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Fast and consistent learning of hidden markov models by incorporating non-consecutive correlations 37

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Fast and consistent learning of hidden markov models by inco...

37th International Conference on Machine Learning, ICML 2020

作者： Mattila, Robert Rojas, Cristian R. Moulines, Eric Krishnamurthy, Vikram Wahlberg, Bo Division of Decision and Control Systems School of Electrical Engineering and Computer Science KTH Royal Institute of Technology Stockholm Sweden Centre de Mathématiques Appliquées de Polytechnique Ecole Polytechnique Paris France HSE University Moscow Russia School of Electrical and Computer Engineering Cornell University IthacaNew York United States

ISBN: (纸本)9781713821120

Can the parameters of a hidden Markov model (HMM) be estimated from a single sweep through the observations - and additionally, without being trapped at a local optimum in the likelihood surface That is the premise of recent method of moments algorithms devised for HMMs. In these, correlations between consecutive pair-or tripletwise observations are empirically estimated and used to compute estimates of the HMM parameters. Albeit computationally very attractive, the main drawback is that by restricting to only loworder correlations in the data, information is being neglected which results in a loss of accuracy (compared to standard maximum likelihood schemes). In this paper, we propose extending these methods (both pair-and triplet-based) by also including non-consecutive correlations in a way which does not significantly increase the computational cost (which scales linearly with the number of additional lags included). We prove strong consistency of the new methods, and demonstrate an improved performance in numerical experiments on both synthetic and real-world financial timeseries datasets. © 2020 37th International Conference on Machine Learning, ICML 2020. All rights reserved.

关键词： Hidden Markov models

Compositional Synthesis of Signal Temporal Logic Tasks via Assume-Guarantee Contracts

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Compositional Synthesis of Signal Temporal Logic Tasks via A...

IEEE Conference on decision and control

作者： Siyuan Liu Adnane Saoud Pushpak Jagtap Dimos V. Dimarogonas Majid Zamani Department of Electrical and Computer Engineering Technical University of Munich Germany Computer Science Department LMU Munich Germany Laboratoire des Signaux et Systèmes CentraleSupélec Univ. Paris Saclay France Robert Bosch Center for Cyber-Physical Systems in Indian Institute of Science Bangalore India Division of Decision and Control Systems KTH Royal Institute of Technology Stockholm Sweden Computer Science Department University of Colorado Boulder USA

ISBN: (数字)9781665467612

ISBN: (纸本)9781665467629

In this paper, we focus on the problem of compositional synthesis of controllers enforcing signal temporal logic (STL) tasks over a class of continuous-time nonlinear interconnected systems. By leveraging the idea of funnel-based control, we show that a fragment of STL specifications can be formulated as assume-guarantee contracts. A new concept of contract satisfaction is then defined to establish our compositionality result, which allows us to guarantee the satisfaction of a global contract by the interconnected system when all subsystems satisfy their local contracts. Based on this compositional framework, we then design closed-form continuous-time feedback controllers to enforce local contracts over subsystems in a decentralized manner. Finally, we demonstrate the effectiveness of our results on a numerical example.

关键词： Interconnected systems Task analysis Adaptive control Contracts

Localizability with Range-Difference Measurements

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arXiv 2021年

作者： Wu, Junfeng Mu, Biqiang Yi, Xinlei Wei, Jieqiang Johansson, Karl Henrik The School of Data Science The Chinese University of Hong Kong Shenzhen China The College of Control Science and Engineering The State Key Laboratory of Industrial Control Technology Zhejiang University China The Key Laboratory of Systems and Control Institute of Systems Science Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China The Division of Decision and Control Systems School of Electrical Engineering and Computer Science KTH Royal Institute of Technology Sweden Ericsson Torshamnsgatan 21 Stockholm16440 Sweden

