Contracting Nonlinear Observers: Convex Optimization and Learning from Data

A new approach to design of nonlinear observers (state estimators) is proposed. The main idea is to (i) construct a convex set of dynamical systems which are contracting observers for a particular system, and (ii) optimize over this set for one which minimizes a bound on state-estimation error on a simulated noisy data set. We construct convex sets of continuous-time and discrete-time observers, as well as contracting sampled-data observers for continuous-time systems. Convex bounds for learning are constructed using Lagrangian relaxation. The utility of the proposed methods are verified using numerical simulation.Comment: conference submissio

Diffusion Maps Kalman Filter for a Class of Systems with Gradient Flows

In this paper, we propose a non-parametric method for state estimation of high-dimensional nonlinear stochastic dynamical systems, which evolve according to gradient flows with isotropic diffusion. We combine diffusion maps, a manifold learning technique, with a linear Kalman filter and with concepts from Koopman operator theory. More concretely, using diffusion maps, we construct data-driven virtual state coordinates, which linearize the system model. Based on these coordinates, we devise a data-driven framework for state estimation using the Kalman filter. We demonstrate the strengths of our method with respect to both parametric and non-parametric algorithms in three tracking problems. In particular, applying the approach to actual recordings of hippocampal neural activity in rodents directly yields a representation of the position of the animals. We show that the proposed method outperforms competing non-parametric algorithms in the examined stochastic problem formulations. Additionally, we obtain results comparable to classical parametric algorithms, which, in contrast to our method, are equipped with model knowledge.Comment: 15 pages, 12 figures, submitted to IEEE TS

Action representation in the mouse parieto-frontal network

The posterior parietal cortex (PPC) and frontal motor areas comprise a cortical network supporting goal-directed behaviour, with functions including sensorimotor transformations and decision making. In primates, this network links performed and observed actions via mirror neurons, which fire both when individuals perform an action and when they observe the same action performed by a conspecific. Mirror neurons are believed to be important for social learning, but it is not known whether mirror-like neurons occur in similar networks in other social species, such as rodents, or if they can be measured in such models using paradigms where observers passively view a demonstrator. Therefore, we imaged Ca2+ responses in PPC and secondary motor cortex (M2) while mice performed and observed pellet-reaching and wheel-running tasks, and found that cell populations in both areas robustly encoded several naturalistic behaviours. However, neural responses to the same set of observed actions were absent, although we verified that observer mice were attentive to performers and that PPC neurons responded reliably to visual cues. Statistical modelling also indicated that executed actions outperformed observed actions in predicting neural responses. These results raise the possibility that sensorimotor action recognition in rodents could take place outside of the parieto-frontal circuit, and underscore that detecting socially-driven neural coding depends critically on the species and behavioural paradigm used

New politics in German labour market policy? The implications of the recent Hartz reforms for the German welfare state

The twin predicaments of German labour market performance and welfare state performance triggered an ongoing debate on reforming the German model. Recently, this debate has yielded an outcome in the form of the so-called Hartz laws, a bundle of labour market policies aimed at the reduction of unemployment and the decrease of non-wage labour costs. The Hartz reforms have played a prominent role in the public discussion, but are they really a watershed as both optimists and pessimists claim? In this article we argue that the Hartz reform is one of the most ambitious German reform projects since World War II, and embed it in an international context. We discuss three views of policy reform: reform as a process of policy-learning, as a process of competitive realignment and as a process of reinforcing path dependence. We show which of the three paradigms accounts for what part of the political result. We find evidence for both policy diffusion and retrenchment, but these follow a traditional German pattern: reforms within institutions rather than of institutions. -- Die Probleme des deutschen Arbeitsmarktes und Sozialstaates als Ganzes haben eine anhaltende Debatte über die Reform des deutschen Wohlfahrtsstaatsmodells ausgelöst. Die Hartz-Reformen können als ein wesentliches Ergebnis dieser Debatte angesehen werden. Hartz hat mehr als jede andere Reform die öffentliche Diskussion der vergangenen zwei Jahre bestimmt. Aber sind die Reformergebnisse wirklich das, was Optimisten und Pessimisten von ihnen erwarten? In diesem Artikel argumentieren wir, dass die Hartz-Reformen tatsächlich eines der ehrgeizigsten Reformprojekte in Deutschland seit dem 2. Weltkrieg sind und beleuchten die Reformen dabei aus einer internationalen Perspektive. Als analytischen Bezugsrahmen diskutieren wir drei Sichtweisen von Politikreformen: Reformen als Policy-Lernen, Reformen als Anpassungsprozess im globalen Wettbewerb und Reformen als Prozess, der die Pfadabhängigkeit weiter stärkt. Wir zeigen, welches Paradigma welchen Teil der Reform erklären kann. Es lassen sich sowohl für das Policy-Lernen als auch den Rückbau des Sozialstaates Anhaltspunkte finden, allerdings folgen diese einem typisch deutschen Muster: eher Reformen innerhalb der Institutionen als die Reform der Institutionen selbst.

