Claude H. Moog

Linearization of Discrete-Time Systems

The algebraic formalism developed in this paper unifies the study of the accessibility problem and various notions of feedback linearizability for discrete-time nonlinear systems. The accessibility problem for nonlinear discrete-time systems is shown to be easy to tackle by means of standard linear algebraic tools, whereas this is not the case for nonlinear continuous-time systems, in which case the most suitable approach is provided by differential geometry. The feedback linearization problem for discrete-time systems is recasted through the language of differential forms. In the event that a system is not feedback linearizable, the largest feedback linearizable subsystem is characterized within the same formalism using the notion of derived flag of a Pfaffian system. A discrete-time system may be linearizable by dynamic state feedback, though it is not linearizable by static state feedback. Necessary and sufficient conditions are given for the existence of a so-called linearizing output, which in turn is a sufficient condition for dynamic state feedback linearizability.

Identifiability of nonlinear systems with application to HIV/AIDS models

In this note, we investigate different concepts of nonlinear identifiability in the generic sense. We work in the linear algebraic framework. Necessary and sufficient conditions are found for geometrical identifiability, algebraic identifiability and identifiability with known initial conditions. Relationships between different concepts are characterized. Constructive procedures are worked out for both generic geometrical and algebraic identifiability of nonlinear systems. As an application of the theory developed, we study the identifiability properties of a four dimensional model of HIV/AIDS. The questions answered in this study include the minimal number of measurement of the variables for a complete determination of all parameters and the best period of time to make such measurements. This information will be useful in formulating guidelines for clinical practice.

Rank invariants of nonlinear systems

A linear algebraic framework for the analysis of rank properties of nonlinear systems is introduced. This framework gives a high-level interpretation of several existing algorithms built around the recursive computation of certain algebraic ranks associated with right-invertibility, left-invertibility, and dynamic decoupling. Furthermore, it can be used to establish links between these algorithms and the differential algebraic approach, as well as to solve some static and dynamic noninteracting control problems.

A linear algebraic framework for dynamic feedback linearization

To any accessible nonlinear system we associate a so-called infinitesimal Brunovsky form. This gives an algebraic criterion for strong accessibility as well as a generalization of Kronecker controllability indices. An output function which defines a right-invertible system without zero dynamics is shown to exist if and only if the basis of the Brunovsky form can be transformed into a system of exact differential forms. This is equivalent to the system being differentially flat and hence constitutes a necessary and sufficient condition for dynamic feedback linearizability. >

New algebraic-geometric conditions for the linearization by input-output injection

The goal of this paper is twofold. It unifies and generalizes existing results on input-output injection linearization of nonlinear systems. The problem is solved as a realization problem since it is based on the analysis of the structure of the input-output differential equation. The necessary and sufficient conditions are derived from a simplified and constructive procedure. For clarity, the paper is limited to the case of single output systems. Exterior differential systems are extensively used throughout the paper, giving constructive conditions.

The disturbance decoupling problem for time-delay nonlinear systems

In this paper, the disturbance decoupling problem (DDP) for a class of SISO nonlinear systems with multiple delays in the input and the state is studied. A pioneering mathematical approach is introduced for this class of systems and is claimed to be the cornerstone of the problem. Necessary and sufficient conditions are given for the existence of a bicausal feedback that solves the DDP. Sufficient conditions for the existence of a solution within other classes of compensators are included as well.

Input-output feedback linearization of time-delay systems

In this note, the input-output linearization problem (IOLP) for a class of single-input-single-output nonlinear systems with multiple delays in the input, the output, and the state is studied. The problem is solved by means of various static or dynamic compensators, including state and output feedback. The mathematical setting is based on some noncommutative algebraic tools and the introduction of a nonlinear version of the so-called Roesser models for this class of systems. These are claimed to be the cornerstones for studying nonlinear time-delay systems. Necessary and sufficient conditions are given for the existence of a static or pure shift output feedback which solves the IOLP. Sufficient conditions for the existence of a dynamic state feedback solution are included as well.

Brief Analysis of nonlinear time-delay systems using modules over non-commutative rings

The theory of non-commutative rings is introduced to provide a basis for the study of nonlinear control systems with time delays. The left Ore ring of non-commutative polynomials defined over the field of meromorphic function is suggested as the framework for such a study. This approach is then generalized to a broader class of nonlinear systems with delays that are called generalized Roesser systems. Finally, the theory is applied to analyze nonlinear time-delay systems. A weak observability is defined and characterized, generalizing the well-known linear result. Properties of closed submodules are then developed to obtain a result on the accessibility of such systems.

Experimental results for the end-effector control of a single flexible robotic arm

Various control schemes for a single flexible robot arm are considered in this paper. They require a limited amount of on-line computations. All trials are performed on the physical process and embody a conclusive, although partial, comparison for this kind of single axis robot. They are representative of some major applied research directions which captured the attention of many researchers throughout the 1980s. Some general conclusions are derived. >

Model matching and factorization for nonlinear systems: a structural approach

The model matching and the left factorization problems for nonlinear systems are investigated using an approach based on the structural algorithm. Sufficient conditions for the solvability of the f...