Abstract
We deal with a problem of target control synthesis for dynamical bilinear discrete-time systems under uncertainties (which describe disturbances, perturbations or unmodelled dynamics) and state constraints. Namely we consider systems with controls that appear not only additively in the right hand sides of the system equations but also in the coefficients of the system. We assume that there are uncertainties of a set-membership kind when we know only the bounding sets of the unknown terms. We presume that we have uncertain terms of two kinds, namely, a parallelotope-bounded additive uncertain term and interval-bounded uncertainties in the coefficients. Moreover the systems are considered under constraints on the state (under viability constraints). We continue to develop the method of control synthesis using polyhedral (parallelotope-valued) solvability tubes. The technique for calculation of the mentioned polyhedral tubes by the recurrent relations is presented. Control strategies, which can be constructed on the base of the polyhedral solvability tubes, are proposed. Illustrative examples are considered.
Highlights
We deal with a problem of target control synthesis for dynamical discrete-time systems with a bilinear structure under uncertainties and state constraints (SC)
The problem of construction of the mentioned trajectory tubes that describe the dynamics of reachable sets, solvability sets, informational domains [24, 25] may be called one of the fundamental problems of the mathematical control theory
Recall that in [19, 21] for cases (A), (B,i), (B,ii) without SC the polyhedral techniques were proposed for synthesis of controls which appear either additively or in the system matrix; such controls can be constructed by explicit formulas
Summary
We deal with a problem of target control synthesis for dynamical discrete-time systems with a bilinear structure under uncertainties and state constraints (SC). Discrete-time systems, uncertain systems, state constraints, control synthesis, polyhedral technique, parallelepipeds, parallelotopes, interval analysis. As for solving the feedback target control problems for differential and discretetime systems, constructive computation schemes using ellipsoidal techniques were proposed [8, 24, 25, 26, 35] and expanded to the polyhedral techniques that use polyhedral (parallelotope-valued) solvability tubes [15, 17, 19, 20, 21, 22] (this had required the development of a quite different techniques).
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