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In this article we introduce the use of recently developed min/max-plus techniques in order to solve the optimal attitude estimation problem in filtering for nonlinear systems on the special orthogonal (SO(3)) group. This work helps obtain computationally efficient methods for the synthesis of deterministic filters for nonlinear systems -- i.e. optimal filters which estimate the state using a related optimal control problem. The technique indicated herein is validated using a set of optimal attitude estimation example problems on SO(3).
We develop a model predictive control (MPC) design for systems with discrete-time dynamics evolving on smooth manifolds. We show that the properties of conventional MPC for dynamics evolving on $mathbb R^n$ are preserved and we develop a design proce
The problem of attitude tracking using rotation matrices is addressed using an approach which combines inverse optimality and $mathcal{L}_{2}$ disturbance attenuation. Conditions are provided which solve the inverse optimal nonlinear $H_{infty}$ cont
A robust (deterministic) filtering approach to the problem of optimal sensor selection is considered herein. For a given system with several sensors, at each time step the output of one of the sensors must be chosen in order to obtain the best state
Low-dimensional embeddings for data from disparate sources play critical roles in multi-modal machine learning, multimedia information retrieval, and bioinformatics. In this paper, we propose a supervised dimensionality reduction method that learns l
We introduce a new hybrid control strategy, which is conceptually different from the commonly used synergistic hybrid approaches, to efficiently deal with the problem of the undesired equilibria that precludes smooth vectors fields on $SO(3)$ from ac