Separation principle in stochastic controlThe separation principle is one of the fundamental principles of stochastic control theory, which states that the problems of optimal control and state estimation can be decoupled under certain conditions.Linear–quadratic–Gaussian controlIn control theory, the linear–quadratic–Gaussian (LQG) control problem is one of the most fundamental optimal control problems, and it can also be operated repeatedly for model predictive control. It concerns linear systems driven by additive white Gaussian noise. The problem is to determine an output feedback law that is optimal in the sense of minimizing the expected value of a quadratic cost criterion.
State observerSystem in control theoryIn control theory, a state observer, state estimator, or Luenberger observer is a system that provides an estimate of the internal state of a given real system, from measurements of the input and output of the real system. It is typically computer-implemented, and provides the basis of many practical applications. Knowing the system state is necessary to solve many control theory problems; for example, stabilizing a system using state feedback.
Kalman filterIn statistics and control theory, Kalman filtering (also known as linear quadratic estimation) is an algorithm that uses a series of measurements observed over time, including statistical noise and other inaccuracies, to produce estimates of unknown variables that tend to be more accurate than those based on a single measurement, by estimating a joint probability distribution over the variables for each time-step.
Control theoryControl theory is a field of control engineering and applied mathematics that deals with the control of dynamical systems. The aim is to develop a model or algorithm governing the application of system inputs to drive the system to a desired state, while minimizing any delay, overshoot, or steady-state error and ensuring a level of control stability; often with the aim to achieve a degree of optimality.Triangular matrixIn mathematics, a triangular matrix is a special kind of square matrix. A square matrix is called lower triangular if all the entries above the main diagonal are zero. Similarly, a square matrix is called upper triangular if all the entries below the main diagonal are zero. Because matrix equations with triangular matrices are easier to solve, they are very important in numerical analysis.
FeedbackFeedback occurs when outputs of a system are routed back as inputs as part of a chain of cause and effect that forms a circuit or loop. The system can then be said to feed back into itself. The notion of cause-and-effect has to be handled carefully when applied to feedback systems: Simple causal reasoning about a feedback system is difficult because the first system influences the second and second system influences the first, leading to a circular argument.
BIBO stabilityIn signal processing, specifically control theory, bounded-input, bounded-output (BIBO) stability is a form of stability for signals and systems that take inputs. If a system is BIBO stable, then the output will be bounded for every input to the system that is bounded.
Linear–quadratic regulatorThe theory of optimal control is concerned with operating a dynamic system at minimum cost. The case where the system dynamics are described by a set of linear differential equations and the cost is described by a quadraticfunction is called the LQ problem. One of the main results in the theory is that the solution is provided by the linear–quadratic regulator (LQR), a feedback controller whose equations are given below.Linear time-invariant systemMathematical model which is both linear and time-invariantBlock diagram illustrating the superposition principle and time invariance for a deterministic continuous-time single-input single-output system. The system satisfies the superposition principle and is time-invariant if and only if y3(t) = a1y1(t – t0) + a2y2(t – t0) for all time t, for all real constants a1, a2, t0 and for all inputs x1(t), x2(t).
Eigenvalues and eigenvectorsConcepts from linear algebraIn linear algebra, an eigenvector ( ) or characteristic vector is a (nonzero) vector that has its direction unchanged (or reversed) by a given linear transformation. More precisely, an eigenvector v{\displaystyle \mathbf {v} } of a linear transformation T{\displaystyle T} is scaled by a constant factorλ{\displaystyle \lambda } when the linear transformation is applied to it: Tv=λv{\displaystyle T\mathbf {v} =\lambda \mathbf {v} }.*As an Amazon Associate I earn from qualifying purchases.