C3D: Cascade Control with Change Point Detection and Deep Koopman Learning for Autonomous Surface Vehicles

In this paper, we discuss the development and deployment of a robust autonomous system capable of performing various tasks in the maritime domain under unknown dynamic conditions. We investigate a data-driven approach based on modular design for ease of transfer of autonomy across different maritime surface vessel platforms. The data-driven approach alleviates issues related to a priori identification of system models that may become deficient under evolving system behaviors or shifting, unanticipated, environmental influences. Our proposed learning-based platform comprises a deep Koopman system model and a change point detector that provides guidance on domain shifts prompting relearning under severe exogenous and endogenous perturbations. Motion control of the autonomous system is achieved via an optimal controller design. The Koopman linearized model naturally lends itself to a linear-quadratic regulator (LQR) control design. We propose the C3D control architecture Cascade Control with Change Point Detection and Deep Koopman Learning. The framework is verified in station keeping task on an ASV in both simulation and real experiments. The approach achieved at least 13.9 percent improvement in mean distance error in all test cases compared to the methods that do not consider system changes.

Online Change Points Detection for Linear Dynamical Systems with Finite Sample Guarantees

The problem of online change point detection is to detect abrupt changes in properties of time series, ideally as soon as possible after those changes occur. Existing work on online change point detection either assumes i.i.d data, focuses on asymptotic analysis, does not present theoretical guarantees on the trade-off between detection accuracy and detection delay, or is only suitable for detecting single change points. In this work, we study the online change point detection problem for linear dynamical systems with unknown dynamics, where the data exhibits temporal correlations and the system could have multiple change points. We develop a data-dependent threshold that can be used in our test that allows one to achieve a pre-specified upper bound on the probability of making a false alarm. We further provide a finite-sample-based bound for the probability of detecting a change point. Our bound demonstrates how parameters used in our algorithm affect the detection probability and delay, and provides guidance on the minimum required time between changes to guarantee detection.

Robust Online Covariance and Sparse Precision Estimation Under Arbitrary Data Corruption

Gaussian graphical models are widely used to represent correlations among entities but remain vulnerable to data corruption. In this work, we introduce a modified trimmed-inner-product algorithm to robustly estimate the covariance in an online scenario even in the presence of arbitrary and adversarial data attacks. At each time step, data points, drawn nominally independently and identically from a multivariate Gaussian distribution, arrive. However, a certain fraction of these points may have been arbitrarily corrupted. We propose an online algorithm to estimate the sparse inverse covariance (i.e., precision) matrix despite this corruption. We provide the error-bound and convergence properties of the estimates to the true precision matrix under our algorithms.

Learning Linearized Models from Nonlinear Systems with Finite Data

Identifying a linear system model from data has wide applications in control theory. The existing work on finite sample analysis for linear system identification typically uses data from a single system trajectory under i.i.d random inputs, and assumes that the underlying dynamics is truly linear. In contrast, we consider the problem of identifying a linearized model when the true underlying dynamics is nonlinear. We provide a multiple trajectories-based deterministic data acquisition algorithm followed by a regularized least squares algorithm, and provide a finite sample error bound on the learned linearized dynamics. Our error bound demonstrates a trade-off between the error due to nonlinearity and the error due to noise, and shows that one can learn the linearized dynamics with arbitrarily small error given sufficiently many samples. We validate our results through experiments, where we also show the potential insufficiency of linear system identification using a single trajectory with i.i.d random inputs, when nonlinearity does exist.

Deep Reinforcement Learning Based Framework for Mobile Energy Disseminator Dispatching to Charge On-the-Road Electric Vehicles

The exponential growth of electric vehicles (EVs) presents novel challenges in preserving battery health and in addressing the persistent problem of vehicle range anxiety. To address these concerns, wireless charging, particularly, Mobile Energy Disseminators (MEDs) have emerged as a promising solution. The MED is mounted behind a large vehicle and charges all participating EVs within a radius upstream of it. Unfortuantely, during such V2V charging, the MED and EVs inadvertently form platoons, thereby occupying multiple lanes and impairing overall corridor travel efficiency. In addition, constrained budgets for MED deployment necessitate the development of an effective dispatching strategy to determine optimal timing and locations for introducing the MEDs into traffic. This paper proposes a deep reinforcement learning (DRL) based methodology to develop a vehicle dispatching framework. In the first component of the framework, we develop a realistic reinforcement learning environment termed "ChargingEnv" which incorporates a reliable charging simulation system that accounts for common practical issues in wireless charging deployment, specifically, the charging panel misalignment. The second component, the Proximal-Policy Optimization (PPO) agent, is trained to control MED dispatching through continuous interactions with ChargingEnv. Numerical experiments were carried out to demonstrate the demonstrate the efficacy of the proposed MED deployment decision processor. The experiment results suggest that the proposed model can significantly enhance EV travel range while efficiently deploying a optimal number of MEDs. The proposed model is found to be not only practical in its applicability but also has promises of real-world effectiveness. The proposed model can help travelers to maximize EV range and help road agencies or private-sector vendors to manage the deployment of MEDs efficiently.

