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Invariant Set-based Methods for the Computation of Input and Disturbance Sets

Mulagaleti, Sampath Kumar (2023) Invariant Set-based Methods for the Computation of Input and Disturbance Sets. Advisor: Bemporad, Prof. Alberto. Coadvisor: Zanon, Prof. Mario . pp. 236. [IMT PhD Thesis]

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This dissertation presents new methods to synthesize disturbance sets and input constraints set for constrained linear time-invariant systems. Broadly, we formulate and solve optimization problems that (a) compute disturbance sets such that the reachable set of outputs approximates an assigned set, and (b) compute input constraint sets guaranteeing the stabilizability of a given set of initial conditions. The proposed methods find application in the synthesis and analysis of several control schemes such as decentralized control, reduced-order control, etc., as well as in practical system design problems such as actuator selection, etc. The key tools supporting the develpment of the aforementioned methods are Robust Positive Invariant (RPI) sets. In particular, the problems that we formulate are such that they co-synthesize disturbance/input constraint sets along with the associated RPI sets. This requires embedding existing techniques to compute RPI sets within an optimization problem framework, that we facilitate by developing new results related to properties of RPI sets, polytope representations, inclusion encoding techniques, etc. In order to solve the resulting optimization problems, we develop specialized structure-exploiting solvers that we numerically demonstrate to outperform conventional solution methods. We also demonstrate several applications of the methods we propose for control design. Finally, we extend the methods to tackle data-driven control synthesis problems in an identification-for-control framework.

Item Type: IMT PhD Thesis
Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
PhD Course: Computer science and systems engineering
Identification Number: https://doi.org/10.13118/imtlucca/e-theses/370
NBN Number: urn:nbn:it:imtlucca-28955
Date Deposited: 18 Jan 2023 08:24
URI: http://e-theses.imtlucca.it/id/eprint/370

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