Optimal Control of a Constrained Bilinear Dynamic System

Ido Halperin (), Grigory Agranovich () and Yuri Ribakov ()
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Ido Halperin: Ariel University
Grigory Agranovich: Ariel University
Yuri Ribakov: Ariel University

Journal of Optimization Theory and Applications, 2017, vol. 174, issue 3, No 11, 803-817

Abstract: Abstract In this paper, an optimal feedback, for a free vibrating semi-active controlled plant, is derived. The problem is represented as a constrained optimal control problem of a single input, free vibrating bilinear system, and a quadratic performance index. It is solved by using Krotov’s method and to this end, a novel sequence of Krotov functions that suits the addressed problem, is derived. The solution is arranged as an algorithm, which requires solving the states equation and a differential Lyapunov equation in each iteration. An outline of the proof for the algorithm convergence is provided. Emphasis is given on semi-active control design for stable free vibrating plants with a single control input. It is shown that a control force, derived by the proposed technique, obeys the physical constraint related with semi-active actuator force without the need of any arbitrary signal clipping. The control efficiency is demonstrated with a numerical example.

Keywords: Optimal control; Feedback; Semi-active structural control; Krotov’s method; Bilinear quadratic regulator; 49K21; 49J15; 93C95; 34H05 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10957-017-1095-2

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