Learning Stable Koopman Models for Identification and Control of Dynamical Systems

Learning models of dynamical systems from data is a widely-studied problem in control theory and machine learning. One recent approach for modelling nonlinear systems considers the class of Koopman models, which embeds the nonlinear dynamics in a higher-dimensional linear subspace. Learning a Koopman embedding would allow for the analysis and control of nonlinear systems using tools from linear systems theory. Many recent methods have been proposed for data-driven learning of such Koopman embeddings, but most of these methods do not consider the stability of the Koopman model. Stability is an important and desirable property for models of dynamical systems. Unstable models tend to be non-robust to input perturbations and can produce unbounded outputs, which are both undesirable when the model is used for prediction and control. In addition, recent work has shown that stability guarantees may act as a regularizer for model fitting. As such, a natural direction would be to construct Koopman models with inherent stability guarantees. Two new classes of Koopman models are proposed that bridge the gap between Koopman-based methods and learning stable nonlinear models. The first model class is guaranteed to be stable, while the second is guaranteed to be stabilizable with an explicit stabilizing controller that renders the model stable in closed-loop. Furthermore, these models are unconstrained in their parameter sets, thereby enabling efficient optimization via gradient-based methods. Theoretical connections between the stability of Koopman models and forms of nonlinear stability such as contraction are established. To demonstrate the effect of the stability guarantees, the stable Koopman model is applied to a system identification problem, while the stabilizable model is applied to an imitation learning problem. Experimental results show empirically that the proposed models achieve better performance over prior methods without stability guarantees

International Conference on Dynamic Control and Optimization - DCO 2021: book of abstracts

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Computational Methods for Cognitive and Cooperative Robotics