The physical position is crucial in location-aware services or protocols based on geographic information, where localization is performed given a set of sensor measurements for acquiring the position of an object with respect to a certain coordinate system. In this paper, we revisit the long-standing localization methods for locating a radiating source from range-difference measurements, or equivalently, time-difference-of-arrival measurements from the perspective of least squares (LS). In particular, we focus on the spherical LS error model, where the error function is defined as the difference between the squared true distance from a signal receiver (sensor) to the source and its squared measured value, and the resulting spherical LS estimation problem. This problem has been known to be challenging due to the non-convex nature of the hyperbolic measurement model. First of all, we prove that the existence of least-square solutions is universal and that solutions are bounded under some assumption on the geometry of the sensor placement. Then a necessary and sufficient condition is presented for the solution characterization based on the method of Lagrange multipliers. Next, we derive a characterization for the uniqueness of the solutions incorporating a second-order optimality condition. The solution structures for some special cases are also established, contributing to insights on the effects of the Lagrangian multipliers on global solutions. These findings establish a comprehensive understanding of the localizability with range-difference measurements, which are also illustrated with numerical examples. Copyright © 2021, The Authors. All rights reserved.

关键词： Time difference of arrival

Robust Data-Driven Predictive control using Reachability Analysis

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arXiv 2021年

作者： Alanwar, Amr Stürz, Yvonne Johansson, Karl Henrik Computer Science & Electrical Engineering Department Jacobs University Bremen Germany Division of Decision and Control Systems KTH Royal Institute of Technology Sweden Model Predictive Control Laboratory University of California Berkeley United States

We present a robust data-driven control scheme for an unknown linear system model with bounded process and measurement noise. Instead of depending on a system model in traditional predictive control, a controller utilizing data-driven reachable regions is proposed. The data-driven reachable regions are based on a matrix zonotope recursion and are computed based on only noisy input-output data of a trajectory of the system. We assume that measurement and process noise are contained in bounded sets. While we assume knowledge of these bounds, no knowledge about the statistical properties of the noise is assumed. In the noise-free case, we prove that the presented purely data-driven control scheme results in an equivalent closed-loop behavior to a nominal model predictive control scheme. In the case of measurement and process noise, our proposed scheme guarantees robust constraint satisfaction, which is essential in safety-critical applications. Numerical experiments show the effectiveness of the proposed data-driven controller in comparison to model-based control schemes. Copyright © 2021, The Authors. All rights reserved.

关键词： controllers

State Estimation for a Class of Linear systems with Quadratic Output ⁎ ⁎

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IFAC-PapersOnLine 2021年第9期54卷 261-266页

作者： Dionysios Theodosis Soulaimane Berkane Dimos V. Dimarogonas Dynamic Systems and Simulation Laboratory School of Production Engineering and Management Technical University of Crete Greece Département d’informatique et d’ingénierie Université du Québec en Outaouis Gatineau Québec Canada Division of Decision and Control Systems School of Electrical Engineering and Computer Science KTH Royal Institute of Technology Sweden

This paper deals with the problem of state estimation for a class of linear time-invariant systems with quadratic output measurements. An immersion-type approach is presented that transforms the system into a state-affine system by adding a finite number of states to the original system. Under suitable persistence of excitation conditions on the input and its higher derivatives, global state estimation is exhibited by means of a Kalman-type observer. A numerical example is provided to illustrate the applicability of the proposed observer design for the problem of position and velocity estimation for a vehicle navigating in the n— dimensional Euclidean space using a single position range measurement.

关键词： Observers observability state estimation linear system quadratic output

Data-driven distributed mitigation strategies and analysis of mutating epidemic processes

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arXiv 2020年

作者： Paré, Philip E. Gracy, Sebin Sandberg, Henrik Johansson, Karl Henrik Division of Decision and Control Systems School of Electrical Engineering and Computer Science KTH Royal Institute of Technology Stockholm Sweden

In this paper we study a discrete-time SIS (susceptible-infected-susceptible) model, where the infection and healing parameters and the underlying network may change over time. We provide conditions for the model to be well-defined and study its stability. For systems with homogeneous infection rates over symmetric graphs, we provide a sufficient condition for global exponential stability (GES) of the healthy state, that is, where the virus is eradicated. For systems with heterogeneous virus spread over directed graphs, provided that the variation is not too fast, a sufficient condition for GES of the healthy state is established. Appealing to the first stability result, we present two data-driven mitigation strategies that set the healing parameters in a centralized and a distributed manner, respectively, in order to drive the system to the healthy state. Copyright © 2020, The Authors. All rights reserved.

