The Problem of Measurement Output Control under Set-membership Uncertainty

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A key problem of control theory is to construct feedback control laws based on available data and to determine how the level of uncertainty in the model and in the information arriving on-line, through noisy measurements, would affect the system performance. In the absence of statistical description such problems of Measurement Output Feedback Control (MOFC) were investigated mostly within the H(inf) setting, with soft-type integral costs, while problems with hard bounds on the unknowns were less developed. The present proposal is aimed to produce a fairly complete investigation of the problem of output feedback control constructed through available measurements under unknown but bounded disturbances subject to hard bounds on the uncertain items. The proposal covers topics from basic theoretical problems to computational methods. The novelty of the suggested solution schemes, applicable to nonlinear systems, with greater specifics for the linear case, lies in the combination of dynamic programming, set-valued analysis and minmax approaches. It is well understood that the overall problem under consideration is a combination of two ? a finite-dimensional problem of guaranteed state estimation and an infinite-dimensional problem of feedback control under set-membership uncertainty. The second problem is especially difficult to formalize and solve. In the proposed solution, based on earlier work, the aim is to reduce the second problem to a finite-dimensional one, which would facilitate calculation. For systems with linear structure and convex constraints the computational procedure is to be based on using and also generalizing the ellipsoidal calculus which proved effective for many problems and allows development of complementary software. It is expected that such approach will produce solutions "to the end," with illuminating examples. For the nonlinear case calculations may be facilitated by using the specifics of the problem and applying modifications of the earlier suggested comparison principles that allow one to relax the original equations or variational inequalities of the Hamilton-Jacobi type through simpler, finite-dimensional relations.The Measurement Output Feedback Control (MOFC) problem has been thoroughly studied in a stochastic setting as a combination of stochastic filtering theory within the theory of stochastic control. However a considerable number of problems in control design have to deal with systems subjected to information conditions that are other than stochastic. Such problems of MOFC are increasingly motivated by applied issues, given the progress in design of high-tech complex systems arising in automation, navigation and the cyber-physical field (including hybrid, impulsive, time-lag, multi-agent, communication-oriented processes and the like). They naturally require new techniques, new types of models and their mathematical formalization, as well as new numerical methods, algorithms and software. The present project is designed in response to the indicated demand.