Abstract
The approximate steering problem is considered in this chapter for a linear distributed parameter system with finite-dimensional control. An approach for solving this problem is proposed by using exact solutions of the steering problem for reduced systems and the spillover analysis. This approach allows also to estimate the reachable sets and to study the approximate controllability. To satisfy the spillover condition, we exploit \(L^2\)-optimal controls for a family of finite-dimensional subsystems. These controls are constructed explicitly for a system of oscillators with one-dimensional input. As a result, we obtain sufficient conditions for the approximate controllability in terms of the distribution of eigenfrequencies in such system. These conditions are applied for the approximate controllability study of a rotating body-beam system.
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Zuyev, A.L. (2015). Reachable Sets and Controllability Conditions. In: Partial Stabilization and Control of Distributed Parameter Systems with Elastic Elements. Lecture Notes in Control and Information Sciences, vol 458. Springer, Cham. https://doi.org/10.1007/978-3-319-11532-0_4
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DOI: https://doi.org/10.1007/978-3-319-11532-0_4
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