Forward Stochastic Reachability Analysis for Uncontrolled Linear Systems using Fourier Transforms

We propose a scalable method for forward stochastic reachability analysis for uncontrolled linear systems with affine disturbance. Our method uses Fourier transforms to efficiently compute the forward stochastic reach probability measure (density) and the forward stochastic reach set. This method is applicable to systems with bounded or unbounded disturbance sets. We also examine the convexity properties of the forward stochastic reach set and its probability density. Motivated by the problem of a robot attempting to capture a stochastically moving, non-adversarial target, we demonstrate our method on two simple examples. Where traditional approaches provide approximations, our method provides exact analytical expressions for the densities and probability of capture.Comment: V3: HSCC 2017 (camera-ready copy), DOI updated, minor changes | V2: Review comments included | V1: 10 pages, 12 figure

The Chrono-geometrical Structure of Special and General Relativity: a Re-Visitation of Canonical Geometrodynamics

A modern re-visitation of the consequences of the lack of an intrinsic notion of instantaneous 3-space in relativistic theories leads to a reformulation of their kinematical basis emphasizing the role of non-inertial frames centered on an arbitrary accelerated observer. In special relativity the exigence of predictability implies the adoption of the 3+1 point of view, which leads to a well posed initial value problem for field equations in a framework where the change of the convention of synchronization of distant clocks is realized by means of a gauge transformation. This point of view is also at the heart of the canonical approach to metric and tetrad gravity in globally hyperbolic asymptotically flat space-times, where the use of Shanmugadhasan canonical transformations allows the separation of the physical degrees of freedom of the gravitational field (the tidal effects) from the arbitrary gauge variables. Since a global vision of the equivalence principle implies that only global non-inertial frames can exist in general relativity, the gauge variables are naturally interpreted as generalized relativistic inertial effects, which have to be fixed to get a deterministic evolution in a given non-inertial frame. As a consequence, in each Einstein's space-time in this class the whole chrono-geometrical structure, including also the clock synchronization convention, is dynamically determined and a new approach to the Hole Argument leads to the conclusion that "gravitational field" and "space-time" are two faces of the same entity. This view allows to get a classical scenario for the unification of the four interactions in a scheme suited to the description of the solar system or our galaxy with a deperametrization to special relativity and the subsequent possibility to take the non-relativistic limit.Comment: 33 pages, Lectures given at the 42nd Karpacz Winter School of Theoretical Physics, "Current Mathematical Topics in Gravitation and Cosmology", Ladek, Poland, 6-11 February 200

Analytic Metaphysics versus Naturalized Metaphysics: The Relevance of Applied Ontology

The relevance of analytic metaphysics has come under criticism: Ladyman & Ross, for instance, have suggested do discontinue the field. French & McKenzie have argued in defense of analytic metaphysics that it develops tools that could turn out to be useful for philosophy of physics. In this article, we show first that this heuristic defense of metaphysics can be extended to the scientific field of applied ontology, which uses constructs from analytic metaphysics. Second, we elaborate on a parallel by French & McKenzie between mathematics and metaphysics to show that the whole field of analytic metaphysics, being useful not only for philosophy but also for science, should continue to exist as a largely autonomous field

On the Relative Degree of Simultaneously Stabilizing Controllers

In this brief paper 1 we present new necessary and sufficient conditions on the controller for the existence of a single controller to stabilize a set of n SISO plants: P1; P2; :::; Pn. As is well known this is equivalent to the existence of a single stable controller that stabilizes n - 1 plants (strong stabilization). It was shown in (Blondel, 1994) that the simultaneous stabilization problem is transcendental and cannot be solved using algebraic functions. Our only hope in approaching the general solution to the simultaneous stabilization problem using algebraic functions is either to enlarge the class of controllers for which sufficient conditions exist, or to restrict the class of controllers from which a controller must exist. This paper restricts the search for existence of simultaneously stabilizing controllers to the class of exactly proper controllers

Survey of the robust control of robots

Browse Conference Publications \u3e American Control Conference, ... Page Help Survey of the Robust Control of Robots This paper appears in: American Control Conference, 1990 Date of Conference: 23-25 May 1990 Author(s): Abdallah, C. CAD Laboratory for Systems and Robotics, Electrical and Computer Engineering Department, University of New Mexico, Albuquerque, NM 87131. Dorato, P. ; Jamshidi, M. On Page(s): 718 - 721 Product Type: Conference Publications 4790827 searchabstract .Abstract In this survey, we discuss current approaches to the robust control of the motion of robots and summarize the available literature on the subject. The three major designs discussed are the Linear-Multivariable Approach, the Passivity approach and the Variable-Structure approach. The survey is limited to rigid robots and nonadaptive controllers

Statistical controller design for the linear benchmark problem

In this paper some fixed-order controllers are designed via statistical methods for the benchmark problem originally presented at the 1990 American Control Conference. Based on some recent results by the authors, it is shown that the statistical approach is a valid method to design robust controllers. Two different controllers are proposed and their performance are compared with controllers with the same structure, designed using different techniques

Survey of robust control for rigid robots

Current approaches to the robust control of the motion of rigid robots are surveyed, and the available literature is summarized. The five major design approaches discussed are the linear-multivariable approach, the passivity approach, the variable-structure approach, the saturation approach, and the robust-adaptive approach. Some guidelines for choosing a method are offered

Suboptimal strong stabilization using fixed-order dynamic compensation

This paper considers the problem of stabilizing a plant using a suboptimal stable compensator of fixed order. The resulting equations are a modified form of the optimal projection equations, with the separation principle not holding in either the full- or reduced-order case

Finite-time control for uncertain linear systems with disturbance inputs

We consider the static output feedback, finite-time disturbance rejection problem for linear systems with time-varying norm-bounded uncertainties. The first result provided in the paper is a sufficient condition for finite-time state feedback disturbance rejection in the presence of constant disturbances. This condition requires the solution of an LMI. Then we consider the more general output feedback case, which is shown to be reducible to the solution of an optimization problem involving bilinear matrix inequalities. Finally we deal with the case in which the disturbance is time-varying and generated by a linear system

Design of strictly positive real, fixed-order dynamic compensators

The authors present sufficient conditions for the design of strictly positive real (SPR), fixed-order dynamic compensators. The primary motivation for designing SPR compensators is for application to positive real (PR) plants. When an SPR compensator is connected to a PR plant in a negative feedback configuration, the closed loop is guaranteed stable for arbitrary plant variations as long as the plant remains PR. Equations that are a modified form of the optimal projection equations, with the separation principle not holding in either the full- or reduced-order case, are given. A solution to the design equations is shown to exist when the plant is PR (or just stable). Finally, the closed-loop system consisting of a PR plant and an SPR compensator is shown to be S-structured Lyapunov stable