We consider the design of structure-preserving discretization methods for the solution of systems of boundary controlled Partial Differential Equations (PDEs) thanks to the port-Hamiltonian formalism. We first provide...We consider the design of structure-preserving discretization methods for the solution of systems of boundary controlled Partial Differential Equations (PDEs) thanks to the port-Hamiltonian formalism. We first provide a novel general structure of infinite-dimensional port-Hamiltonian systems (pHs) for which the Partitioned Finite Element Method (PFEM) straightforwardly applies. The proposed strategy is applied to abstract multidimensional linear hyperbolic and parabolic systems of PDEs. Then we show that instructional model problems based on the wave equation, Mindlin equation and heat equation fit within this unified framework. Secondly, we introduce the ongoing project SCRIMP (Simulation and Control of Interactions in Multi-Physics) developed for the numerical simulation of infinite-dimensional pHs. SCRIMP notably relies on the FEniCS open-source computing platform for the finite element spatial discretization. Finally, we illustrate how to solve the considered model problems within this framework by carefully explaining the methodology. As additional support, companion interactive Jupyter notebooks are available.展开更多
In this paper, we use Port-Hamiltonian framework to stabilize the Lagrange <span style="font-family:Verdana;">points in the Sun-Earth three-dimensional Circular Restricted Three-Body Problem (CRTBP). T...In this paper, we use Port-Hamiltonian framework to stabilize the Lagrange <span style="font-family:Verdana;">points in the Sun-Earth three-dimensional Circular Restricted Three-Body Problem (CRTBP). Through rewriting the CRTBP into Port-Hamiltonian framework, we are allowed to design the feedback controller through ener</span><span style="font-family:Verdana;">gy-shaping and dissipation injection. The closed-loop Hamiltonian is </span><span style="font-family:Verdana;">a candidate of the Lyapunov function to establish nonlinear stability of the designed equilibrium, which enlarges the application region of feedback controller compared with that based on linearized dynamics. Results show that th</span><span style="font-family:Verdana;">e Port-Hamiltonian</span><span style="font-family:Verdana;"> a</span><span style="font-family:Verdana;">pproach allows us to successfully stabilize the Lagrange points, where the Linear Quadratic Regulator (LQR) may fail. The feedback </span><span style="font-family:Verdana;">system based on Port-Hamiltonian approach is also robust against whit</span><span style="font-family:Verdana;">e noise in the inputs.</span>展开更多
In this paper, the asymptotic stability of Port-Hamiltonian (PH) systems with constant inputs is studied. Constant inputs are useful for stabilizing systems at their nonzero equilibria and can be realized by step sign...In this paper, the asymptotic stability of Port-Hamiltonian (PH) systems with constant inputs is studied. Constant inputs are useful for stabilizing systems at their nonzero equilibria and can be realized by step signals. To achieve this goal, two methods based on integral action and comparison principle are presented in this paper. These methods change the convex Hamiltonian function and the restricted damping matrix of the previous results into a Hamiltonian function with a local minimum and a positive semidefinite matrix, respectively. Due to common conditions of Hamiltonian function and damping matrix, the proposed method asymptotically stabilizes more classes of PH systems with constant inputs than the existing methods. Finally, the validity and advantages of the presented methods are shown in an example.展开更多
This paper investigates the simultaneous stabilization of Port-Hamiltonian(PH) systems subject to actuation saturation(AS) and input delay. Firstly, two parallel connecting PH systems subject to the AS and input delay...This paper investigates the simultaneous stabilization of Port-Hamiltonian(PH) systems subject to actuation saturation(AS) and input delay. Firstly, two parallel connecting PH systems subject to the AS and input delay are proposed. Secondly, a simultaneous stabilization control law is designed by a difference between the two feedback control laws containing the input delay.Thirdly, computing a Lyapunov-Krasovskii function assures the simultaneous stabilization of the above systems. Finally, simulation is given to show the correctness of the proposed contents.展开更多
文摘We consider the design of structure-preserving discretization methods for the solution of systems of boundary controlled Partial Differential Equations (PDEs) thanks to the port-Hamiltonian formalism. We first provide a novel general structure of infinite-dimensional port-Hamiltonian systems (pHs) for which the Partitioned Finite Element Method (PFEM) straightforwardly applies. The proposed strategy is applied to abstract multidimensional linear hyperbolic and parabolic systems of PDEs. Then we show that instructional model problems based on the wave equation, Mindlin equation and heat equation fit within this unified framework. Secondly, we introduce the ongoing project SCRIMP (Simulation and Control of Interactions in Multi-Physics) developed for the numerical simulation of infinite-dimensional pHs. SCRIMP notably relies on the FEniCS open-source computing platform for the finite element spatial discretization. Finally, we illustrate how to solve the considered model problems within this framework by carefully explaining the methodology. As additional support, companion interactive Jupyter notebooks are available.
文摘In this paper, we use Port-Hamiltonian framework to stabilize the Lagrange <span style="font-family:Verdana;">points in the Sun-Earth three-dimensional Circular Restricted Three-Body Problem (CRTBP). Through rewriting the CRTBP into Port-Hamiltonian framework, we are allowed to design the feedback controller through ener</span><span style="font-family:Verdana;">gy-shaping and dissipation injection. The closed-loop Hamiltonian is </span><span style="font-family:Verdana;">a candidate of the Lyapunov function to establish nonlinear stability of the designed equilibrium, which enlarges the application region of feedback controller compared with that based on linearized dynamics. Results show that th</span><span style="font-family:Verdana;">e Port-Hamiltonian</span><span style="font-family:Verdana;"> a</span><span style="font-family:Verdana;">pproach allows us to successfully stabilize the Lagrange points, where the Linear Quadratic Regulator (LQR) may fail. The feedback </span><span style="font-family:Verdana;">system based on Port-Hamiltonian approach is also robust against whit</span><span style="font-family:Verdana;">e noise in the inputs.</span>
基金supported by the National Nature Science Fund of China(No.61603311).
文摘In this paper, the asymptotic stability of Port-Hamiltonian (PH) systems with constant inputs is studied. Constant inputs are useful for stabilizing systems at their nonzero equilibria and can be realized by step signals. To achieve this goal, two methods based on integral action and comparison principle are presented in this paper. These methods change the convex Hamiltonian function and the restricted damping matrix of the previous results into a Hamiltonian function with a local minimum and a positive semidefinite matrix, respectively. Due to common conditions of Hamiltonian function and damping matrix, the proposed method asymptotically stabilizes more classes of PH systems with constant inputs than the existing methods. Finally, the validity and advantages of the presented methods are shown in an example.
基金supported by Fundamental Research Funds for the Central Universities of China(No.2682014BR009EM)。
文摘This paper investigates the simultaneous stabilization of Port-Hamiltonian(PH) systems subject to actuation saturation(AS) and input delay. Firstly, two parallel connecting PH systems subject to the AS and input delay are proposed. Secondly, a simultaneous stabilization control law is designed by a difference between the two feedback control laws containing the input delay.Thirdly, computing a Lyapunov-Krasovskii function assures the simultaneous stabilization of the above systems. Finally, simulation is given to show the correctness of the proposed contents.
