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A hybrid filtered basis function (FBF) approach is proposed in this paper for feedforward tracking control of linear systems with unmodeled nonlinear dynamics. Unlike most available tracking control techniques, the FBF approach is very versatile; it is applicable to any type of linear system, regardless of its underlying dynamics. The FBF approach expresses the control input to a system as a linear combination of basis functions with unknown coefficients. The basis functions are forward filtered through a linear model of the system's dynamics and the unknown coefficients are selected such that tracking error is minimized. The linear models used in existing implementations of the FBF approach are typically physics-based representations of the linear dynamics of a system. The proposed hybrid FBF approach expands the application of the FBF approach to systems with unmodeled nonlinearities by learning from data. A hybrid model is formulated by combining a physics-based model of the system's linear dynamics with a data-driven linear model that approximates the unmodeled nonlinear dynamics. The hybrid model is used online in receding horizon to compute optimal control commands that minimize tracking errors. The proposed hybrid FBF approach is shown in simulations on a model of a vibration-prone 3D printer to improve tracking accuracy by up to 65.4%, compared to an existing FBF approach that does not incorporate data.
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Adjoint Based Hessians for Optimization Problems in System Identification
An adjoint sensitivity based approach to determine the gradient and Hessian of cost functions for system identification is presented. The motivation is the development of a computationally efficient approach relative to the direct differentiation technique and which overcomes the challenges of the step size selection in finite difference approaches. The discrete time measurements result in discontinuities in the Lagrange multipliers. The proposed approach is illustrated on the Lorenz 63 model where part of the initial conditions and model parameters are estimated.
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- Award ID(s):
- 1537210
- PAR ID:
- 10113121
- Date Published:
- Journal Name:
- 2017 IEEE Conference on Control Technology and Applications
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
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