Modern control algorithms require tuning of square weight/penalty matrices
appearing in quadratic functions/costs to improve performance and/or stability
output. Due to simplicity in gain-tuning and enforcing positive-definiteness,
diagonal penalty matrices are used extensively in control methods such as
linear quadratic regulator (LQR), model predictive control, and Lyapunov-based
control. In this paper, we propose an eigendecomposition approach to
parameterize penalty matrices, allowing positive-definiteness with non-zero
off-diagonal entries to be implicitly satisfied, which not only offers notable
computational and implementation advantages, but broadens the class of
achievable controls. We solve three control problems: 1) a variation of
Zermelo’s navigation problem, 2) minimum-energy spacecraft attitude control
using both LQR and Lyapunov-based methods, and 3) minimum-fuel and minimum-time
Lyapunov-based low-thrust trajectory design. Particle swarm optimization is
used to optimize the decision variables, which will parameterize the penalty
matrices. The results demonstrate improvements of up to 65% in the performance
objective in the example problems utilizing the proposed method.

Este artículo explora los viajes en el tiempo y sus implicaciones.

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