In the last decades design methods in control engineering made substantial progress in the areas of robotics and computer animation. Nowadays these methods incorporate the newest developments in machine learning and artificial intelligence. But the problems of flexible and online-adaptive combinations of motor behaviors remain challenging for human-like animations and for humanoid robotics. In this context, biologically-motivated methods for the analysis and re-synthesis of human motor programs provide new insights in and models for the anticipatory motion synthesis. This thesis presents the author’s achievements in the areas of cognitive and developmental robotics, cooperative and humanoid robotics and intelligent and machine learning methods in computer graphics. The first part of the thesis in the chapter “Goal-directed Imitation for Robots” considers imitation learning in cognitive and developmental robotics. The work presented here details the author’s progress in the development of hierarchical motion recognition and planning inspired by recent discoveries of the functions of mirror-neuron cortical circuits in primates. The overall architecture is capable of ‘learning for imitation’ and ‘learning by imitation’. The complete system includes a low-level real-time capable path planning subsystem for obstacle avoidance during arm reaching. The learning-based path planning subsystem is universal for all types of anthropomorphic robot arms, and is capable of knowledge transfer at the level of individual motor acts. Next, the problems of learning and synthesis of motor synergies, the spatial and spatio-temporal combinations of motor features in sequential multi-action behavior, and the problems of task-related action transitions are considered in the second part of the thesis “Kinematic Motion Synthesis for Computer Graphics and Robotics”. In this part, a new approach of modeling complex full-body human actions by mixtures of time-shift invariant motor primitives in presented. The online-capable full-body motion generation architecture based on dynamic movement primitives driving the time-shift invariant motor synergies was implemented as an online-reactive adaptive motion synthesis for computer graphics and robotics applications. The last chapter of the thesis entitled “Contraction Theory and Self-organized Scenarios in Computer Graphics and Robotics” is dedicated to optimal control strategies in multi-agent scenarios of large crowds of agents expressing highly nonlinear behaviors. This last part presents new mathematical tools for stability analysis and synthesis of multi-agent cooperative scenarios.In den letzten Jahrzehnten hat die Forschung in den Bereichen der Steuerung und Regelung komplexer Systeme erhebliche Fortschritte gemacht, insbesondere in den Bereichen Robotik und Computeranimation. Die Entwicklung solcher Systeme verwendet heutzutage neueste Methoden und Entwicklungen im Bereich des maschinellen Lernens und der künstlichen Intelligenz. Die flexible und echtzeitfähige Kombination von motorischen Verhaltensweisen ist eine wesentliche Herausforderung für die Generierung menschenähnlicher Animationen und in der humanoiden Robotik. In diesem Zusammenhang liefern biologisch motivierte Methoden zur Analyse und Resynthese menschlicher motorischer Programme neue Erkenntnisse und Modelle für die antizipatorische Bewegungssynthese. Diese Dissertation präsentiert die Ergebnisse der Arbeiten des Autors im Gebiet der kognitiven und Entwicklungsrobotik, kooperativer und humanoider Robotersysteme sowie intelligenter und maschineller Lernmethoden in der Computergrafik. Der erste Teil der Dissertation im Kapitel “Zielgerichtete Nachahmung für Roboter” behandelt das Imitationslernen in der kognitiven und Entwicklungsrobotik. Die vorgestellten Arbeiten beschreiben neue Methoden für die hierarchische Bewegungserkennung und -planung, die durch Erkenntnisse zur Funktion der kortikalen Spiegelneuronen-Schaltkreise bei Primaten inspiriert wurden. Die entwickelte Architektur ist in der Lage, ‘durch Imitation zu lernen’ und ‘zu lernen zu imitieren’. Das komplette entwickelte System enthält ein echtzeitfähiges Pfadplanungssubsystem zur Hindernisvermeidung während der Durchführung von Armbewegungen. Das lernbasierte Pfadplanungssubsystem ist universell und für alle Arten von anthropomorphen Roboterarmen in der Lage, Wissen auf der Ebene einzelner motorischer Handlungen zu übertragen. Im zweiten Teil der Arbeit “Kinematische Bewegungssynthese für Computergrafik und Robotik” werden die Probleme des Lernens und der Synthese motorischer Synergien, d.h. von räumlichen und räumlich-zeitlichen Kombinationen motorischer Bewegungselemente bei Bewegungssequenzen und bei aufgabenbezogenen Handlungs übergängen behandelt. Es wird ein neuer Ansatz zur Modellierung komplexer menschlicher Ganzkörperaktionen durch Mischungen von zeitverschiebungsinvarianten Motorprimitiven vorgestellt. Zudem wurde ein online-fähiger Synthesealgorithmus für Ganzköperbewegungen entwickelt, der auf dynamischen Bewegungsprimitiven basiert, die wiederum auf der Basis der gelernten verschiebungsinvarianten Primitive konstruiert werden. Dieser Algorithmus wurde für verschiedene Probleme der Bewegungssynthese für die Computergrafik- und Roboteranwendungen implementiert. Das letzte Kapitel der Dissertation mit dem Titel “Kontraktionstheorie und selbstorganisierte Szenarien in der Computergrafik und Robotik” widmet sich optimalen Kontrollstrategien in Multi-Agenten-Szenarien, wobei die Agenten durch eine hochgradig nichtlineare Kinematik gekennzeichnet sind. Dieser letzte Teil präsentiert neue mathematische Werkzeuge für die Stabilitätsanalyse und Synthese von kooperativen Multi-Agenten-Szenarien