This paper presents a design framework of discrete-time regulators for linear, port-Hamiltonian, boundary control systems. The contribution is twofold. At first, a discrete-time approximation of the plant dynamics originally described by a linear PDE with boundary actuation is introduced. The discretisation is performed in time only. Thus, the 'distributed nature' of the state is maintained. Such a system inherits the passivity of the original one and is well-posed, namely the 'next' state always exists. The second result is the characterisation of discrete-time, linear controllers in the port-Hamiltonian form that render the closed-loop dynamics asymptotically stable. A numerical example illustrates the effectiveness of the proposed framework.
MacChelli A. (2023). Distributed-Parameter Port-Hamiltonian Systems in Discrete-Time. Institute of Electrical and Electronics Engineers Inc. [10.1109/CDC49753.2023.10383674].
Distributed-Parameter Port-Hamiltonian Systems in Discrete-Time
MacChelli A.
2023
Abstract
This paper presents a design framework of discrete-time regulators for linear, port-Hamiltonian, boundary control systems. The contribution is twofold. At first, a discrete-time approximation of the plant dynamics originally described by a linear PDE with boundary actuation is introduced. The discretisation is performed in time only. Thus, the 'distributed nature' of the state is maintained. Such a system inherits the passivity of the original one and is well-posed, namely the 'next' state always exists. The second result is the characterisation of discrete-time, linear controllers in the port-Hamiltonian form that render the closed-loop dynamics asymptotically stable. A numerical example illustrates the effectiveness of the proposed framework.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.