530,450 research outputs found
Trajectory Tracking Control Design for Large-Scale Linear Dynamical Systems With Applications to Soft Robotics
International audienceThis article presents new results to control process modeled through linear large-scale systems. Numerical methods are widely used to model physical systems, and the finite-element method is one of the most common methods. However, for this method to be precise, it requires a precise spatial mesh of the process. Large-scale dynamical systems arise from this spatial discretization. We propose a methodology to design an observer-based output feedback controller. First, a model reduction step is used to get a system of acceptable dimension. Based on this low-order system, two linear matrix inequality problems provide us, respectively, with the observer and controller gains. In both the cases, model and reduction errors are taken into account in the computations. This provides robustness with respect to the reduction step and guarantees the stability of the original large-scale system. Finally, the proposed method is applied to a physical setup-a soft robotics platform-to show its feasibility
Rhythmic dynamics and synchronization via dimensionality reduction : application to human gait
Reliable characterization of locomotor dynamics of human walking is vital to understanding the neuromuscular control of human locomotion and disease diagnosis. However, the inherent oscillation and ubiquity of noise in such non-strictly periodic signals pose great challenges to current methodologies. To this end, we exploit the state-of-the-art technology in pattern recognition and, specifically, dimensionality reduction techniques, and propose to reconstruct and characterize the dynamics accurately on the cycle scale of the signal. This is achieved by deriving a low-dimensional representation of the cycles through global optimization, which effectively preserves the topology of the cycles that are embedded in a high-dimensional Euclidian space. Our approach demonstrates a clear advantage in capturing the intrinsic dynamics and probing the subtle synchronization patterns from uni/bivariate oscillatory signals over traditional methods. Application to human gait data for healthy subjects and diabetics reveals a significant difference in the dynamics of ankle movements and ankle-knee coordination, but not in knee movements. These results indicate that the impaired sensory feedback from the feet due to diabetes does not influence the knee movement in general, and that normal human walking is not critically dependent on the feedback from the peripheral nervous system
Order reduction approaches for the algebraic Riccati equation and the LQR problem
We explore order reduction techniques for solving the algebraic Riccati
equation (ARE), and investigating the numerical solution of the
linear-quadratic regulator problem (LQR). A classical approach is to build a
surrogate low dimensional model of the dynamical system, for instance by means
of balanced truncation, and then solve the corresponding ARE. Alternatively,
iterative methods can be used to directly solve the ARE and use its approximate
solution to estimate quantities associated with the LQR. We propose a class of
Petrov-Galerkin strategies that simultaneously reduce the dynamical system
while approximately solving the ARE by projection. This methodology
significantly generalizes a recently developed Galerkin method by using a pair
of projection spaces, as it is often done in model order reduction of dynamical
systems. Numerical experiments illustrate the advantages of the new class of
methods over classical approaches when dealing with large matrices
A Numerical Slow Manifold Approach to Model Reduction for Optimal Control of Multiple Time Scale ODE
Time scale separation is a natural property of many control systems that can
be ex- ploited, theoretically and numerically. We present a numerical scheme to
solve optimal control problems with considerable time scale separation that is
based on a model reduction approach that does not need the system to be
explicitly stated in singularly perturbed form. We present examples that
highlight the advantages and disadvantages of the method
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