Superposition in a class of nonlinear systems.
Nonlinear systems satisfying generalized principle of superposition, noting application to feedback control
SIGNAL TRANSMISSION↗
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Superposition in a class of nonlinear systems
Nonlinear systems satisfying generalized principle of superposition, noting application to feedback control
NONLINEAR SYSTEM↗
A natural coordinate system for nonlinear systems
A natural coordinate system for nonlinear systems of the form x = f(x) + g(x)u is discussed where x is a element of R(N), u is an element of R, and f and g are analytic, vector-valued functions on R(N). It is shown that in these coordinates the equation becomes a system with only feedback paths (no feedforwards), if feedback linearizability conditions are satisfied.
Su, R.↗
The effect of system nonlinearities on system noise statistics
The effects are studied of nonlinearities in a baseline communications system on the system noise amplitude statistics. So that a meaningful identification of system nonlinearities can be made, the baseline system is assumed to transmit a single biphase-modulated signal through a relay satellite to the receiving equipment. The significant nonlinearities thus identified include square-law or product devices (e.g., in the carrier reference recovery loops in the receivers), bandpass limiters, and traveling wave tube amplifiers.
Robinson, L. H., Jr.↗
A method for high order linear system reduction and nonlinear system simplification
Least-squares-type algorithms for reducing the order of linear systems in the frequency domain and simplifying nonlinear systems in time domain are developed and demonstrated. The possible model structures are represented as nodes in a tree, and costs along the branches are assigned using the repeated-Gram-Schmidt orthogonalization procedure of Desrochers and Saridis (1980), permitting identification of the optimal n-term model by searching the tree to depth n, with no need for parameter identification. The efficiency and flexibility of the algorithms is shown in applications to the eighth-order linear system studied by Hsia (1972), a three-state eight-nonlinear-term aircraft-dynamics problem, and the related linear-controller problem (Garrard and Jordan, 1977).
Desrochers, A. A.↗
Analysis and design of space vehicle flight control systems. Volume IV - Nonlinear systems
Analysis and design of nonlinear space vehicle flight control systems
SPACE VEHICLE CONTROL↗
A note on Stratonovich's equation for the conditional probability distribution of the state of a nonlinear system, with application to nonlinear filtering
Analysis of equation for conditional probability distribution of state of nonlinear system and application to nonlinear filtering
STATE EQUATION↗
The stabilization of a nonlinear system using a linear system estimator
Nonlinear systems stabilization with linear system estimator output state to provide feedback for asymptotic stability of overall system
Strane, R. E.↗
Maximized Gust Loads of a Closed-Loop, Nonlinear Aeroelastic System Using Nonlinear Systems Theory
The problem of computing the maximized gust load for a nonlinear, closed-loop aeroelastic aircraft is discusses. The Volterra theory of nonlinear systems is applied in order to define a linearized system that provides a bounds on the response of the nonlinear system of interest. The method is applied to a simplified model of an Airbus A310.
Silva, Walter A.↗
Superposition in a class of nonlinear systems
Characterization of nonlinear systems based on linear algebra
NONLINEAR SYSTEM↗
A design methodology for nonlinear systems containing parameter uncertainty: Application to nonlinear controller design
A design methodology capable of dealing with nonlinear systems, such as a controlled ecological life support system (CELSS), containing parameter uncertainty is discussed. The methodology was applied to the design of discrete time nonlinear controllers. The nonlinear controllers can be used to control either linear or nonlinear systems. Several controller strategies are presented to illustrate the design procedure.
Young, G.↗
Model reference adaptive control for linear time varying and nonlinear systems
Model reference adaptive control is applied to linear time varying systems and to nonlinear systems amenable to virtual linearization. Asymptotic stability is guaranteed even if the perfect model following conditions do not hold, provided that some sufficient conditions are satisfied. Simulations show the scheme to be capable of effectively controlling certain nonlinear systems.
Abida, L.↗
Nonlinear system approximations
The approximation of a nonlinear system by a feedback linearizable system instead of a linear system is considered. Two approaches presently exist in the literature. One involves the concept of involutivity to a certain order, and the other considers a canonical expansion and pure feedback approximation. The relationship between these two methods is shown. This provides insight into lower-order invariants in the equivalence problem for two nonlinear systems. The output time responses for a nonlinear system and its feedback linearizable approximation are outlined.
Goldthwait, Richard G.↗
Controllability for linear and nonlinear systems
Controllability for linear and nonlinear systems
NONLINEAR SYSTEM↗
Feedback invariants for nonlinear systems
The effect of nonlinear feedback on nonlinear systems is discussed for problems where the controls are entered linearly. The invariance of certain quantities under feedback are established, and it is shown that these quantities contain enough information to determine if the system can be linearized using feedback and change of coordinates. Attention is given to scalar input systems emphasizing a new F-invariant property.
Brockett, R. W.↗
Application of the comparison principle to analysis of nonlinear systems
A comparison principle based on a Kamke theorem and Lipschitz conditions is presented along with its possible applications and modifications. It is shown that the comparison lemma can be used in the study of such areas as classical stability theory, higher order trajectory derivatives, Liapunov functions, boundary value problems, approximate dynamic systems, linear and nonlinear systems, and bifurcation analysis.
Gunderson, R. W.↗
Global transformations of nonlinear systems
Necessary and sufficient conditions for a nonlinear system of equations to be locally equivalent, in a neighborhood of the origin in the real number system, to a controllable linear system are combined with several versions of the global inverse function theorem to define sufficient conditions for transforming the nonlinear system into a linear system. Additionally, a technique is introduced for developing a transformation under the assumptions that the columns of a controllability matrix span an n-dimensional space. Finally, the n-l form of the controllability matrix columns is demonstrated to be involutive
Hunt, L. R.↗
A canonical form for nonlinear systems
The concepts of transformation and canonical form have been used in analyzing linear systems. These ideas are extended to nonlinear systems. A coordinate system and a corresponding canonical form are developed for general nonlinear control systems. Their usefulness is demonstrated by showing that every feedback linearizable system becomes a system with only feedback paths in the canonical form. For control design involving a nonlinear system, one approach is to put the system in its canonical form and approximate by that part having only feedback paths.
Su, R.↗