List of uniform polyhedraIn geometry, a uniform polyhedron is a polyhedron which has regular polygons as faces and is vertex-transitive (transitive on its vertices, isogonal, i.e. there is an isometry mapping any vertex onto any other). It follows that all vertices are congruent, and the polyhedron has a high degree of reflectional and rotational symmetry. Uniform polyhedra can be divided between convex forms with convex regular polygon faces and star forms. Star forms have either regular star polygon faces or vertex figures or both.
Adaptive controlAdaptive control is the control method used by a controller which must adapt to a controlled system with parameters which vary, or are initially uncertain.cite journal|author=Chengyu Cao, Lili Ma, Yunjun Xu|title="Adaptive Control Theory and Applications", Journal of Control Science and Engineering'|volume=2012|issue=1|year=2012|doi=10.1155/2012/827353|pages=1,2|doi-access=free For example, as an aircraft flies, its mass will slowly decrease as a result of fuel consumption; a control law is needed that adapts itself to such changing conditions.
StellationIn geometry, stellation is the process of extending a polygon in two dimensions, polyhedron in three dimensions, or, in general, a polytope in n dimensions to form a new figure. Starting with an original figure, the process extends specific elements such as its edges or face planes, usually in a symmetrical way, until they meet each other again to form the closed boundary of a new figure. The new figure is a stellation of the original. The word stellation comes from the Latin stellātus, "starred", which in turn comes from Latin stella, "star".
Regular Polytopes (book)Regular Polytopes is a geometry book on regular polytopes written by Harold Scott MacDonald Coxeter. It was originally published by Methuen in 1947 and by Pitman Publishing in 1948, with a second edition published by Macmillan in 1963 and a third edition by Dover Publications in 1973. The Basic Library List Committee of the Mathematical Association of America has recommended that it be included in undergraduate mathematics libraries. The main topics of the book are the Platonic solids (regular convex polyhedra), related polyhedra, and their higher-dimensional generalizations.
Linear mapIn mathematics, and more specifically in linear algebra, a linear map (also called a linear mapping, linear transformation, vector space homomorphism, or in some contexts linear function) is a mapping between two vector spaces that preserves the operations of vector addition and scalar multiplication. The same names and the same definition are also used for the more general case of modules over a ring; see Module homomorphism. If a linear map is a bijection then it is called a .
Linear independenceIn the theory of vector spaces, a set of vectors is said to be if there exists no nontrivial linear combination of the vectors that equals the zero vector. If such a linear combination exists, then the vectors are said to be . These concepts are central to the definition of dimension. A vector space can be of finite dimension or infinite dimension depending on the maximum number of linearly independent vectors. The definition of linear dependence and the ability to determine whether a subset of vectors in a vector space is linearly dependent are central to determining the dimension of a vector space.
Polyhedral combinatoricsPolyhedral combinatorics is a branch of mathematics, within combinatorics and discrete geometry, that studies the problems of counting and describing the faces of convex polyhedra and higher-dimensional convex polytopes. Research in polyhedral combinatorics falls into two distinct areas. Mathematicians in this area study the combinatorics of polytopes; for instance, they seek inequalities that describe the relations between the numbers of vertices, edges, and faces of higher dimensions in arbitrary polytopes or in certain important subclasses of polytopes, and study other combinatorial properties of polytopes such as their connectivity and diameter (number of steps needed to reach any vertex from any other vertex).
ControllabilityControllability is an important property of a control system and plays a crucial role in many control problems, such as stabilization of unstable systems by feedback, or optimal control. Controllability and observability are dual aspects of the same problem. Roughly, the concept of controllability denotes the ability to move a system around in its entire configuration space using only certain admissible manipulations. The exact definition varies slightly within the framework or the type of models applied.
Nonlinear controlNonlinear control theory is the area of control theory which deals with systems that are nonlinear, time-variant, or both. Control theory is an interdisciplinary branch of engineering and mathematics that is concerned with the behavior of dynamical systems with inputs, and how to modify the output by changes in the input using feedback, feedforward, or signal filtering. The system to be controlled is called the "plant".
Sliding mode controlIn control systems, sliding mode control (SMC) is a nonlinear control method that alters the dynamics of a nonlinear system by applying a discontinuous control signal (or more rigorously, a set-valued control signal) that forces the system to "slide" along a cross-section of the system's normal behavior. The state-feedback control law is not a continuous function of time. Instead, it can switch from one continuous structure to another based on the current position in the state space.
