Algorithms and Theory in Filtering and Control (Mathematical Programming Study, 18) (Pt. 1)

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This volume and its companion, that together constitute the Proceedings of the Workshop on Numerical Techniques for Systems Engineering Problems held in Lexington, Kentucky (June 1980), are dedicated to the premise that modern techniques of linear algebra and non-classical optimization could be exploited to devise computational schemes for systems engineering problems that have all the desirable numerical qualifications. In this volume we record actual advances made in this direction as well as some recent theoretical developments in systems theory that appear to be intimately related. The variational and optimization techniques that appear to promise further development are reviewed in Part 2 of the Proceedings.

This collection begins with the demonstration by M. Pavon and R. J.-B. Wets that the duality between linear estimation and control follows from basic duality principles for convex optimization problems. The result is obtained by casting the estimation problem in the form of a stochastic convex optimization problem and showing that the control problem is its deterministic dual. This shows that nonlinear optimization, estimation, and control problems are intrinsically tied together. Recursive relations that yield the optimal estimators of a dynamical system are derived from this point of view. In the next paper Pavon illustrates the role played by the conjugate process y? in discrete time stochastic realization theory. Given a certain process y, the problem is to determine a Markov process x of smallest possible dimensions such that (x y) is Markov. In particular he shows that the input of every internal realization of y can be generated by an anticausal filter driven by the conjugate process.

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