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13 relations: Algebraic Riccati equation, Control theory, Costate equation, Dynamical system, Full state feedback, Functional (mathematics), Linear differential equation, Linear–quadratic–Gaussian control, Loss function, Optimal control, Quadratic function, Riccati equation, State-space representation.
Algebraic Riccati equation
An algebraic Riccati equation is a type of nonlinear equation that arises in the context of infinite-horizon optimal control problems in continuous time or discrete time.
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Control theory
Control theory in control systems engineering deals with the control of continuously operating dynamical systems in engineered processes and machines.
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Costate equation
The costate equation is related to the state equation used in optimal control.
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Dynamical system
In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in a geometrical space.
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Full state feedback
Full state feedback (FSF), or pole placement, is a method employed in feedback control system theory to place the closed-loop poles of a plant in pre-determined locations in the s-plane.
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Functional (mathematics)
In mathematics, the term functional (as a noun) has at least two meanings.
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Linear differential equation
In mathematics, a linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form where,..., and are arbitrary differentiable functions that do not need to be linear, and are the successive derivatives of an unknown function of the variable.
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Linear–quadratic–Gaussian control
In control theory, the linear–quadratic–Gaussian (LQG) control problem is one of the most fundamental optimal control problems.
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Loss function
In mathematical optimization, statistics, econometrics, decision theory, machine learning and computational neuroscience, a loss function or cost function is a function that maps an event or values of one or more variables onto a real number intuitively representing some "cost" associated with the event.
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Optimal control
Optimal control theory deals with the problem of finding a control law for a given system such that a certain optimality criterion is achieved.
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Quadratic function
In algebra, a quadratic function, a quadratic polynomial, a polynomial of degree 2, or simply a quadratic, is a polynomial function in one or more variables in which the highest-degree term is of the second degree.
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Riccati equation
In mathematics, a Riccati equation in the narrowest sense is any first-order ordinary differential equation that is quadratic in the unknown function.
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State-space representation
In control engineering, a state-space representation is a mathematical model of a physical system as a set of input, output and state variables related by first-order differential equations or difference equations.
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Dynamic Riccati equation, Linear-quadratic regulator.
References
[1] https://en.wikipedia.org/wiki/Linear–quadratic_regulator
