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Algebraic Matrix Equation

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Rolf Johansson – One of the best experts on this subject based on the ideXlab platform.

  • Optimal coordination and control of posture and movements.
    Journal of Physiology-paris, 2009
    Co-Authors: Rolf Johansson, Per-anders Fransson, Måns Magnusson
    Abstract:

    This paper presents a theoretical model of stability and coordination of posture and locomotion, together with algorithms for continuous-time quadratic optimization of motion control. Explicit solutions to the Hamilton-Jacobi Equation for optimal control of rigid-body motion are obtained by solving an Algebraic Matrix Equation. The stability is investigated with Lyapunov function theory and it is shown that global asymptotic stability holds. It is also shown how optimal control and adaptive control may act in concert in the case of unknown or uncertain system parameters. The solution describes motion strategies of minimum effort and variance. The proposed optimal control is formulated to be suitable as a posture and movement model for experimental validation and verification. The combination of adaptive and optimal control makes this algorithm a candidate for coordination and control of functional neuromuscular stimulation as well as of prostheses. Validation examples with experimental data are provided.

  • Optimal coordination and control of posture and locomotion.
    Mathematical biosciences, 1991
    Co-Authors: Rolf Johansson, Måns Magnusson
    Abstract:

    This paper presents a theoretical model of stability and coordination of posture and locomotion, together with algorithms for continuous-time quadratic optimization of motion control. Explicit solutions to the Hamilton-Jacobi Equation for optimal control of rigid-body motion are obtained by solving an Algebraic Matrix Equation. The stability is investigated with Lyapunov function theory, and it is shown that global asymptotic stability holds. It is also shown how optimal control and adaptive control may act in concert in the case of unknown or uncertain system parameters. The solution describes motion strategies of minimum effort and variance. The proposed optimal control is formulated to be suitable as a posture and stance model for experimental validation and verification. The combination of adaptive and optimal control makes this algorithm a candidate for coordination and control of functional neuromuscular stimulation as well as of prostheses.

  • ICRA – Quadratic optimization of impedance control
    Proceedings of the 1994 IEEE International Conference on Robotics and Automation, 1
    Co-Authors: Rolf Johansson, Mark W. Spong
    Abstract:

    This paper presents algorithms for continuous-time quadratic optimization of impedance control. Explicit solutions to the Hamilton-Jacobi Equation for optimal control of rigid-body motion are found by solving an Algebraic Matrix Equation. System stability is investigated according to Lyapunov function theory, and it is shown that global asymptotic stability holds. The solution results in design parameters in the form of square weighting matrices or impedance matrices as known from linear quadratic optimal control. The proposed optimal control is useful both for motion control and force control. >

Måns Magnusson – One of the best experts on this subject based on the ideXlab platform.

  • Optimal coordination and control of posture and movements.
    Journal of Physiology-paris, 2009
    Co-Authors: Rolf Johansson, Per-anders Fransson, Måns Magnusson
    Abstract:

    This paper presents a theoretical model of stability and coordination of posture and locomotion, together with algorithms for continuous-time quadratic optimization of motion control. Explicit solutions to the Hamilton-Jacobi Equation for optimal control of rigid-body motion are obtained by solving an Algebraic Matrix Equation. The stability is investigated with Lyapunov function theory and it is shown that global asymptotic stability holds. It is also shown how optimal control and adaptive control may act in concert in the case of unknown or uncertain system parameters. The solution describes motion strategies of minimum effort and variance. The proposed optimal control is formulated to be suitable as a posture and movement model for experimental validation and verification. The combination of adaptive and optimal control makes this algorithm a candidate for coordination and control of functional neuromuscular stimulation as well as of prostheses. Validation examples with experimental data are provided.

  • Optimal coordination and control of posture and locomotion.
    Mathematical biosciences, 1991
    Co-Authors: Rolf Johansson, Måns Magnusson
    Abstract:

    This paper presents a theoretical model of stability and coordination of posture and locomotion, together with algorithms for continuous-time quadratic optimization of motion control. Explicit solutions to the Hamilton-Jacobi Equation for optimal control of rigid-body motion are obtained by solving an Algebraic Matrix Equation. The stability is investigated with Lyapunov function theory, and it is shown that global asymptotic stability holds. It is also shown how optimal control and adaptive control may act in concert in the case of unknown or uncertain system parameters. The solution describes motion strategies of minimum effort and variance. The proposed optimal control is formulated to be suitable as a posture and stance model for experimental validation and verification. The combination of adaptive and optimal control makes this algorithm a candidate for coordination and control of functional neuromuscular stimulation as well as of prostheses.

Zidong Wang – One of the best experts on this subject based on the ideXlab platform.

Mark W. Spong – One of the best experts on this subject based on the ideXlab platform.

  • ICRA – Quadratic optimization of impedance control
    Proceedings of the 1994 IEEE International Conference on Robotics and Automation, 1
    Co-Authors: Rolf Johansson, Mark W. Spong
    Abstract:

    This paper presents algorithms for continuous-time quadratic optimization of impedance control. Explicit solutions to the Hamilton-Jacobi Equation for optimal control of rigid-body motion are found by solving an Algebraic Matrix Equation. System stability is investigated according to Lyapunov function theory, and it is shown that global asymptotic stability holds. The solution results in design parameters in the form of square weighting matrices or impedance matrices as known from linear quadratic optimal control. The proposed optimal control is useful both for motion control and force control. >

Ian Postlethwaite – One of the best experts on this subject based on the ideXlab platform.