Robust Nonlinear Control. Port-controlled Hamiltonian Systems: Towards a Theory for Control and Design of Nonlinear Physical Systems.

It is shown how network modeling of lumped-parameter physical systems naturally leads to a geometrically defined class of systems, called port-controlled Hamiltonian systems with dissipation. The structural properties of these systems are discussed, in particular the existence of Casimir functions and their implications for stability. It is shown how a power-conserving interconnection of port-controlled Hamiltonian systems defines another port-controlled Hamiltonian system, and how this may be used for design and for control by shaping the internal energy.

[1]  A. Schaft,et al.  On Representations and Integrability of Mathematical Structures in Energy-Conserving Physical Systems , 1999 .

[2]  Arjan van der Schaft,et al.  Interconnected mechanical systems, part I: geometry of interconnection and implicit Hamiltonian systems , 1997 .

[3]  I. Neĭmark,et al.  Dynamics of Nonholonomic Systems , 1972 .

[4]  Bernhard Maschke,et al.  An intrinsic Hamiltonian formulation of network dynamics: Non-standard Poisson structures and gyrators , 1992 .

[5]  Arjan van der Schaft,et al.  Energy-based Lyapunov functions for forced Hamiltonian systems with dissipation , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).

[6]  Bernhard Maschke,et al.  Modelling and Control of Mechanical Systems , 1997 .

[7]  Romeo Ortega,et al.  An energy-based derivation of lyapunov functions for forced systems with application to stabilizing control , 1999 .

[8]  Arjan van der Schaft,et al.  Non-linear dynamical control systems , 1990 .

[9]  Arjan van der Schaft,et al.  Screw-vector bond graphs for the kinestatic and dynamic modeling of multibody systems , 1994 .

[10]  A. Schaft,et al.  An intrinsic Hamiltonian formulation of the dynamics of LC-circuits , 1995 .

[11]  Arjan van der Schaft.  Interconnection and geometry , 1999 .

[12]  Arjan van der Schaft,et al.  Stabilization of port-controlled Hamiltonian systems via energy balancing , 1999 .

[13]  Stefano Stramigioli.  From differentiable manifold to interactive robot control , 1998 .

[14]  Arjan van der Schaft,et al.  Interconnected mechanical systems, part II: the dynamics of spatial mechanical networks , 1997 .

[15]  Romeo Ortega,et al.  Passivity-based Control of Euler-Lagrange Systems , 1998 .

[16]  van der Arjan Schaft,et al.  On the Hamiltonian Formulation of Nonholonomic Mechanical Systems , 1994 .

[17]  J. Willems.  Dissipative dynamical systems part I: General theory , 1972 .

[18]  P. Moylan,et al.  The stability of nonlinear dissipative systems , 1976 .

[19]  Arjan van der Schaft,et al.  A Hamiltonian viewpoint in the modelling of switching power converters , 1999 .

[20]  A. Schaft,et al.  Port-controlled Hamiltonian systems : modelling origins and systemtheoretic properties , 1992 .

[21]  J. Marsden,et al.  Introduction to mechanics and symmetry , 1994 .

[22]  A. J. Schaft,et al.  Stabilization of Hamiltonian systems , 1986 .

[23]  Suguru Arimoto,et al.  A New Feedback Method for Dynamic Control of Manipulators , 1981 .

[24]  A. Schaft,et al.  Variational and Hamiltonian Control Systems , 1987 .

[25]  Romeo Ortega,et al.  A Hamiltonian viewpoint in the modeling of switching power converters , 1999, Autom..

[26]  A. J. van der Schaft.  System theoretic properties of Hamiltonian systems with external forces , 1984 .

[27]  A. Schaft,et al.  The Hamiltonian formulation of energy conserving physical systems with external ports , 1995 .

[28]  Harry L. Trentelman,et al.  The mathematics of systems and control: from intelligent control to behavioral systems , 1999 .

[29]  Naomi Ehrich Leonard,et al.  Matching and stabilization by the method of controlled Lagrangians , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).

[30]  Arjan van der Schaft,et al.  Passive output feedback and port interconnection , 1998 .