Abstract
This paper introduces a new method for the computation of an optimal semi-active feedback of a plant, which is controlled by multiple semi-active control dampers and subjected to external, a priori known deterministic disturbance input. The control force is written in bilinear form in equivalent damping gains and a linear combination of the states. This form leads to a bilinear state-space model with corresponding damping gain constraints. An optimal control problem, denoted as constrained bilinear quadratic regulator, is formulated with a performance index, which is quadratic in the states and the equivalent damping gains. The methodology, which is used for solving this problem, is Krotov’s method. In this study, the sequence of improving functions, which enables the use of Krotov’s method in this case, is formulated. Its incorporation in Krotov’s algorithm leads to the suggested novel algorithm for solution of the constrained bilinear quadratic regulator problem for excited optimal semi-active control design. The results are demonstrated numerically by constrained bilinear quadratic regulator control design of controlled structure with seismic disturbance input.
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Notes
Recall that \({\mathbf {M}}>0\), \({\mathbf {K}}>0\) iff \({\mathbf {z}}^T{\mathbf {M}}{\mathbf {z}}>0\), \({\mathbf {z}}^T{\mathbf {K}}{\mathbf {z}}>0\) for all \({\mathbf {z}}\in \mathbb {R}^{n_z}\), \({\mathbf {z}}\ne {\mathbf {0}}\) and \({\mathbf {C}}_d\ge 0\) iff \({\mathbf {z}}^T{\mathbf {C}}_d{\mathbf {z}}\ge 0\) for all \({\mathbf {z}}\in \mathbb {R}^{n_z}\).
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Communicated by Paolo Maria Mariano.
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Halperin, I., Agranovich, G. & Ribakov, Y. Extension of the Constrained Bilinear Quadratic Regulator to the Excited Multi-input Case. J Optim Theory Appl 184, 277–292 (2020). https://doi.org/10.1007/s10957-019-01479-x
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DOI: https://doi.org/10.1007/s10957-019-01479-x