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A mathematical model of the microalgal growth under various light regimes is required for the optimization of design parameters and operating conditions in a photobioreactor. As its modelling framework, bilinear system with single input is chosen in this paper. The earlier theoretical results on bilinear systems are adapted and applied to the special class of the so-called intermittent controls which are characterized by rapid switching of light and dark cycles. Based on such approach, the following...
This article proposes a decentralized navigation controller for a group of differential mobile robots that yields autonomous navigation, which allows reaching a certain desired position with a specific desired orientation, while avoiding collisions with dynamic and static obstacles. The navigation controller is constituted by two control loops, the so-called external control loop is based on crowd dynamics, it brings autonomous navigation properties to the system, the internal control loop transforms...
Block-based physical modeling is a methodology for modeling physical systems with different subsystems. Each subsystem may be modeled according to a different paradigm. Connecting systems of diverse nature in the discrete-time domain requires a unified interconnection strategy. Such a strategy is provided by the well-known wave digital principle, which had been introduced initially for the design of digital filters. It serves as a starting point for the more general idea of blockbased physical modeling,...
Since the release of the Bio 2010 report in 2003, significant emphasis has been placed on initiating changes in the way undergraduate biology and mathematics courses are taught and on creating new educational materials to facilitate those changes. Quantitative approaches, including mathematical models, are now considered critical for the education of the next generation of biologists. In response, mathematics departments across the country have initiated changes to their introductory calculus sequence,...
The theory of partially observable Markov decision processes (POMDPs) is a useful tool for developing various intelligent agents, and learning hierarchical POMDP models is one of the key approaches for building such agents when the environments of the agents are unknown and large. To learn hierarchical models, bottom-up learning methods in which learning takes place in a layer-by-layer manner from the lowest to the highest layer are already extensively used in some research fields such as hidden...
The paper deals with a boundary control problem for the Maxwell dynamical
system in a bounbed domain
Ω ⊂ R3. Let ΩT ⊂ Ω be the subdomain
filled by waves at the moment T,
T* the moment at which the waves fill the whole
of Ω. The following effect occurs: for small enough
T the system is approximately controllable in ΩT whereas for
larger T < T* a lack of controllability is possible. The subspace of unreachable states
is of finite dimension determined by topological characteristics of ΩT.
We consider transmission problems for general second order linear hyperbolic
systems having piecewise constant coefficients in a bounded, open connected
set with smooth boundary and controlled through the Dirichlet boundary
condition. It is proved that such a system is exactly controllable in an
appropriate function space provided the interfaces where the coefficients
have a jump discontinuity are all star-shaped with respect to one and the
same point and the coefficients satisfy a certain...
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