Singular control refers to a specific type of control problem in the field of optimal control theory. It typically arises in situations where the control variables are subject to constraints or limits, and the system's dynamics can exhibit singularities. In mathematical terms, a control problem is considered "singular" when the usual assumptions about the behavior of the control signals break down, often leading to the need for special techniques to analyze and solve the problem.

Space Vector Modulation (SVM) is a sophisticated technique used in pulse width modulation (PWM) for controlling power converters, specifically in the context of three-phase voltage source inverters. SVM is employed to represent the output voltage of an inverter as a vector in a two-dimensional space, which allows for more efficient and optimized control of the switching states of the inverter.

Nothing personal, just Ciro Santilli strongly disagrees with the moderation philosophies of these users.

One particular type of user Ciro particularly dislikes are those who do more moderation than content. Ciro finds it very hard to understand why some people spend so much time moderating. Maybe that's how politicians exist, some people just like that kind of activity.

The moderators tend to have lower intermediate rep. They spend too much time moderating and too little time coding.

TBD:

Not so strong, but bad experience:

Deleted answers are dumped at: github.com/cirosantilli/cirosantilli.github.io/issues

A state-transition equation is a mathematical representation used in various fields, such as control theory, systems engineering, and economics, to describe how a system transitions from one state to another over time. The equation typically relates the current state of the system to its next state and incorporates dynamic aspects of the system, such as time, input variables, or external influences.

The concept of a "tensor product model transformation" is related to tensor products in mathematics and physics, especially in the context of linear algebra, quantum mechanics, and machine learning. Here's a brief overview of the key concepts involved: ### Tensor Product 1. **Tensor Product in Linear Algebra**: - The tensor product is a mathematical operation that takes two tensors (multi-dimensional arrays) and produces a new tensor.

Terminal sliding mode control is an advanced control strategy that is a refinement of conventional sliding mode control (SMC). It is designed to achieve faster convergence to the desired state by introducing a terminal sliding surface, which ensures that the system will reach the desired state in a finite time.

A time-variant system is a type of system in which the system characteristics change over time. This means that the output response of the system to a given input can vary depending on when the input is applied. In contrast, a time-invariant system has consistent properties, and the response to an input is always the same, regardless of when the input is applied.

A unicycle cart is typically a small cart or platform that is designed to be ridden or balanced on a unicycle. It might also refer to a cart that can be pulled or pushed while riding a unicycle, or a specialized wheeled vehicle that combines aspects of both unicycles and carts. In some cases, unicycle carts are used for various activities like tricks, stunts, or games, often found in performance contexts or in playful settings.

Whetstone is a benchmark test that measures the performance of a computer's floating-point arithmetic, particularly focusing on its ability to perform basic mathematical operations. It was developed in the 1970s and is used to evaluate the speed of floating-point calculations and to compare the performance of different computer systems, especially those with different architectures or configurations. The Whetstone benchmark consists of a series of floating-point calculations, including operations such as addition, subtraction, multiplication, division, and square roots.

In mathematical terms, a "function problem" typically refers to a scenario in which an individual is tasked with finding a function or determining a property of a function based on given conditions or constraints.

XTEA, or Extended Tiny Encryption Algorithm, is a symmetric key block cipher designed for fast and secure data encryption. It was developed by David Wheeler and Roger Needham in 1997 as an improvement to the original Tiny Encryption Algorithm (TEA). XTEA addresses some of the weaknesses found in TEA and offers enhanced security. ### Key Features of XTEA: 1. **Block Size**: XTEA operates on 64-bit blocks of data.

The term "Aberdeen chronograph" does not refer to a widely known or specific chronograph model or brand in the watchmaking industry as of my last knowledge update in October 2023. However, it may refer to a specific chronograph watch that is perhaps associated with a brand named "Aberdeen" or might be an informal name for a style of chronograph. Chronographs are watches that feature a stopwatch function alongside telling time.

Ivan Cherednik is known for his contributions to the field of mathematics, particularly in areas related to representation theory and special functions. He is most recognized for his work on Cherednik algebras, which are an important topic in the intersection of algebra, geometry, and mathematical physics. Cherednik's research often involves the study of quantum groups, harmonic analysis, and combinatorial aspects of representation theory.

The Unscented Transform (UT) is a mathematical technique used primarily in the field of nonlinear estimation and filtering, particularly within the context of the Unscented Kalman Filter (UKF). Its primary purpose is to approximate the mean and covariance of a random variable that is passed through a nonlinear function, which can be challenging due to the nonlinearity involved.

A vector measure is a mathematical concept that extends the idea of a measure (as found in measure theory) to a vector-valued function. In classical measure theory, a measure assigns a non-negative real number to subsets of a given space, typically based on the size or volume of those sets. In the context of vector measures, the concept is generalized to allow for values that are vectors instead of just scalars.

Viscous damping refers to a type of damping that is proportional to the velocity of an object moving through a fluid or a material. This phenomenon is commonly observed in mechanical systems, particularly in oscillating or vibrating systems, where energy is dissipated as heat due to the resistance of the fluid or medium. In the context of mechanical vibrations, viscous damping can be described using a damping force that is proportional to the velocity (\(v\)) of the object.

The term "weighting pattern" can refer to different concepts depending on the context in which it is used. Here are a few possible interpretations: 1. **Statistics and Data Analysis**: In statistical analyses, a weighting pattern may refer to the way different observations in a dataset are given different levels of importance or weight. This could involve assigning higher weights to certain groups or data points based on their relevance or significance to the analysis.

Maurice Auslander is a prominent mathematician known for his significant contributions to various areas of mathematics, particularly in the fields of algebra and representation theory. Born on April 15, 1927, he has had a long and influential career in mathematics. He is best known for his work on homological algebra and for developing concepts such as the Auslander-Riedel theorem, which pertains to the representation theory of algebras.

Witsenhausen's counterexample is a seminal problem in the field of control theory and information theory, specifically illustrating the challenges associated with decentralized control systems. It was introduced by Hans Witsenhausen in 1968. The counterexample involves a two-player scenario where each player must make decisions based on partial information, and their decisions are interdependent.