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Volume 6 Issue 2
Mar.  2019

IEEE/CAA Journal of Automatica Sinica

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K. D. Do and A. D. Lucey, "Inverse Optimal Control of Evolution Systems and Its Application to Extensible and Shearable Slender Beams," IEEE/CAA J. Autom. Sinica, vol. 6, no. 2, pp. 395-409, Mar. 2019. doi: 10.1109/JAS.2019.1911381
Citation: K. D. Do and A. D. Lucey, "Inverse Optimal Control of Evolution Systems and Its Application to Extensible and Shearable Slender Beams," IEEE/CAA J. Autom. Sinica, vol. 6, no. 2, pp. 395-409, Mar. 2019. doi: 10.1109/JAS.2019.1911381

Inverse Optimal Control of Evolution Systems and Its Application to Extensible and Shearable Slender Beams

doi: 10.1109/JAS.2019.1911381
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  • An optimal (practical) stabilization problem is formulated in an inverse approach and solved for nonlinear evolution systems in Hilbert spaces. The optimal control design ensures global well-posedness and global practical $\mathcal{K}_{\infty}$-exponential stability of the closed-loop system, minimizes a cost functional, which appropriately penalizes both state and control in the sense that it is positive definite (and radially unbounded) in the state and control, without having to solve a Hamilton-Jacobi-Belman equation (HJBE). The Lyapunov functional used in the control design explicitly solves a family of HJBEs. The results are applied to design inverse optimal boundary stabilization control laws for extensible and shearable slender beams governed by fully nonlinear partial differential equations.


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