This paper considers actuator redundancy management for a class of overactuated nonlinear systems. Two tools for distributing the control effort among a redundant set of actuators are optimal control design and control allocation. In this paper, we investigate the relationship between these two design tools when the performance indexes are quadratic in the control input. We show that for a particular class of nonlinear systems, they give exactly the same design freedom in distributing the control effort among the actuators. Linear quadratic optimal control is contained as a special case. A benefit of using a separate control allocator is that actuator constraints can be considered, which is illustrated with a flight control example.

Calculus of Variations and Optimal Control Theory.

Resolving actuator redundancy: optimal control vs. control allocation

The one sentence answer to the question in the title is that the ability to prove depends on forms of knowledge to which most students are rarely if ever exposed. The paper gives a more detailed analysis, drawing on research in mathematics education and classroom experiences.

Why Johnny Can't Prove

In this paper, we propose an image segmentation technique based on augmenting the conformal (or geodesic) active contour framework with directional information. In the isotropic case, the euclidean metric is locally multiplied by a scalar conformal factor based on image information such that the weighted length of curves lying on points of interest (typically edges) is small. The conformal factor that is chosen depends only upon position and is in this sense isotropic. Although directional information has been studied previously for other segmentation frameworks, here, we show that if one desires to add directionality in the conformal active contour framework, then one gets a well-defined minimization problem in the case that the factor defines a Finsler metric. Optimal curves may be obtained using the calculus of variations or dynamic programming-based schemes. Finally, we demonstrate the technique by extracting roads from aerial imagery, blood vessels from medical angiograms, and neural tracts from diffusion-weighted magnetic resonance imagery.

/pdf/finsler-active-contours-1cpr3kbac0.pdf

Finsler Active Contours

Optimal Continuous Torque Attitude Maneuvers

The search for the optimal profile for a longitudinal fin has occupied a portion of the mathematics and engineering communities for almost 60 years. Heuristic and rigorous arguments have led to definitive answers only when the “length of arc” idealization is involved. This paper reviews the chronology of these research efforts and offers some counterexamples, with regard to the usual models, which indicate that fins of mathematically unbounded performance are theoretically (although not practically) achievable. The construction of such fins, in the practical limit, suggests some promising new horizons in extended-surface heal transfer.

Calculus of Variations and Optimal Control Theory.

Citations

Resolving actuator redundancy: optimal control vs. control allocation

Why Johnny Can't Prove

Finsler Active Contours

Optimal Continuous Torque Attitude Maneuvers

The Quest for the Optimum Longitudinal Fin Profile

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