Multi-Robot Persistent Monitoring: Minimizing Latency and Number of Robots with Recharging Constraints

In this paper we study multi-robot path planning for persistent monitoring tasks. We consider the case where robots have a limited battery capacity with a discharge time $D$. We represent the areas to be monitored as the vertices of a weighted graph. For each vertex, there is a constraint on the maximum allowable time between robot visits, called the latency. The objective is to find the minimum number of robots that can satisfy these latency constraints while also ensuring that the robots periodically charge at a recharging depot. The decision version of this problem is known to be PSPACE-complete. We present a $O(\frac{\log D}{\log \log D}\log \rho)$ approximation algorithm for the problem where $\rho$ is the ratio of the maximum and the minimum latency constraints. We also present an orienteering based heuristic to solve the problem and show empirically that it typically provides higher quality solutions than the approximation algorithm. We extend our results to provide an algorithm for the problem of minimizing the maximum weighted latency given a fixed number of robots. We evaluate our algorithms on large problem instances in a patrolling scenario and in a wildfire monitoring application. We also compare the algorithms with an existing solver on benchmark instances.

On the Benefits of Leveraging Structural Information in Planning Over the Learned Model

Model-based Reinforcement Learning (RL) integrates learning and planning and has received increasing attention in recent years. However, learning the model can incur a significant cost (in terms of sample complexity), due to the need to obtain a sufficient number of samples for each state-action pair. In this paper, we investigate the benefits of leveraging structural information about the system in terms of reducing sample complexity. Specifically, we consider the setting where the transition probability matrix is a known function of a number of structural parameters, whose values are initially unknown. We then consider the problem of estimating those parameters based on the interactions with the environment. We characterize the difference between the Q estimates and the optimal Q value as a function of the number of samples. Our analysis shows that there can be a significant saving in sample complexity by leveraging structural information about the model. We illustrate the findings by considering several problems including controlling a queuing system with heterogeneous servers, and seeking an optimal path in a stochastic windy gridworld.

Learning Dynamical Systems by Leveraging Data from Similar Systems

We consider the problem of learning the dynamics of a linear system when one has access to data generated by an auxiliary system that shares similar (but not identical) dynamics, in addition to data from the true system. We use a weighted least squares approach, and provide a finite sample error bound of the learned model as a function of the number of samples and various system parameters from the two systems as well as the weight assigned to the auxiliary data. We show that the auxiliary data can help to reduce the intrinsic system identification error due to noise, at the price of adding a portion of error that is due to the differences between the two system models. We further provide a data-dependent bound that is computable when some prior knowledge about the systems is available. This bound can also be used to determine the weight that should be assigned to the auxiliary data during the model training stage.

Robust Online and Distributed Mean Estimation Under Adversarial Data Corruption

We study robust mean estimation in an online and distributed scenario in the presence of adversarial data attacks. At each time step, each agent in a network receives a potentially corrupted data point, where the data points were originally independent and identically distributed samples of a random variable. We propose online and distributed algorithms for all agents to asymptotically estimate the mean. We provide the error-bound and the convergence properties of the estimates to the true mean under our algorithms. Based on the network topology, we further evaluate each agent's trade-off in convergence rate between incorporating data from neighbors and learning with only local observations.

Finite Sample Guarantees for Distributed Online Parameter Estimation with Communication Costs

We study the problem of estimating an unknown parameter in a distributed and online manner. Existing work on distributed online learning typically either focuses on asymptotic analysis, or provides bounds on regret. However, these results may not directly translate into bounds on the error of the learned model after a finite number of time-steps. In this paper, we propose a distributed online estimation algorithm which enables each agent in a network to improve its estimation accuracy by communicating with neighbors. We provide non-asymptotic bounds on the estimation error, leveraging the statistical properties of the underlying model. Our analysis demonstrates a trade-off between estimation error and communication costs. Further, our analysis allows us to determine a time at which the communication can be stopped (due to the costs associated with communications), while meeting a desired estimation accuracy. We also provide a numerical example to validate our results.