Equations of motion for Hamiltonian systems with constraints

In this paper the problem of obtaining the equations of motion for Hamiltonian systems with constraints is considered. Conditions are given which ensure that the phase space points satisfying the primary and secondary constraints form a symplectic manifold, on which the resulting equations of motion are Hamiltonian and uniquely determine

Linearization and input-output decoupling for general nonlinear systems

Necessary and sufficient conditions are obtained for the linearization and input decoupling (by state feedback) of general nonlinear systems. It is shown how these conditions can be derived from the already known conditions for affine nonlinear systems, thereby also elucidating the existing theory for affine systems

Robust stabilization of nonlinear systems via stable kernel representations with L2-gain bounded uncertainty

The approach to robust stabilization of linear systems using normalized left coprime factorizations with H∞ bounded uncertainty is generalized to nonlinear systems. A nonlinear perturbation model is derived, based on the concept of a stable kernel representation of nonlinear systems. The robust stabilization problem is then translated into a nonlinear disturbance feedforward H∞ optimal control problem, whose solution depends on the solvability of a single Hamilton-Jacobi equation

Representing a nonlinear state space system as a set of higher-order differential equations in the inputs and ouputs

An algorithm is presented for transforming a nonlinear state space system into a threefold set of equations; the first subset describing the dynamics of the unobservable part of the system, the second subset representing the remaining state variables as functions of inputs and outputs and their derivatives, and the last subset defining the external behaviour of the system

Controlled invariance for hamiltonian systems

A notion of controlled invariance is developed which is suited to Hamiltonian control systems. This is done by replacing the controlled invariantdistribution, as used for general nonlinear control systems, by the controlled invariantfunction group. It is shown how Lagrangian or coisotropic controlled invariant function groups can be made invariant by static, respectively dynamic, Hamiltonian feedback. This constitutes a first step in the development of a geometric control theory for Hamiltonian systems that explicitly uses the given structure

Input-output decoupling with stability for Hamiltonian systems

The input-output decoupling problem with stability for Hamiltonian systems is treated using decoupling feedbacks, all of which make the system maximally unobservable. Using the fact that the dynamics of the maximal unobservable subsystem are again Hamiltonian, an easily checked condition for input-output decoupling with (critical) stability is deduced

Hamiltonian formulation of distributed-parameter systems with boundary energy flow

A Hamiltonian formulation of classes of distributed-parameter systems is presented, which incorporates the energy flow through the boundary of the spatial domain of the system, and which allows to represent the system as a boundary control Hamiltonian system. The system is Hamiltonian with respect to an infinite-dimensional Dirac structure associated with the exterior derivative and based on Stokes' theorem. The theory is applied to the telegraph equations for an ideal transmission line, Maxwell's equations on a bounded domain with non-zero Poynting vector at its boundary, and a vibrating string with traction forces at its ends. Furthermore the framework is extended to cover Euler's equations for an ideal fluid on a domain with permeable boundary. Finally, some properties of the Stokes-Dirac structure are investigated, including the analysis of conservation laws. \u

Symmetry and reduction in implicit generalized Hamiltonian systems

In this paper the notion of symmetry for implicit generalized Hamiltonian systems will be studied and a reduction theorem, generalizing the 'classical' reduction theorems of symplectic and Poisson-Hamiltonian systems, will be derived. \u