The Experts below are selected from a list of 312 Experts worldwide ranked by ideXlab platform

Jeffrey Uhlmann - One of the best experts on this subject based on the ideXlab platform.

  • Applying a Unit-Consistent Generalized Matrix Inverse for Stable Control of Robotic Systems
    Journal of Mechanisms and Robotics, 2019
    Co-Authors: Bo Zhang, Jeffrey Uhlmann
    Abstract:

    It is well understood that the robustness of mechanical and robotic control systems depends critically on minimizing sensitivity to arbitrary application-specific details whenever possible. For example, if a system is defined and performs well in one particular Euclidean coordinate frame then it should be expected to perform identically if that coordinate frame is arbitrarily rotated or scaled. Similarly, the performance of the system should not be affected if its key parameters are all consistently defined in metric units or in imperial units. In this paper we show that a recently introduced generalized Matrix Inverse permits performance consistency to be rigorously guaranteed in control systems that require solutions to underdetermined and/or overdetermined systems of equations. We analyze and empirically demonstrate how these theoretical guarantees can be directly obtained in a practical robotic arm system.

  • Applying a Unit-Consistent Generalized Matrix Inverse for Stable Control of Robotic Systems
    Journal of Mechanisms and Robotics, 2019
    Co-Authors: Bo Zhang, Jeffrey Uhlmann
    Abstract:

    It is well understood that the robustness of mechanical and robotic control systems depends critically on minimizing sensitivity to arbitrary application-specific details whenever possible. For example, if a system is defined and performs well in one particular Euclidean coordinate frame then it should be expected to perform identically if that coordinate frame is arbitrarily rotated or scaled. Similarly, the performance of the system should not be affected if its key parameters are all consistently defined in metric units or in imperial units. In this paper we show that a recently introduced generalized Matrix Inverse permits performance consistency to be rigorously guaranteed in control systems that require solutions to underdetermined and/or overdetermined systems of equations. We analyze and empirically demonstrate how these theoretical guarantees can be directly obtained in a practical robotic arm system.

  • a rank preserving generalized Matrix Inverse for consistency with respect to similarity
    IEEE Control Systems Letters, 2019
    Co-Authors: Jeffrey Uhlmann
    Abstract:

    There has recently been renewed recognition of the need to understand the consistency properties that must be preserved when a generalized Matrix Inverse is required. The most widely known generalized Inverse, the Moore-Penrose pseudoInverse, provides consistency with respect to orthonormal transformations (e.g., rotations of a coordinate frame), and a recently derived Inverse provides consistency with respect to diagonal transformations (e.g., a change of units on state variables). Another well-known and theoretically important generalized Inverse is the Drazin Inverse, which preserves consistency with respect to similarity transformations. In this letter we note that the Drazin Inverse suffers a significant practical limitation in that it does not generally preserve the rank of the linear system of interest. We then introduce an alternative generalized Inverse that both preserves rank and provides consistency with respect to similarity transformations. We discuss practical implementation considerations and demonstrate with an example.

  • a generalized Matrix Inverse that is consistent with respect to diagonal transformations
    SIAM Journal on Matrix Analysis and Applications, 2018
    Co-Authors: Jeffrey Uhlmann
    Abstract:

    A new generalized Matrix Inverse is derived which is consistent with respect to arbitrary nonsingular diagonal transformations, e.g., it preserves units associated with variables under state space ...

  • A Generalized Matrix Inverse with Applications to Robotic Systems.
    arXiv: Signal Processing, 2018
    Co-Authors: Bo Zhang, Jeffrey Uhlmann
    Abstract:

    It is well-understood that the robustness of mechanical and robotic control systems depends critically on minimizing sensitivity to arbitrary application-specific details whenever possible. For example, if a system is defined and performs well in one particular Euclidean coordinate frame then it should be expected to perform identically if that coordinate frame is arbitrarily rotated or scaled. Similarly, the performance of the system should not be affected if its key parameters are all consistently defined in metric units or in imperial units. In this paper we show that a recently introduced generalized Matrix Inverse permits performance consistency to be rigorously guaranteed in control systems that require solutions to underdetermined and/or overdetermined systems of equations.

Bo Zhang - One of the best experts on this subject based on the ideXlab platform.

