Nonlinear Controllability via Lie Theory
01 Nov 1970-Siam Journal on Control (Society for Industrial and Applied Mathematics)-Vol. 8, Iss: 4, pp 450-460
TL;DR: In this paper, the authors discuss trajectories uniform approximation and nonlinear controllability conditions based on linear partial differential equation (LPDE) for complete system associated with given control.
Abstract: Complete system associated with given control, discussing trajectories uniform approximation and nonlinear controllability conditions based on linear partial differential equation
Citations
More filters
TL;DR: The properties of controllability, observability, and the theory of minimal realization for linear systems are well-understood and have been very useful in analyzing such systems as discussed by the authors.
Abstract: The properties of controllability, observability, and the theory of minimal realization for linear systems are well-understood and have been very useful in analyzing such systems. This paper deals with analogous questions for nonlinear systems.
2,306 citations
TL;DR: In this article, the controllability of nonlinear systems described by the equation dx/dt - F(x,u) was discussed and it was shown that strong accessibility implies strong accessibility for a large class of manifolds including Euclidean spaces.
718 citations
TL;DR: The controllability properties of systems which are described by an evolution equation in a Lie group are studied in this paper, where revelant Lie algebras induced by a right invariant system are singled out, and the basic properties of attainable sets are derived.
610 citations
TL;DR: A planner for finding stable pushing paths among obstacles is described, and the planner is demon strated on several manipulation tasks.
Abstract: We would like to give robots the ability to position and orient parts in the plane by pushing, particularly when the parts are too large or heavy to be grasped and lifted. Unfortunately, the motion of a pushed object is generally unpredictable due to unknown support friction forces. With multiple pushing contact points, however, it is possible to find pushing directions that cause the object to remain fixed to the manipulator. These are called stable pushing directions. In this article we consider the problem of planning pushing paths using stable pushes. Pushing imposes a set of nonholonomic velocity constraints on the motion of the object, and we study the issues of local and global controllability during pushing with point contact or stable line contact. We describe a planner for finding stable pushing paths among obstacles, and the planner is demon strated on several manipulation tasks.
513 citations
TL;DR: Recent advances on the controllability and the control of complex networks are reviewed, exploring the intricate interplay between a system's structure, captured by its network topology, and the dynamical laws that govern the interactions between the components.
Abstract: A reflection of our ultimate understanding of a complex system is our ability to control its behavior. Typically, control has multiple prerequisites: It requires an accurate map of the network that governs the interactions between the system's components, a quantitative description of the dynamical laws that govern the temporal behavior of each component, and an ability to influence the state and temporal behavior of a selected subset of the components. With deep roots in nonlinear dynamics and control theory, notions of control and controllability have taken a new life recently in the study of complex networks, inspiring several fundamental questions: What are the control principles of complex systems? How do networks organize themselves to balance control with functionality? To address these here we review recent advances on the controllability and the control of complex networks, exploring the intricate interplay between a system's structure, captured by its network topology, and the dynamical laws that govern the interactions between the components. We match the pertinent mathematical results with empirical findings and applications. We show that uncovering the control principles of complex systems can help us explore and ultimately understand the fundamental laws that govern their behavior.
503 citations
Cites background from "Nonlinear Controllability via Lie T..."
...…systems has been extensively studied since the early 1970s (Brockett, 1972; Conte et al., 2007; Elliot, 1970; de Figueiredo and Chen, 1993; Haynes and Hermes, 1970; Hermann and Krener, 1977; Isidori, 1995; Lobry, 1970; Nijmeijer and van der Schaft, 1990; Rugh, 1981; Sontag, 1998; Sussmann…...
[...]