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Algebraic Matrix Equation
The Experts below are selected from a list of 126 Experts worldwide ranked by ideXlab platform
Rolf Johansson – One of the best experts on this subject based on the ideXlab platform.
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Optimal coordination and control of posture and movements.
Journal of Physiology-paris, 2009Co-Authors: Rolf Johansson, Per-anders Fransson, Måns MagnussonAbstract: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.
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Optimal coordination and control of posture and locomotion.
Mathematical biosciences, 1991Co-Authors: Rolf Johansson, Måns MagnussonAbstract: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.
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ICRA – Quadratic optimization of impedance control
Proceedings of the 1994 IEEE International Conference on Robotics and Automation, 1Co-Authors: Rolf Johansson, Mark W. SpongAbstract: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.
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Optimal coordination and control of posture and movements.
Journal of Physiology-paris, 2009Co-Authors: Rolf Johansson, Per-anders Fransson, Måns MagnussonAbstract: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.
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Optimal coordination and control of posture and locomotion.
Mathematical biosciences, 1991Co-Authors: Rolf Johansson, Måns MagnussonAbstract: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.
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Stability analysis and observer design for neutral delay systems
IEEE Transactions on Automatic Control, 2002Co-Authors: Zidong Wang, James Lam, Keith J. BurnhamAbstract:This paper deals with the observer design problem for a class of linear delay systems of the neutral-type. The problem addressed is that of designing a full-order observer that guarantees the exponential stability of the error dynamic system. An effective Algebraic Matrix Equation approach is developed to solve this problem. In particular, both the observer analysis and design problems are investigated. By using the singular value decomposition technique and the generalized inverse theory, sufficient conditions for a neutral-type delay system to be exponentially stable are first established. Then, an explicit expression of the desired observers is derived in terms of some free parameters. Furthermore, an illustrative example is used to demonstrate the validity of the proposed design procedure.
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Robust H infinity Control for Systems with Time-varying Parameter Uncertainty and Variance Constraints.
Cybernetics and Systems, 2000Co-Authors: Zidong Wang, Heinz UnbehauenAbstract:In this paper, the problem of designing robust Hinfinity controllers for linear continuous-time systems subjected to time-varying paraparameter uncertainty and steady-state variance constraints is considered. The goal of this problem is to design the state feedback controller, such that for all admissible time-varying parameter perturbations, the steady-state variance of each state is not more than the individual prespecified upper bound and the Hinfinity norm of the transfer function from disturbance inputs to system outputs meets the prespecified upper bound constraint, simultaneously. The parameter uncertainties are allowed to be time-varying and norm-bounded. A purely Algebraic Matrix Equation approach is effectively utilized to solve the problem addressed. The existence conditions as well as the explicit expression of desired controllers are presented, and two illustrative examples are used to demonstrate the applicability of the proposed design procedure.
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Robust state estimation for perturbed systems with error variance and circular pole constraints: The discrete-time case
International Journal of Control, 2000Co-Authors: Zidong WangAbstract:This paper is concerned with the problem of robust state estimation for linear perturbed discrete-time systems with error variance and circular pole constraints. The goal of this problem addressed is the design of a linear state estimator such that, for all admissible uncertainties in both state and output Equations, the following two performance requirements are simultaneously satisfied: (1) the poles of the filtering Matrix are all constrained to lie inside a prespecified circular region; and (2) the steady-state variance of the estimation error for each state is not more than the individual prespecified value. It is shown that this problem can be converted to an auxiliary Matrix assignment problem and solved by using an Algebraic Matrix Equation/inequality approach. Specifically, the conditions for the existence of desired estimators are obtained and the explicit expression of these estimators is also derived. The main results are then extended to the case when an H performance requirement is added. Fi…
Mark W. Spong – One of the best experts on this subject based on the ideXlab platform.
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ICRA – Quadratic optimization of impedance control
Proceedings of the 1994 IEEE International Conference on Robotics and Automation, 1Co-Authors: Rolf Johansson, Mark W. SpongAbstract: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.
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An algorithm for the numerical solution of an important Algebraic Matrix Equation in control system design
1999 European Control Conference (ECC), 1999Co-Authors: V. A. Tsachouridis, Ian PostlethwaiteAbstract:An algorithm for the numerical solution of an important Algebraic Matrix Equation in control system design is developed. It is based on ideas arising from probability-1 homotopy methods, for the solution of Algebraic systems of Equations. The specialisation of this Matrix Equation into the Algebraic Riccati Matrix Equation for continuous time systems is discussed. The proposed algorithm can be used to solve the optimal projection Equations appearing in a reduced order compensator synthesis problem and in an anti-windup compensator synthesis problem. In addition, solutions to second order Algebraic Matrix polynomial Equations are successfully obtained as solutions to special forms of the Equation in question. Numerical examples show the advantage of the proposed method over other algorithms.