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 K∞-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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