AN OPTIMAL CONTROL MODEL FOR TUBERCULOSIS-DIABETES DYNAMICS

Taking the full-vehicle eight-freedom dynamic model of a type of bus as the simulation object , a new optimal control method is introduced. This method is based on the genetic algorithm, and the full-vehicle optimal control model is built in the MatLab. The weight matrix of the optimal control is optimized through the genetic algorithm; then the outcome is compared with the artificially-set optimal control simulation, which shows that the genetic-algorithm based optimal control presents better performance, thereby creating a smoother ride and improving the steering stability of the vehicle.

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Mathematical modeling and optimal control of corruption dynamics

Asian-European Journal of Mathematics ◽

10.1142/s1793557118500900 ◽

2018 ◽

Vol 11 (06) ◽

pp. 1850090 ◽

Cited By ~ 6

Author(s):

S. Athithan ◽

Mini Ghosh ◽

Xue-Zhi Li

Keyword(s):

Mathematical Modeling ◽

Optimal Control ◽

Developing Countries ◽

Numerical Simulations ◽

Equilibrium Point ◽

Present Model ◽

Control Model ◽

Asymptotically Stable ◽

Epidemiological Modeling ◽

Control Of Corruption

The problem of corruption is of serious concern in all the nations, more so in the developing countries. This paper presents the formulation of a corruption control model and its analysis using the theory of differential equations. We found the equilibria of the model and stability of these equilibria are discussed in detail. The threshold quantity [Formula: see text] which has a similar implication here as in the epidemiological modeling is obtained for the present model. The corruption free equilibrium is found to be stable when [Formula: see text] is less than [Formula: see text] and unstable for [Formula: see text]. The endemic equilibrium which signifies the presence of corrupted individuals in the society exists only when [Formula: see text]. This equilibrium point is locally asymptotically stable whenever it exists. We perform extensive numerical simulations to support the analytical findings. Furthermore, we extend the model to include optimal control and the optimal control profile is obtained to get the maximum control within a stipulated period of time. Our presented results show that the level of corruption in the society can be reduced if corruption control efforts through media/punishments etc. are increased and put in place.

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Spectrum of power laws for curved hand movements

Proceedings of the National Academy of Sciences ◽

10.1073/pnas.1510208112 ◽

2015 ◽

Vol 112 (29) ◽

pp. E3950-E3958 ◽

Cited By ~ 31

Author(s):

Dongsung Huh ◽

Terrence J. Sejnowski

Keyword(s):

Optimal Control ◽

Motor Planning ◽

Power Laws ◽

Angular Frequency ◽

Control Model ◽

Hand Movements ◽

Local Curvature ◽

Scale Invariant ◽

The Past ◽

Invariant Features

In a planar free-hand drawing of an ellipse, the speed of movement is proportional to the −1/3 power of the local curvature, which is widely thought to hold for general curved shapes. We investigated this phenomenon for general curved hand movements by analyzing an optimal control model that maximizes a smoothness cost and exhibits the −1/3 power for ellipses. For the analysis, we introduced a new representation for curved movements based on a moving reference frame and a dimensionless angle coordinate that revealed scale-invariant features of curved movements. The analysis confirmed the power law for drawing ellipses but also predicted a spectrum of power laws with exponents ranging between 0 and −2/3 for simple movements that can be characterized by a single angular frequency. Moreover, it predicted mixtures of power laws for more complex, multifrequency movements that were confirmed with human drawing experiments. The speed profiles of arbitrary doodling movements that exhibit broadband curvature profiles were accurately predicted as well. These findings have implications for motor planning and predict that movements only depend on one radian of angle coordinate in the past and only need to be planned one radian ahead.

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