  • Applying a Unit-Consistent Generalized Matrix Inverse for Stable Control of Robotic Systems
    Journal of Mechanisms and Robotics, 2019
    Co-Authors: Bo Zhang, Jeffrey Uhlmann
    Abstract:

    It is well understood that the robustness of mechanical and robotic control systems depends critically on minimizing sensitivity to arbitrary application-specific details whenever possible. For example, if a system is defined and performs well in one particular Euclidean coordinate frame then it should be expected to perform identically if that coordinate frame is arbitrarily rotated or scaled. Similarly, the performance of the system should not be affected if its key parameters are all consistently defined in metric units or in imperial units. In this paper we show that a recently introduced generalized Matrix Inverse permits performance consistency to be rigorously guaranteed in control systems that require solutions to underdetermined and/or overdetermined systems of equations. We analyze and empirically demonstrate how these theoretical guarantees can be directly obtained in a practical robotic arm system.

  • Applying a Unit-Consistent Generalized Matrix Inverse for Stable Control of Robotic Systems
    Journal of Mechanisms and Robotics, 2019
    Co-Authors: Bo Zhang, Jeffrey Uhlmann
    Abstract:

    It is well understood that the robustness of mechanical and robotic control systems depends critically on minimizing sensitivity to arbitrary application-specific details whenever possible. For example, if a system is defined and performs well in one particular Euclidean coordinate frame then it should be expected to perform identically if that coordinate frame is arbitrarily rotated or scaled. Similarly, the performance of the system should not be affected if its key parameters are all consistently defined in metric units or in imperial units. In this paper we show that a recently introduced generalized Matrix Inverse permits performance consistency to be rigorously guaranteed in control systems that require solutions to underdetermined and/or overdetermined systems of equations. We analyze and empirically demonstrate how these theoretical guarantees can be directly obtained in a practical robotic arm system.

  • A Generalized Matrix Inverse with Applications to Robotic Systems.
    arXiv: Signal Processing, 2018
    Co-Authors: Bo Zhang, Jeffrey Uhlmann
    Abstract:

    It is well-understood that the robustness of mechanical and robotic control systems depends critically on minimizing sensitivity to arbitrary application-specific details whenever possible. For example, if a system is defined and performs well in one particular Euclidean coordinate frame then it should be expected to perform identically if that coordinate frame is arbitrarily rotated or scaled. Similarly, the performance of the system should not be affected if its key parameters are all consistently defined in metric units or in imperial units. In this paper we show that a recently introduced generalized Matrix Inverse permits performance consistency to be rigorously guaranteed in control systems that require solutions to underdetermined and/or overdetermined systems of equations.

Piotr Sankowski - One of the best experts on this subject based on the ideXlab platform.

  • dynamic transitive closure via dynamic Matrix Inverse extended abstract
    Foundations of Computer Science, 2004
    Co-Authors: Piotr Sankowski
    Abstract:

    We consider dynamic evaluation of algebraic functions such as computing determinant, Matrix adjoint, Matrix Inverse and solving linear system of equations. We show that in the dynamic setup the above problems can be solved faster than evaluating everything from scratch. In the case when rows and columns of the Matrix can change we show an algorithm that achieves O(n/sup 2/) arithmetic operations per update and O(1) arithmetic operations per query. Next, we describe two algorithms, with different tradeoffs, for updating the Inverse and determinant when single entries of the Matrix are changed. The fastest update for the first tradeoff is O(n/sup 1.575/) arithmetic operations per update and O(n/sup 0.575/) arithmetic operations per query. The second tradeoff gives O(n/sup 1.495/) arithmetic operations per update and O(n/sup 1.495/) arithmetic operations per query. We also consider the case when some number of columns or rows can change. We use dynamic determinant computations to solve the following problems in the dynamic setup: computing the number of spanning trees in a graph and testing if an edge in a graph is contained in some perfect matching. These are the first dynamic algorithms for these problems. Next, with the use of dynamic Matrix Inverse, we solve fully dynamic transitive closure in general directed graphs. The bounds on arithmetic operations for dynamic Matrix Inverse translate directly to time bounds for dynamic transitive closure. Thus we obtain the first known algorithm with O(n/sup 2/) worst-case update time and constant query time and two algorithms for transitive closure in general digraphs with subquadratic update and query times. Our algorithms for transitive closure are randomized with one-sided error. We also consider for the first time the case when the edges incident with a part of vertices of the graph can be changed.

