Inverse optimal control of evolution systems and its application to extensible and shearable slender beams

An optimal ( practical ) stabilization problem is for mulated 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.