This paper presents an approach to trajectory-centric learning control based on contraction metrics and disturbance estimation for nonlinear systems subject to matched uncertainties. The proposed approach allows for the use of deep neural networks to learn uncertain dynamics while still providing guarantees of transient tracking performance throughout the learning phase. Within the proposed approach, a disturbance estimation law is adopted to estimate the pointwise value of the uncertainty, with pre-computable estimation error bounds (EEBs). The learned dynamics, the estimated disturbances, and the EEBs are then incorporated in a robust Riemannian energy condition to compute the control law that guarantees exponential convergence of actual trajectories to desired ones throughout the learning phase, even when the learned model is poor. On the other hand, with improved accuracy, the learned model can be incorporated into a high-level planner to plan better trajectories with improved performance, e.g., lower energy consumption and shorter travel time. The proposed framework is validated on a planar quadrotor navigation example.
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Search engines and recommendation systems attempt to continually improve the quality of the experience they afford to their users. Refining the ranker that produces the lists displayed in response to user requests is an important component of this process. A common practice is for the service providers to make changes (e.g. new ranking features, different ranking models) and A/B test them on a fraction of their users to establish the value of the change. An alternative approach estimates the effectiveness of the proposed changes offline, utilising previously collected clickthrough data on the old ranker to posit what the user behaviour on ranked lists produced by the new ranker would have been. A majority of offline evaluation approaches invoke the well studied inverse propensity weighting to adjust for biases inherent in logged data. In this paper, we propose the use of parametric estimates for these propensities. Specifically, by leveraging well known learning-to-rank methods as subroutines, we show how accurate offline evaluation can be achieved when the new rankings to be evaluated differ from the logged ones.
The ensemble Kalman filter (EnKF) is a Monte Carlo approximation of the Kalman filter for high dimensional linear Gaussian state space models. EnKF methods have also been developed for parameter inference of static Bayesian models with a Gaussian likelihood, in a way that is analogous to likelihood tempering sequential Monte Carlo (SMC). These methods are commonly referred to as ensemble Kalman inversion (EKI). Unlike SMC, the inference from EKI is only asymptotically unbiased if the likelihood is linear Gaussian and the priors are Gaussian. However, EKI is significantly faster to run. Currently, a large limitation of EKI methods is that the covariance of the measurement error is assumed to be fully known. We develop a new method, which we call component-wise iterative ensemble Kalman inversion (CW-IEKI), that allows elements of the covariance matrix to be inferred alongside the model parameters at negligible extra cost. This novel method is compared to SMC on three different application examples: a model of nitrogen mineralisation in soil that is based on the Agricultural Production Systems Simulator (APSIM), a model predicting seagrass decline due to stress from water temperature and light, and a model predicting coral calcification rates. On all of these examples, we find that CW-IEKI has relatively similar predictive performance to SMC, albeit with greater uncertainty, and it has a significantly faster run time.
Due to the importance of the lower bounding distances and the attractiveness of symbolic representations, the family of symbolic aggregate approximations (SAX) has been used extensively for encoding time series data. However, typical SAX-based methods rely on two restrictive assumptions; the Gaussian distribution and equiprobable symbols. This paper proposes two novel data-driven SAX-based symbolic representations, distinguished by their discretization steps. The first representation, oriented for general data compaction and indexing scenarios, is based on the combination of kernel density estimation and Lloyd-Max quantization to minimize the information loss and mean squared error in the discretization step. The second method, oriented for high-level mining tasks, employs the Mean-Shift clustering method and is shown to enhance anomaly detection in the lower-dimensional space. Besides, we verify on a theoretical basis a previously observed phenomenon of the intrinsic process that results in a lower than the expected variance of the intermediate piecewise aggregate approximation. This phenomenon causes an additional information loss but can be avoided with a simple modification. The proposed representations possess all the attractive properties of the conventional SAX method. Furthermore, experimental evaluation on real-world datasets demonstrates their superiority compared to the traditional SAX and an alternative data-driven SAX variant.
Quasi-SMC based on MPC for a constrained continuous-time nonlinear system with external disturbances
In this article, a quasi-sliding mode control (QSMC) based on MPC is proposed for the constrained continuous-time nonlinear system with external disturbances. The MPC problem is formulated relating to the design of QSMC, to generate the control input, which can imitate the control process of QSMC and guarantee the satisfaction of state and input constraints. Meanwhile, the cost function of MPC problem is reconstructed, in which the QSMC based on MPC can show better convergence rate by tuning the weight parameters. Finally, a simulation case is provided to demonstate the effectiveness of the proposed approach.
Social robots are expected to be a human labor support technology, and one application of them is an advertising medium in public spaces. When social robots provide information, such as recommended shops, adaptive communication according to the user's state is desired. User engagement, which is also defined as the level of interest in the robot, is likely to play an important role in adaptive communication. Therefore, in this paper, we propose a new framework to estimate user engagement. The proposed method focuses on four unsolved open problems: multi-party interactions, process of state change in engagement, difficulty in annotating engagement, and interaction dataset in the real world. The accuracy of the proposed method for estimating engagement was evaluated using interaction duration. The results show that the interaction duration can be accurately estimated by considering the influence of the behaviors of other people; this also implies that the proposed model accurately estimates the level of engagement during interaction with the robot.
