Abstract
In this paper we consider the problem of controlling the rotational motion of a rigid body using three independent control torques. Given a quadratic cost we seek stabilizing state feedback controllers which guarantee that all motions starting within a specified bounded set have cost less than a given number; i.e., we seek suboptimal stabilizing controllers. For a special class of cost functions, we present explicit expressions for suboptimal stabilizing controllers yielding a cost arbitrarily close to the infimal cost. For the general case, we present sufficient conditions which guarantee the existence of linear, suboptimal, stabilizing controllers.
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Rotea, M.A., Tsiotras, P. & Corless, M. Suboptimal Control of Rigid Body Motion with a Quadratic Cost. Dynamics and Control 8, 55–81 (1998). https://doi.org/10.1023/A:1008278929841
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DOI: https://doi.org/10.1023/A:1008278929841