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Deterministic Control Theory
In this chapter we focus our attention on the open loop control of deterministic problems. We will see that the language of deterministic control...
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Optimization Problems
Several problems, for example Pontryagin’s maximum principle or the minimax problems of game theoretical approaches, require the determination of an...
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Optimal Control of Stochastic Processes
Many control problems appearing for complex systems are subject to imperfectly known disturbances. As we have learned in the previous chapter, these...
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Chaos Control
In the previous chapters we have discussed the control theory from a mechanical and field theoretical point of view. This control theory is, of...
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Game Theory
All systems analyzed up to now were more or less predictable. That means, we had some information about the initial state and the dynamics of the...
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Control of Fields
The theoretical representation of classical mechanics and field theory is very similar in some ways. This also applies to the axiomatic structure. It...
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Nonequilibrium Statistical Physics
Although most many-body systems are beyond the technical possibilities of the mathematical calculus of mechanics, we are able to calculate the...
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Filters and Predictors
Suppose we have a system under control, described by dynamical equations of motion for the N-dimensional state vector X(t), and we have obtained an...
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Introduction
Control theory plays an important role in several .elds of economics, technological sciences, and mathematics. On the other hand, control theory is...
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Linear Quadratic Problems
Suppose we have a deterministic system under control, described by dynamical equations of motion for an N-dimensional state vector X(t). Usually,...
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A Globally Convergent Inertial First-Order Optimization Method for Multidimensional Scaling
Multidimensional scaling (MDS) is a popular tool for dimensionality reduction and data visualization. Given distances between data points and a...
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Bilevel Optimization of the Kantorovich Problem and Its Quadratic Regularization
This paper is concerned with an optimization problem which is governed by the Kantorovich problem of optimal transport. More precisely, we consider a...
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Dimensional reduction technique for the prediction of global and local responses of unidirectional composite with matrix nonlinearity and varying fiber packing geometry
The problem associated with the computational homogenization of composite materials often results in expensive computational cost that prevents...
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Second order necessary condition for a strong minimum in the classical problem of calculus of variations
The paper offers a second order necessary condition for a strong minimum in the standard problem of calculus of variations. No idea of such a result...