On feedback target control for uncertain discrete-time bilinear systems with state constraints through polyhedral technique

Estimation and Synthesis of Reachable Set for Singular Markovian Jump Systems

“…On the other hand, the problem of controller design for specifications involved with the reachable set of a control system is also a very important issue [33]. The controller design problems concerning reachable set were studied in [34] and [35] by using ellipsoidal method and polyhedron method, respectively. Two issues were raised in [34]: the first one is to design a controller such that the reachable set of the closed-loop system is contained in an ellipsoid, and the admissible ellipsoid should be as small as possible; the second one is to design a controller such that the reachable set of the closed-loop system is contained in a given ellipsoid.…”

On polyhedral control synthesis for dynamical discrete-time systems under uncertainties and state constraints

“…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 then 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). In [30,31], the polyhedral technique from [19,Sec.…”

“…An important for investigations class of dynamical systems is produced by systems with a bilinear structure, where matrices of coefficients may contain not only uncertainties but also controls. Such models may be useful in many applied areas from physics and engineering to biology, ecology, socioeconomics [32,33], [22,Ref. 23].…”

“…Moreover we consider the systems under constraints on the state ("under viability constraints"). To solve the problem of target control synthesis under these conditions we expand the techniques from [17,19,20,21,22] (some additional comments about these works will be given below). The technique for calculation of the polyhedral tubes by the recurrent relations is presented.…”

“…To solve Problem 2 for the general case we expand the techniques from [19,20,21,22]. As a result we can construct controls u and U by explicit formulas and obtain more rich family of the tubes P − [·] than it could be obtained using constructions from [18] as it was done in [19,22]. Note that expanding the technique from [17] for the general case with both controls u and U is an open question yet.…”