2018/04/27 by Jochen Schmid, Schmid, Jochen, Hans Zwart +1 · 2 citations
Computer Science · Engineering · #35L65 #93C20 #93D09 #93D15 #Advanced Mathematical Modeling in Engineering #Control and Stability of Dynamical Systems #FOS: Mathematics #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.1804.10598
openalex publication_date 2018/04/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we are concerned with the stabilization of linear\nport-Hamiltonian systems of arbitrary order N \∈ \ℕ on a bounded\n1-dimensional spatial domain (a,b). In order to achieve stabilization, we\ncouple the system to a dynamic boundary controller, that is, a controller that\nacts on the system only via the boundary points a,b of the spatial domain. We\nuse a nonlinear controller in order to capture the nonlinear behavior that\nrealistic actuators often exhibit and, moreover, we allow the output of the\ncontroller to be corrupted by actuator disturbances before it is fed back into\nthe system. What we show here is that the resulting nonlinear closed-loop\nsystem is input-to-state stable w.r.t.~square-integrable disturbance inputs. In\nparticular, we obtain uniform input-to-state stability for systems of order\nN=1 and a special class of nonlinear controllers, and weak input-to-state\nstability for systems of arbitrary order N \∈ \ℕ and a more general\nclass of nonlinear controllers. Also, in both cases, we obtain convergence to\n0 of all solutions as t \→ \∞. Applications are given to vibrating\nstrings and beams.\n