Balancing for unstable nonlinear systems

A previously obtained method of balancing for stable nonlinear systems is extended to unstable nonlinear systems. The similarity invariants obtained by the concept of LQG balancing for an unstable linear system can also be obtained by considering a past and future energy function of the system. By considering a past and future energy function for an unstable nonlinear system, the concept of these similarity invariants for linear systems is extended to nonlinear systems. Furthermore the relation of this balancing method with the previously obtained method of balancing the coprime factorization of an unstable nonlinear system is considered. Both methods are introduced with the aim of using it as a tool for model reductio

Identification of Non-linear Nonautonomous State Space Systems from Input-Output Measurements

This paper presents a method to determine a nonlinear state-space model from a finite number of measurements of the inputs and outputs. The method is based on embedding theory for nonlinear systems, and can be viewed as an extension of the subspace identification method for linear systems. The paper describes the underlying theory and provides some guidelines for using the method in practice. To illustrate the use of the identification method, it was applied to a second-order nonlinear system

Power-based adaptive and integral control of standard mechanical systems

Recently a power-based modeling framework was introduced for mechanical systems, based on the Brayton-Moser framework. In this paper it is shown how this power-based framework is used for control of standard mechanical systems. For systems which are affected by parameter uncertainty or other unknown disturbances adaptive control and integral control are also described in this framework. The power-based control approach is also compared with the energy-shaping control of port-Hamiltonian systems. The most interesting difference is the possibility of having adaptive and integrator dynamics depending on position errors, while preserving the physical structure