Multirotor Ensemble Model Predictive Control I: Simulation Experiments

Nonlinear receding horizon model predictive control is a powerful approach to controlling nonlinear dynamical systems. However, typical approaches that use the Jacobian, adjoint, and forward-backward passes may lose fidelity and efficacy for highly nonlinear problems. Here, we develop an Ensemble Model Predictive Control (EMPC) approach wherein the forward model remains fully nonlinear, and an ensemble-represented Gaussian process performs the backward calculations to determine optimal gains for the initial time. EMPC admits black box, possible non-differentiable models, simulations are executable in parallel over long horizons, and control is uncertainty quantifying and applicable to stochastic settings. We construct the EMPC for terminal control and regulation problems and apply it to the control of a quadrotor in a simulated, identical-twin study. Results suggest that the easily implemented approach is promising and amenable to controlling autonomous robotic systems with added state/parameter estimation and parallel computing.

A Stochastic Compound Failure Model for Testing Resilience of Autonomous Fixed-Wing Aircraft I: Formulation and Simulation

This paper presents a simulation process to dynamically emulate the effects of certain adversarial flight conditions on fixed-wing, autonomous aircraft system actuators. We implement a PX4 Autopilot flight stack module that replaces the generated attitude control inputs with perturbed inputs to the plane's actuator mixer. The perturbed inputs rely on a Markov chain to model failure states that emulate adversarial (failing) actuator flight conditions. Simulated flight failures on a fixed-wing autonomous aircraft test the controller response to a stochastic failure sequence on a range of turning radii. Statistical measures between of the differences between unaffected and perturbed flight paths provides analyses, indicating that a well-tuned PID controller remains competitive in the cascading, compound, transient failure regime.

Learning Inter-Annual Flood Loss Risk Models From Historical Flood Insurance Claims and Extreme Rainfall Data

Flooding is one of the most disastrous natural hazards, responsible for substantial economic losses. A predictive model for flood-induced financial damages is useful for many applications such as climate change adaptation planning and insurance underwriting. This research assesses the predictive capability of regressors constructed on the National Flood Insurance Program (NFIP) dataset using neural networks (Conditional Generative Adversarial Networks), decision trees (Extreme Gradient Boosting), and kernel-based regressors (Gaussian Process). The assessment highlights the most informative predictors for regression. The distribution for claims amount inference is modeled with a Burr distribution permitting the introduction of a bias correction scheme and increasing the regressor's predictive capability. Aiming to study the interaction with physical variables, we incorporate Daymet rainfall estimation to NFIP as an additional predictor. A study on the coastal counties in the eight US South-West states resulted in an $R^2=0.807$. Further analysis of 11 counties with a significant number of claims in the NFIP dataset reveals that Extreme Gradient Boosting provides the best results, that bias correction significantly improves the similarity with the reference distribution, and that the rainfall predictor strengthens the regressor performance.

Downscaling Extreme Rainfall Using Physical-Statistical Generative Adversarial Learning

Modeling the risk of extreme weather events in a changing climate is essential for developing effective adaptation and mitigation strategies. Although the available low-resolution climate models capture different scenarios, accurate risk assessment for mitigation and adaption often demands detail that they typically cannot resolve. Here, we develop a dynamic data-driven downscaling (super-resolution) method that incorporates physics and statistics in a generative framework to learn the fine-scale spatial details of rainfall. Our method transforms coarse-resolution ($0.25^{\circ} \times 0.25^{\circ}$) climate model outputs into high-resolution ($0.01^{\circ} \times 0.01^{\circ}$) rainfall fields while efficaciously quantifying uncertainty. Results indicate that the downscaled rainfall fields closely match observed spatial fields and their risk distributions.

An Adaptive Digital Autopilot for Fixed-Wing Aircraft with Actuator Faults

This paper develops an adaptive digital autopilot for a fixed-wing aircraft and compares its performance with a fixed-gain autopilot. The adaptive digital autopilot is constructed by augmenting the autopilot architecture implemented in PX4 flight stack with adaptive digital control laws that are updated using the retrospective cost adaptive control algorithm. In order to investigate the performance of the adaptive digital autopilot, the default gains of the fixed-gain autopilot are scaled down to degrade its performance. This scenario provides a venue for determining the ability of the adaptive digital autopilot to compensate for the detuned fixed-gain autopilot. Next, the performance of the adaptive autopilot is examined under failure conditions by simulating a scenario where one of the control surfaces is assumed to be stuck at an unknown angular position. The adaptive digital autopilot is tested in simulation, and the resulting performance improvements are examined.