The ability to accurately predict human behavior is central to the safety and efficiency of robot autonomy in interactive settings. Unfortunately, robots often lack access to key information on which these predictions may hinge, such as people's goals, attention, and willingness to cooperate. Dual control theory addresses this challenge by treating unknown parameters of a predictive model as stochastic hidden states and inferring their values at runtime using information gathered during system operation. While able to optimally and automatically trade off exploration and exploitation, dual control is computationally intractable for general interactive motion planning, mainly due to the fundamental coupling between robot trajectory optimization and human intent inference. In this paper, we present a novel algorithmic approach to enable active uncertainty reduction for interactive motion planning based on the implicit dual control paradigm. Our approach relies on sampling-based approximation of stochastic dynamic programming, leading to a model predictive control problem that can be readily solved by real-time gradient-based optimization methods. The resulting policy is shown to preserve the dual control effect for a broad class of predictive human models with both continuous and categorical uncertainty. The efficacy of our approach is demonstrated with simulated driving examples.
In this paper we propose a solution strategy for the Cahn-Larch\'e equations, which is a model for linearized elasticity in a medium with two elastic phases that evolve subject to a Ginzburg-Landau type energy functional. The system can be seen as a combination of the Cahn-Hilliard regularized interface equation and linearized elasticity, and is non-linearly coupled, has a fourth order term that comes from the Cahn-Hilliard subsystem, and is non-convex and nonlinear in both the phase-field and displacement variables. We propose a novel semi-implicit discretization in time that uses a standard convex-concave splitting method of the nonlinear double-well potential, as well as special treatment to the elastic energy. We show that the resulting discrete system is equivalent to a convex minimization problem, and propose and prove the convergence of alternating minimization applied to it. Finally, we present numerical experiments that show the robustness and effectiveness of both alternating minimization and the monolithic Newton method applied to the newly proposed discrete system of equations. We compare it to a system of equations that has been discretized with a standard convex-concave splitting of the double-well potential, and implicit evaluations of the elasticity contributions and show that the newly proposed discrete system is better conditioned for linearization techniques.
Biometrics on mobile devices has attracted a lot of attention in recent years as it is considered a user-friendly authentication method. This interest has also been motivated by the success of Deep Learning (DL). Architectures based on Convolutional Neural Networks (CNNs) and Recurrent Neural Networks (RNNs) have been established to be convenient for the task, improving the performance and robustness in comparison to traditional machine learning techniques. However, some aspects must still be revisited and improved. To the best of our knowledge, this is the first article that intends to explore and propose novel gait biometric recognition systems based on Transformers, which currently obtain state-of-the-art performance in many applications. Several state-of-the-art architectures (Vanilla, Informer, Autoformer, Block-Recurrent Transformer, and THAT) are considered in the experimental framework. In addition, new configurations of the Transformers are proposed to further increase the performance. Experiments are carried out using the two popular public databases whuGAIT and OU-ISIR. The results achieved prove the high ability of the proposed Transformer, outperforming state-of-the-art CNN and RNN architectures.
Trajectory Distribution Control for Model Predictive Path Integral Control using Covariance Steering
This paper presents a novel control approach for autonomous systems operating under uncertainty. We combine Model Predictive Path Integral (MPPI) control with Covariance Steering (CS) theory to obtain a robust controller for general nonlinear systems. The proposed Covariance-Controlled Model Predictive Path Integral (CC-MPPI) controller addresses the performance degradation observed in some MPPI implementations owing to unexpected disturbances and uncertainties. Namely, in cases where the environment changes too fast or the simulated dynamics during the MPPI rollouts do not capture the noise and uncertainty in the actual dynamics, the baseline MPPI implementation may lead to divergence. The proposed CC-MPPI controller avoids divergence by controlling the dispersion of the rollout trajectories at the end of the prediction horizon. Furthermore, the CC-MPPI has adjustable trajectory sampling distributions that can be changed according to the environment to achieve efficient sampling. Numerical examples using a ground vehicle navigating in challenging environments demonstrate the proposed approach.
Radiogenomics is an emerging field in cancer research that combines medical imaging data with genomic data to predict patients clinical outcomes. In this paper, we propose a multivariate sparse group lasso joint model to integrate imaging and genomic data for building prediction models. Specifically, we jointly consider two models, one regresses imaging features on genomic features, and the other regresses patients clinical outcomes on genomic features. The regularization penalties through sparse group lasso allow incorporation of intrinsic group information, e.g. biological pathway and imaging category, to select both important intrinsic groups and important features within a group. To integrate information from the two models, in each model, we introduce a weight in the penalty term of each individual genomic feature, where the weight is inversely correlated with the model coefficient of that feature in the other model. This weight allows a feature to have a higher chance of selection by one model if it is selected by the other model. Our model is applicable to both continuous and time to event outcomes. It also allows the use of two separate datasets to fit the two models, addressing a practical challenge that many genomic datasets do not have imaging data available. Simulations and real data analyses demonstrate that our method outperforms existing methods in the literature.
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