关键词： Directed graphs

Toward Tractable Global Solutions to Bayesian Point Estimation Problems via Sparse Sum-of-Squares Relaxations

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Toward Tractable Global Solutions to Bayesian Point Estimati...

American control Conference

作者： Diogo Rodrigues Mohamed R. Abdalmoaty Hakan Hjalmarsson Division of Decision and Control Systems School of Electrical Engineering and Computer Science KTH Royal Institute of Technology Stockholm Sweden

ISBN: (数字)9781538682661

ISBN: (纸本)9781538682678

Bayesian point estimation is commonly used for system identification owing to its good properties for small sample sizes. Although this type of estimator is usually nonparametric, Bayes estimates can also be obtained for rational parametric models, which is often of interest. However, as in maximum-likelihood methods, the Bayes estimate is typically computed via local numerical optimization that requires good initialization and cannot guarantee global optimality. In this contribution, we propose a computationally tractable method that computes the Bayesian parameter estimates with posterior certification of global optimality via sum-of-squares polynomials and sparse semidefinite relaxations. It is shown that the method is applicable to certain discrete-time linear models, which takes advantage of the rational structure of these models and the sparsity in the Bayesian parameter estimation problem. The method is illustrated on a simulation model of a resonant system that is difficult to handle when the sample size is small.

关键词： Bayesian inference Sample Size Simulation models Bayes System identification optimality

How to Protect Your Privacy? A Framework for Counter-Adversarial decision Making

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arXiv 2020年

作者： Lourenço, Inês Mattila, Robert Rojas, Cristian R. Wahlberg, Bo Division of Decision and Control Systems School of Electrical Engineering and Computer Science KTH Royal Institute of Technology Stockholm Sweden

We consider a counter-adversarial sequential decision-making problem where an agent computes its private belief (posterior distribution) of the current state of the world, by filtering private information. According to its private belief, the agent performs an action, which is observed by an adversarial agent. We have recently shown how the adversarial agent can reconstruct the private belief of the decision-making agent via inverse optimization. The main contribution of this paper is a method to obfuscate the private belief of the agent from the adversary, by performing a suboptimal action. The proposed method optimizes the trade-off between obfuscating the private belief and limiting the increase in cost accrued due to taking a suboptimal action. We propose a probabilistic relaxation to obtain a linear optimization problem for solving the trade-off. In numerical examples, we show that the proposed methods enable the agent to obfuscate its private belief without compromising its cost budget. Copyright © 2020, The Authors. All rights reserved.

关键词： decision making

Actuator Security Index for Structured systems

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arXiv 2020年

作者： Gracy, Sebin Milošević, Jezdimir Sandberg, Henrik Division of Decision and Control Systems School of Electrical Engineering and Computer Science KTH Royal Institute of Technology Stockholm Sweden

Given a network with the set of vulnerable actuators (and sensors), the security index of an actuator equals the minimum number of sensors and actuators that needs to be compromised so as to conduct a perfectly undetectable attack using the said actuator. This paper deals with the problem of computing actuator security indices for discrete-time LTI network systems. Firstly, we show that, under a structured systems framework, the actuator security index is generic. Thereafter, we provide graph-theoretic conditions for computing the structural actuator security index. The said conditions are in terms of existence of linkings on appropriately-defined directed (sub)graphs. Based on these conditions, we present an algorithm for computing the structural index. Copyright © 2020, The Authors. All rights reserved.

关键词： Actuators