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The term "online model" can have different meanings depending on the context in which it is used. Here are a few common interpretations of the term in various fields: 1. **Online Learning Model**: In education, an online model refers to a system where courses or educational programs are delivered over the internet. This model allows students to access learning materials, participate in discussions, and complete assignments from anywhere, often at their own pace.

Optimal projection equations are mathematical formulations used in various fields, particularly in optimization and data analysis, to find the best representation of data in a reduced-dimensional space. These equations help to project high-dimensional data onto a lower-dimensional space while preserving essential characteristics of the data. ### Key Concepts 1. **Projection**: In a mathematical and geometrical sense, projection refers to mapping points from a higher-dimensional space to a lower-dimensional space. This is often done through linear transformations.

Optogenetics is a neuroscientific technique that involves the use of light to control the activity of genetically modified neurons. This method combines genetics and optics to manipulate specific neurons in living tissue, usually in animal models, allowing researchers to activate or inhibit neuronal activity with high precision and temporal resolution. In optogenetics, genes that code for light-sensitive proteins (often derived from certain types of algae and bacteria) are introduced into specific neurons.

In the context of control theory, "orbit" often refers to the trajectory or path that a dynamical system follows in its state space over time. Specifically, an orbit is defined as the set of states that a system can reach from a given initial state under the influence of its governing dynamics.

Supervisory control theory is a framework used in the field of control systems and automated systems for managing and regulating complex processes. It focuses on the design and implementation of supervisory controllers that oversee the operation of subordinate systems, ensuring that they behave according to specified requirements and constraints. Key elements of supervisory control theory include: 1. **Hierarchy**: The supervisory controller operates at a higher level than the controlled systems (or plants).

The Switching Kalman Filter (SKF) is an extension of the classical Kalman filter used to handle systems that exhibit switching behavior among multiple models or modes. It is particularly useful in situations where the system dynamics or measurements can switch between different states or regimes, leading to changes in the parameters governing the state estimation. ### Key Characteristics: 1. **Multiple Models**: The SKF operates under the assumption that the system can be described by multiple linear or nonlinear models.

Human presence in space refers to human activities, exploration, and habitation beyond Earth’s atmosphere. This includes a wide range of activities and achievements, from early space flights to current operations on the International Space Station (ISS) and future plans for lunar and Martian exploration. Here are some key aspects: 1. **Crewed Space Missions**: Human spaceflight began with missions like Vostok 1 in 1961, which carried Yuri Gagarin, the first human in space.

Perceptual Control Theory (PCT) is a psychological framework developed by William T. Powers in the 1960s. It is rooted in systems theory and focuses on understanding behavior as a form of control rather than a direct response to stimuli. At its core, PCT posits that individuals act in ways that maintain certain perceptions within their desired levels, which Powers refers to as "reference levels.

A Pfaffian constraint refers to a specific type of condition in the field of differential geometry and control theory, often related to the study of differential forms, mechanical systems, and constraints in dynamical systems.

Positive systems refer to a class of dynamic systems characterized by non-negativity in their states and outputs. In control theory and systems engineering, a system is considered positive if, given non-negative initial conditions and non-negative inputs, the system's states and outputs will remain non-negative for all time. ### Key Characteristics of Positive Systems: 1. **Non-Negativity**: All states and outputs of the system must stay non-negative whenever initial conditions and inputs are non-negative.

A process variable (PV) is a measurable quantity that indicates the state or condition of a system or process in control engineering and automation. It represents a critical parameter that can be monitored and controlled to ensure optimal operation of equipment or processes. Common examples of process variables include: - **Temperature**: Used in heating and cooling processes. - **Pressure**: Critical in gas and liquid systems. - **Flow rate**: Important in fluid transport and processing systems.

In control theory and signal processing, a **proper transfer function** is a type of transfer function that has certain mathematical properties. A transfer function \( H(s) \) is expressed as the ratio of two polynomials in the Laplace variable \( s \): \[ H(s) = \frac{N(s)}{D(s)} \] where: - \( N(s) \) is the numerator polynomial, - \( D(s) \) is the denominator polynomial.

A pulse-swallowing counter is a type of digital counter used in electronics and computer hardware, particularly in applications involving frequency division or time measurement. The term typically refers to a counting mechanism where the counter increments or decrements its count based on specific pulses that are "swallowed" or ignored for control purposes. In more detail, the concept often applies to designs where the frequency of incoming signals (like clock pulses) is reduced or divided by a certain factor.

Quantitative Feedback Theory (QFT) is a control theory framework developed for designing control systems that can meet specified performance and robustness requirements. It is particularly useful in situations where a system has significant uncertainties or where traditional control design methods might struggle to achieve desired specifications. ### Key Features of QFT: 1. **Modeling Uncertainty**: QFT explicitly takes into account the uncertainties in system models.

A Real-Time Control System is a type of computing system that is designed to control physical processes in real-time. In these systems, the timing of inputs and outputs is critical because they must respond within strict time constraints. The primary goal of a real-time control system is to ensure that the control actions occur within a defined time frame to guarantee the correct operation of the system being controlled.

Recursive economics is a concept that generally refers to economic models or analyses that utilize recursive methods to understand and evaluate economic behaviors and systems over time. The term "recursive" itself indicates that the process involves referencing or repeating a certain operation or set of operations. In the context of economics, recursive methods can often be found in: 1. **Dynamic Programming**: This approach is used to solve optimization problems where decisions are made at various time periods, and the outcomes depend on previous decisions.

A Reed receiver is a type of sensor or switch that utilizes a reed switch to detect the presence of a magnetic field. Reed switches consist of two ferromagnetic contacts enclosed in a glass tube. When a magnetic field (often from a magnet) is brought close to the switch, it causes the contacts to close, completing a circuit. This allows the Reed receiver to act as an input device, often used in various applications, such as security systems, door/window sensors, and industrial automation.

The Leibniz–Clarke correspondence refers to a philosophical exchange between the German philosopher Gottfried Wilhelm Leibniz and the English bishop Samuel Clarke during the early 18th century. This correspondence primarily focused on the nature of space, time, and God, and is considered one of the early significant debates in metaphysics and philosophy of science. **Key aspects of the correspondence include:** 1.

Repetitive control is a control strategy used primarily in control systems and automation that focuses on improving the performance of systems when subjected to repetitive tasks or periodic disturbances. This approach is particularly useful in scenarios where the same input or set of conditions is encountered repeatedly, allowing for the system to learn from past experiences and adjust its responses accordingly. ### Key Features of Repetitive Control: 1. **Periodicity**: Repetitive control is highly effective for systems that experience periodic inputs or disturbances.

Rise time is a term used in various fields, particularly in electronics and signal processing, to describe the time it takes for a signal to change from a specified low level to a specified high level. It is often measured from 10% to 90% of the maximum amplitude of the waveform.