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Linear dynamical systems can be solved exactly, in contrast to most nonlinear ones. Occasionally, a nonlinear system can be solved exactly by a change of variables to a linear system. Moreover, the solutions of (almost) any nonlinear system can be well-approximated by an equivalent linear system near its fixed points. Hence, understanding ...
LQG control applies to both linear time-invariant systems as well as linear time-varying systems, and constitutes a linear dynamic feedback control law that is easily computed and implemented: the LQG controller itself is a dynamic system like the system it controls. Both systems have the same state dimension.
In terms of mathematical optimization, dynamic programming usually refers to simplifying a decision by breaking it down into a sequence of decision steps over time. This is done by defining a sequence of value functions V 1, V 2, ..., V n taking y as an argument representing the state of the system at times i from 1 to n.
The Kalman filter is an efficient recursive filter estimating the internal state of a linear dynamic system from a series of noisy measurements. It is used in a wide range of engineering and econometric applications from radar and computer vision to estimation of structural macroeconomic models, [ 25 ] [ 26 ] and is an important topic in ...
The case where the system dynamics are described by a set of linear differential equations and the cost is described by a quadratic function 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.
Lyapunov was a pioneer in successful endeavors to develop a global approach to the analysis of the stability of nonlinear dynamical systems by comparison with the widely spread local method of linearizing them about points of equilibrium.
A real dynamical system, real-time dynamical system, continuous time dynamical system, or flow is a tuple (T, M, Φ) with T an open interval in the real numbers R, M a manifold locally diffeomorphic to a Banach space, and Φ a continuous function. If Φ is continuously differentiable we say the system is a differentiable dynamical system.
A dynamic mathematical model in this context is a mathematical description of the dynamic behavior of a system or process in either the time or frequency domain. Examples include: Examples include: physical processes such as the movement of a falling body under the influence of gravity ;