Stochastic adaptive estimation with applications to nonlinear control

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Virginia Tech


This dissertation is concerned with the development of two adaptive state estimators that are capable of tracking linear plants that undergo rapid configuration changes. The first is a modification of the Partitioned Adaptive Estimator, PAE, first introduced by Magill in 1965, improved and named by Lainiotis, and used in a number of applications, primarily aerospace. The PAE algorithm was derived for the problem of identifying which, of N, configurations that a linear plant is in; the key assumption being that the configuration is unknown but unchanging. There are two main difficulties in extending the PAE algorithm to the problem of estimating the state of a linear plant that can undergo configuration changes (the switched-linear plant problem). These two difficulties are addressed and solved in this dissertation. The result is called the modified PAE algorithm.

The second adaptive estimator developed in this dissertation is the "Sliding Window Detector/Estimator” or SWDE algorithm. Unlike the modified PAE algorithm whose basic structure is designed to solve a different problem, the SWDE algorithm is designed specifically for the switched-linear plant problem. It uses a joint detection/estimation approach to give a very close approximation to the unrealizable optimum switched-linear estimator.

The advantages and disadvantages of the two adaptive estimators are discussed, and it is found that a very reliable and accurate estimator can be constructed by combining both algorithms. Several different examples are given to clarify the operation of the estimator.

A second contribution of this dissertation is in the application of the above estimators to the nonlinear estimation problem. The motivation for this approach is that a nonlinear plant can be approximated by a sequence of linear approximations, or configurations. Thus, an estimator that works for a switched-linear plant can perform as a sub-optimum nonlinear estimator. In addition, a stochastic nonlinear controller can be constructed using the nonlinear estimator as the observer. This approach has several significant implementation and design advantages which are discussed in the dissertation and illustrated by two examples, a set-point control example and a trajectory-following aircraft example.

The above examples and algorithms were fully verified by extensive computer simulation. The implementation advantages afforded by these methods make them practical in a wide variety of applications.