Identification of LTV Dynamical Models with Smooth or Discontinuous Time Evolution by means of Convex Optimization

We establish a connection between trend filtering and system identification which results in a family of new identification methods for linear, time-varying (LTV) dynamical models based on convex optimization. We demonstrate how the design of the cost function promotes a model with either a continuous change in dynamics over time, or causes discontinuous changes in model coefficients occurring at a finite (sparse) set of time instances. We further discuss the introduction of priors on the model parameters for situations where excitation is insufficient for identification. The identification problems are cast as convex optimization problems and are applicable to, e.g., ARX models and state-space models with time-varying parameters. We illustrate usage of the methods in simulations of jump-linear systems, a nonlinear robot arm with non-smooth friction and stiff contacts as well as in model-based, trajectory centric reinforcement learning on a smooth nonlinear system

Machine Learning and System Identification for Estimation in Physical Systems

In this thesis, we draw inspiration from both classical system identification and modern machine learning in order to solve estimation problems for real-world, physical systems. The main approach to estimation and learning adopted is optimization based. Concepts such as regularization will be utilized for encoding of prior knowledge and basis-function expansions will be used to add nonlinear modeling power while keeping data requirements practical.The thesis covers a wide range of applications, many inspired by applications within robotics, but also extending outside this already wide field.Usage of the proposed methods and algorithms are in many cases illustrated in the real-world applications that motivated the research.Topics covered include dynamics modeling and estimation, model-based reinforcement learning, spectral estimation, friction modeling and state estimation and calibration in robotic machining.In the work on modeling and identification of dynamics, we develop regularization strategies that allow us to incorporate prior domain knowledge into flexible, overparameterized models. We make use of classical control theory to gain insight into training and regularization while using tools from modern deep learning. A particular focus of the work is to allow use of modern methods in scenarios where gathering data is associated with a high cost.In the robotics-inspired parts of the thesis, we develop methods that are practically motivated and make sure that they are implementable also outside the research setting. We demonstrate this by performing experiments in realistic settings and providing open-source implementations of all proposed methods and algorithms

Robust nonlinear control of vectored thrust aircraft

An interdisciplinary program in robust control for nonlinear systems with applications to a variety of engineering problems is outlined. Major emphasis will be placed on flight control, with both experimental and analytical studies. This program builds on recent new results in control theory for stability, stabilization, robust stability, robust performance, synthesis, and model reduction in a unified framework using Linear Fractional Transformations (LFT's), Linear Matrix Inequalities (LMI's), and the structured singular value micron. Most of these new advances have been accomplished by the Caltech controls group independently or in collaboration with researchers in other institutions. These recent results offer a new and remarkably unified framework for all aspects of robust control, but what is particularly important for this program is that they also have important implications for system identification and control of nonlinear systems. This combines well with Caltech's expertise in nonlinear control theory, both in geometric methods and methods for systems with constraints and saturations

PEBO-SLAM: Observer design for visual inertial SLAM with convergence guarantees

This paper introduces a new linear parameterization to the problem of visual inertial simultaneous localization and mapping (VI-SLAM) -- without any approximation -- for the case only using information from a single monocular camera and an inertial measurement unit. In this problem set, the system state evolves on the nonlinear manifold $SE(3)\times \mathbb{R}^{3n}$, on which we design dynamic extensions carefully to generate invariant foliations, such that the problem can be reformulated into online \emph{constant parameter} identification, then interestingly with linear regression models obtained. It demonstrates that VI-SLAM can be translated into a linear least squares problem, in the deterministic sense, \emph{globally} and \emph{exactly}. Based on this observation, we propose a novel SLAM observer, following the recently established parameter estimation-based observer (PEBO) methodology. A notable merit is that the proposed observer enjoys almost global asymptotic stability, requiring neither persistency of excitation nor uniform complete observability, which, however, are widely adopted in most existing works with provable stability but can hardly be assured in many practical scenarios

TS fuzzy approach for modeling, analysis and design of non-smooth dynamical systems

There has been growing interest in the past two decades in studying the physical model of dynamical systems that can be described by nonlinear, non-smooth differential equations, i.e. non-smooth dynamical systems. These systems exhibit more colourful and complex dynamics compared to their smooth counterparts; however, their qualitative analysis and design are not yet fully developed and still open to exploration. At the same time, Takagi-Sugeno (TS) fuzzy systems have been shown to have a great ability to represent a large class of nonlinear systems and approximate their inherent uncertainties. This thesis explores an area of TS fuzzy systems that have not been considered before; that is, modelling, stability analysis and design for non-smooth dynamical systems. TS fuzzy model structures capable of representing or approximating the essential dis- continuous dynamics of non-smooth systems are proposed in this thesis. It is shown that by incorporating discrete event systems, the proposed structure for TS fuzzy models, which we will call non-smooth TS fuzzy models, can accurately represent the smooth (or contin- uous) as well as non-smooth (or discontinuous) dynamics of different classes of electrical and mechanical non-smooth systems including (sliding and non-sliding) Filippov's systems and impacting systems. The different properties of the TS fuzzy modelling (or formalism) are discussed. It is highlighted that the TS fuzzy formalism, taking advantage of its simple structure, does not need a special platform for its implementation. Stability in its new notion of structural stability (stability of a periodic solution) is one of the most important issues in the qualitative analysis of non-smooth systems. An important part of this thesis is focused on addressing stability issues by extending non- smooth Lyapunov theory for verifying the stability of local orbits, which the non-smooth TS fuzzy models can contain. Stability conditions are proposed for Filippov-type and impacting systems and it is shown that by formulating the conditions as Linear Matrix inequalities (LMIs), the onset of non-smooth bifurcations or chaotic phenomena can be detected by solving a feasibility problem. A number of examples are given to validate the proposed approach. Stability robustness of non-smooth TS fuzzy systems in the presence of model uncertainties is discussed in terms of non-smoothness rather than traditional observer design. The LMI stabilization problem is employed as a building block for devising design strategies to suppress the unwanted chaotic behaviour in non-smooth TS fuzzy models. There have been a large number of control applications in which the overall closed-loop sys tem can be stabilized by switching between pre-designed sub-controllers. Inspired by this idea, the design part of this thesis concentrates on fuzzy-chaos control strategies for Filippov-type systems. These strategies approach the design problem by switching be- tween local state-feedback controllers such that the closed-loop TS fuzzy system of interest rapidly converges to the stable periodic solution of the system. All control strategies are also automated as a design problem recast on linear matrix inequality conditions to be solved by modern optimization techniques. Keywords: Takagi-Sugeno fuzzy systems, non-smooth Lyapunov theory, non-smooth dy- namical systems, piecewise-smooth dynamical systems, structural stability, discontinuity- induced bifurcation, chaos controllers, dc-dc converters, Filippov's system, impacting system, linear matrix inequalities.EThOS - Electronic Theses Online ServiceGBUnited Kingdo