Learn Like The Pro: Norms from Theory to Size Neural Computation

The optimal design of neural networks is a critical problem in many applications. Here, we investigate how dynamical systems with polynomial nonlinearities can inform the design of neural systems that seek to emulate them. We propose a Learnability metric and its associated features to quantify the near-equilibrium behavior of learning dynamics. Equating the Learnability of neural systems with equivalent parameter estimation metric of the reference system establishes bounds on network structure. In this way, norms from theory provide a good first guess for neural structure, which may then further adapt with data. The proposed approach neither requires training nor training data. It reveals exact sizing for a class of neural networks with multiplicative nodes that mimic continuous- or discrete-time polynomial dynamics. It also provides relatively tight lower size bounds for classical feed-forward networks that is consistent with simulated assessments.

Informative Neural Ensemble Kalman Learning

In stochastic systems, informative approaches select key measurement or decision variables that maximize information gain to enhance the efficacy of model-related inferences. Neural Learning also embodies stochastic dynamics, but informative Learning is less developed. Here, we propose Informative Ensemble Kalman Learning, which replaces backpropagation with an adaptive Ensemble Kalman Filter to quantify uncertainty and enables maximizing information gain during Learning. After demonstrating Ensemble Kalman Learning's competitive performance on standard datasets, we apply the informative approach to neural structure learning. In particular, we show that when trained from the Lorenz-63 system's simulations, the efficaciously learned structure recovers the dynamical equations. To the best of our knowledge, Informative Ensemble Kalman Learning is new. Results suggest that this approach to optimized Learning is promising.

Machine Learning for Robust Identification of Complex Nonlinear Dynamical Systems: Applications to Earth Systems Modeling

Systems exhibiting nonlinear dynamics, including but not limited to chaos, are ubiquitous across Earth Sciences such as Meteorology, Hydrology, Climate and Ecology, as well as Biology such as neural and cardiac processes. However, System Identification remains a challenge. In climate and earth systems models, while governing equations follow from first principles and understanding of key processes has steadily improved, the largest uncertainties are often caused by parameterizations such as cloud physics, which in turn have witnessed limited improvements over the last several decades. Climate scientists have pointed to Machine Learning enhanced parameter estimation as a possible solution, with proof-of-concept methodological adaptations being examined on idealized systems. While climate science has been highlighted as a "Big Data" challenge owing to the volume and complexity of archived model-simulations and observations from remote and in-situ sensors, the parameter estimation process is often relatively a "small data" problem. A crucial question for data scientists in this context is the relevance of state-of-the-art data-driven approaches including those based on deep neural networks or kernel-based processes. Here we consider a chaotic system - two-level Lorenz-96 - used as a benchmark model in the climate science literature, adopt a methodology based on Gaussian Processes for parameter estimation and compare the gains in predictive understanding with a suite of Deep Learning and strawman Linear Regression methods. Our results show that adaptations of kernel-based Gaussian Processes can outperform other approaches under small data constraints along with uncertainty quantification; and needs to be considered as a viable approach in climate science and earth system modeling.

Adaptive Digital PID Control of a Quadcopter with Unknown Dynamics

This paper develops an adaptive autopilot for quadcopters with unknown dynamics. To do this, the PX4 autopilot architecture is modified so that the feedback and feedforward controllers are replaced by adaptive control laws based on retrospective cost adaptive control (RCAC). The present paper provides a numerical investigation of the performance of the adaptive autopilot on a quadcopter with unknown dynamics. In order to reflect the absence of prior modeling information, all of the adaptive digital controllers are initialized at zero gains. In addition, moment-of-inertia of the quadcopter is varied to test the robustness of the adaptive autopilot. In all test cases, the vehicle is commanded to follow a given trajectory, and the resulting performance is examined.

The Sloop System for Individual Animal Identification with Deep Learning

The MIT Sloop system indexes and retrieves photographs from databases of non-stationary animal population distributions. To do this, it adaptively represents and matches generic visual feature representations using sparse relevance feedback from experts and crowds. Here, we describe the Sloop system and its application, then compare its approach to a standard deep learning formulation. We then show that priming with amplitude and deformation features requires very shallow networks to produce superior recognition results. Results suggest that relevance feedback, which enables Sloop's high-recall performance may also be essential for deep learning approaches to individual identification to deliver comparable results.