Partial symmetries for nonlinear systems

We define the concept of partial symmetry for nonlinear systems, which is an intermediate notion between the concepts of symmetry and controlled invariance. It is shown how this concept can be used for a decomposition theory of nonlinear systems and is particularly suited as a framework for treating input-output decoupling problems

Energy-Storage Balanced Reduction of Port-Hamiltonian Systems

Supported by the framework of dissipativity theory, a procedure based on physical energy to balance and reduce port-Hamiltonian systems with collocated inputs and outputs is presented. Additionally, some relations with the methods of nonlinear balanced reduction are exposed. Finally a structure-preserving reduction method based on singular perturbations is shown.

Nonsquare Spectral Factorization for Nonlinear Control Systems

This paper considers nonsquare spectral factorization of nonlinear input affine state space systems in continuous time. More specifically, we obtain a parametrization of nonsquare spectral factors in terms of invariant Lagrangian submanifolds and associated solutions of Hamilton–Jacobi inequalities. This inequality is a nonlinear analogue of the bounded real lemma and the control algebraic Riccati inequality. By way of an application, we discuss an alternative characterization of minimum and maximum phase spectral factors and introduce the notion of a rigid nonlinear system.

A geometric approach to differential Hamiltonian systems and differential Riccati equations

Motivated by research on contraction analysis and incremental stability/stabilizability the study of 'differential properties' has attracted increasing attention lately. Previously lifts of functions and vector fields to the tangent bundle of the state space manifold have been employed for a geometric approach to differential passivity and dissipativity. In the same vein, the present paper aims at a geometric underpinning and elucidation of recent work on 'control contraction metrics' and 'generalized differential Riccati equations'

Controllability distributions and systems approximations: a geometric approach

Given a nonlinear system we determine a relation at an equilibrium between controllability distributions defined for a nonlinear system and a Taylor series approximation of it. The value of such a relation is appreciated if we recall that the solvability conditions as well as the solutions to some control synthesis problems can be stated in terms of geometric concepts like controlled invariant (controllability) distributions. The relation between these distributions at the equilibrium will help us to decide when the solvability conditions of this kind of problems are equivalent for the nonlinear system and its approximatio

A passivity approach to controller-observer design for robots

Passivity-based control methods for robots, which achieve the control objective by reshaping the robot system's natural energy via state feedback, have, from a practical point of view, some very attractive properties. However, the poor quality of velocity measurements may significantly deteriorate the control performance of these methods. In this paper the authors propose a design strategy that utilizes the passivity concept in order to develop combined controller-observer systems for robot motion control using position measurements only. To this end, first a desired energy function for the closed-loop system is introduced, and next the controller-observer combination is constructed such that the closed-loop system matches this energy function, whereas damping is included in the controller- observer system to assure asymptotic stability of the closed-loop system. A key point in this design strategy is a fine tuning of the controller and observer structure to each other, which provides solutions to the output-feedback robot control problem that are conceptually simple and easily implementable in industrial robot applications. Experimental tests on a two-DOF manipulator system illustrate that the proposed controller-observer systems enable the achievement of higher performance levels compared to the frequently used practice of numerical position differentiation for obtaining a velocity estimat

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