Discretization and model reduction for a class of nonlinear systems
Abstract
Nonlinear analysis for control design is required in many modern engineering systems. Strict performance requirements over wide ranges of operation cannot be met using linear models. The lack of structure in nonlinear models has hindered the development of analysis techniques. Many engineering systems are computer controlled so that methods of attaining structured discrete-time nonlinear models are needed. Many of these nonlinear models have high model order, and effective methods for order reduction need to be developed. This research addresses both the discretization problem and the model reduction problem for a large class of nonlinear systems. A method is developed for discretizing linear-analytic continuous-time systems. The solution for this class of nonlinear systems can be expressed as a Volterra series. Two steps are implemented in the method: first a bilinearization of the original system is formed to yield a model whose Volterra series solution matches the Volterra series of the original system through a given number of terms. Next, by assuming piecewise constant input variables a discretization of the bilinear model is performed by explicitly evaluating those terms that are matched in the bilinearization step. The result is a state-affine discrete-time system that represents an exact discretization of a specified number of terms in the Volterra series solution of a given linear-analytic continuous-time system. An algorithm is presented for constructing low order approximations of state-affine discrete-time systems. A set of reduced order models that are not related by a similarity transformation evolve from factorizations of two matrices that reflect the reachability and observability properties of the full order model. The reduced order models match exactly a specified number of two types of system parameters: a set of Volterra parameters and a set of covariance parameters. The infinite sets of these parameters provide fundamental descriptions for the deterministic input-output characteristics and the steady state stochastic input-output correlations of the full order state-affine discrete-time system. The model reduction algorithm for state-affine systems is based on a new approach for constructing q-Markov covariance equivalent realizations of linear discrete-time systems. In the linear discrete-time case, the algorithm solves a model reduction problem and a partial realization problem.
Degree
Ph.D.
Advisors
Skelton, Purdue University.
Subject Area
Aerospace materials
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