  • FOCS - Dynamic transitive closure via dynamic Matrix Inverse: extended abstract
    45th Annual IEEE Symposium on Foundations of Computer Science, 1
    Co-Authors: Piotr Sankowski
    Abstract:

    We consider dynamic evaluation of algebraic functions such as computing determinant, Matrix adjoint, Matrix Inverse and solving linear system of equations. We show that in the dynamic setup the above problems can be solved faster than evaluating everything from scratch. In the case when rows and columns of the Matrix can change we show an algorithm that achieves O(n/sup 2/) arithmetic operations per update and O(1) arithmetic operations per query. Next, we describe two algorithms, with different tradeoffs, for updating the Inverse and determinant when single entries of the Matrix are changed. The fastest update for the first tradeoff is O(n/sup 1.575/) arithmetic operations per update and O(n/sup 0.575/) arithmetic operations per query. The second tradeoff gives O(n/sup 1.495/) arithmetic operations per update and O(n/sup 1.495/) arithmetic operations per query. We also consider the case when some number of columns or rows can change. We use dynamic determinant computations to solve the following problems in the dynamic setup: computing the number of spanning trees in a graph and testing if an edge in a graph is contained in some perfect matching. These are the first dynamic algorithms for these problems. Next, with the use of dynamic Matrix Inverse, we solve fully dynamic transitive closure in general directed graphs. The bounds on arithmetic operations for dynamic Matrix Inverse translate directly to time bounds for dynamic transitive closure. Thus we obtain the first known algorithm with O(n/sup 2/) worst-case update time and constant query time and two algorithms for transitive closure in general digraphs with subquadratic update and query times. Our algorithms for transitive closure are randomized with one-sided error. We also consider for the first time the case when the edges incident with a part of vertices of the graph can be changed.

Hang Liu - One of the best experts on this subject based on the ideXlab platform.

  • a secure and verifiable outsourcing scheme for Matrix Inverse computation
    International Conference on Computer Communications, 2017
    Co-Authors: Abdulrahman Alhothaily, Arwa Alrawais, Xiuzhen Cheng, Carl Sturtivant, Hang Liu
    Abstract:

    Matrix Inverse computation is one of the most fundamental mathematical problems in large-scale data analytics and computing. It is often too expensive to be solved in resource-constrained devices such as sensors. Outsourcing the computation task to a cloud server or a fog server is a potential approach as the server is able to perform large-scale scientific computations on behalf of resource-constrained users with special software. However, outsourcing brings in new security concerns and challenges such as data privacy violations and result invalidation. In this paper, we propose a secure and verifiable outsourcing scheme to compute the Matrix Inverse in a server. In our scheme, the client generates two secret key sets based on two chaotic systems, which are utilized to create two sparse matrices whose permuted versions are used for Matrix encryption and decryption to protect input and output privacy. The server computes the Inverse over the ciphertext Matrix and returns the result to the client who can verify the validity of the Inverse. We analyze the proposed scheme in terms of correctness, security, verifiability, and attack resistance, and compare its performance (computation, storage, and communication overheads) with those of the state-of-the-art. Our theoretical results and comparison study demonstrate that the proposed scheme provides a secure and efficient outsourcing mechanism for Matrix Inverse computation.

  • INFOCOM - A secure and verifiable outsourcing scheme for Matrix Inverse computation
    IEEE INFOCOM 2017 - IEEE Conference on Computer Communications, 2017
    Co-Authors: Abdulrahman Alhothaily, Arwa Alrawais, Xiuzhen Cheng, Carl Sturtivant, Hang Liu
    Abstract:

    Matrix Inverse computation is one of the most fundamental mathematical problems in large-scale data analytics and computing. It is often too expensive to be solved in resource-constrained devices such as sensors. Outsourcing the computation task to a cloud server or a fog server is a potential approach as the server is able to perform large-scale scientific computations on behalf of resource-constrained users with special software. However, outsourcing brings in new security concerns and challenges such as data privacy violations and result invalidation. In this paper, we propose a secure and verifiable outsourcing scheme to compute the Matrix Inverse in a server. In our scheme, the client generates two secret key sets based on two chaotic systems, which are utilized to create two sparse matrices whose permuted versions are used for Matrix encryption and decryption to protect input and output privacy. The server computes the Inverse over the ciphertext Matrix and returns the result to the client who can verify the validity of the Inverse. We analyze the proposed scheme in terms of correctness, security, verifiability, and attack resistance, and compare its performance (computation, storage, and communication overheads) with those of the state-of-the-art. Our theoretical results and comparison study demonstrate that the proposed scheme provides a secure and efficient outsourcing mechanism for Matrix Inverse computation.

Li Jie-hong - One of the best experts on this subject based on the ideXlab platform.