Inverse Optimal Control of Evolution Systems and Its Application to Extensible and Shearable Slender Beams |
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| Authors: | K D Do A D Lucey |
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| Affiliation: | Department of Mechanical Engineering, Curtin University, Kent Street, Bentley, WA 6102, Australia |
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| Abstract: | 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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| Keywords: | Boundary control evolution system Hilbert space inverse optimal control slender beams |
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