out-of-training domain events. This result is enabled by a two-step modelling approach: the policy is learned on an agent-agnostic, cell-based Markov Decision Process and individual taxis are coordinated using the learned policy in a distributed game-theoretic task assignment. We validate our algorithm against a receding horizon control baseline in a Gridworld environment with a simulated customer dataset, where the proposed solution decreases average customer waiting time by 50% over a wide range of parameters. We also validate in a Chicago city environment with real customer requests from the Chicago taxi public dataset where the proposed solution decreases average customer waiting time by 26% over irregular customer distributions during a 2016 Major League Baseball World Series game.

eess.SY↗

arXiv2021

Rules of the Road: Safety and Liveness Guarantees for Autonomous Vehicles

The ability to guarantee safety and progress for all vehicles is vital to the success of the autonomous vehicle industry. We present a framework for designing autonomous vehicle behavior in a way that is safe and guarantees progress for all agents. In this paper, we first introduce a new game paradigm which we term the quasi-simultaneous game. We then define an agent protocol that all agents must use to make decisions in this quasi-simultaneous game setting. According to the protocol, agents first select an intended action using a behavioral profile. Then, the protocol defines whether an agent has precedence to take its intended action or must take a sub-optimal action. The protocol ensures safety under all traffic conditions and liveness for all agents under `sparse' traffic conditions. We provide proofs of correctness of the protocol and validate our results in simulation.

cs.MA↗

arXiv2021

Online Optimization with Memory and Competitive Control

This paper presents competitive algorithms for a novel class of online optimization problems with memory. We consider a setting where the learner seeks to minimize the sum of a hitting cost and a switching cost that depends on the previous $p$ decisions. This setting generalizes Smoothed Online Convex Optimization. The proposed approach, Optimistic Regularized Online Balanced Descent, achieves a constant, dimension-free competitive ratio. Further, we show a connection between online optimization with memory and online control with adversarial disturbances. This connection, in turn, leads to a new constant-competitive policy for a rich class of online control problems.

cs.LG↗

arXiv2021

The Power of Predictions in Online Control

We study the impact of predictions in online Linear Quadratic Regulator control with both stochastic and adversarial disturbances in the dynamics. In both settings, we characterize the optimal policy and derive tight bounds on the minimum cost and dynamic regret. Perhaps surprisingly, our analysis shows that the conventional greedy MPC approach is a near-optimal policy in both stochastic and adversarial settings. Specifically, for length-$T$ problems, MPC requires only $O(\log T)$ predictions to reach $O(1)$ dynamic regret, which matches (up to lower-order terms) our lower bound on the required prediction horizon for constant regret.

math.OC↗