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Control (optimal Control Theory)
In optimal control theory, a control is a variable chosen by the controller or agent to manipulate state variables, similar to an actual control valve. Unlike the state variable, it does not have a predetermined equation of motion. The goal of optimal control theory is to find some sequence of controls (within an admissible set) to achieve an optimal path for the state variables (with respect to a loss function). A control given as a function of time only is referred to as an '' open-loop control''. In contrast, a control that gives optimal solution during some remainder period as a function of the state variable at the beginning of the period is called a ''closed-loop control''. See also * Control loop A control loop is the fundamental building block of control systems in general and industrial control systems in particular. It consists of the process sensor, the controller function, and the final control element (FCE) which controls the proce ... References Contro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Optimal Control Theory
Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criteria, from some set of available alternatives. It is generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems arise in all quantitative disciplines from computer science and engineering to operations research and economics, and the development of solution methods has been of interest in mathematics for centuries. In the more general approach, an optimization problem consists of maximizing or minimizing a real function by systematically choosing input values from within an allowed set and computing the value of the function. The generalization of optimization theory and techniques to other formulations constitutes a large area of applied mathematics. Optimization problems Optimization problems can be divided into two categories, depending on whether the variables ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Agent (economics)
In economics, an agent is an actor (more specifically, a decision maker) in a model of some aspect of the economy. Typically, every agent makes decisions by solving a well- or ill-defined optimization or choice problem. For example, ''buyers'' (consumers) and ''sellers'' ( producers) are two common types of agents in partial equilibrium models of a single market. Macroeconomic models, especially dynamic stochastic general equilibrium models that are explicitly based on microfoundations, often distinguish households, firms, and governments or central banks as the main types of agents in the economy. Each of these agents may play multiple roles in the economy; households, for example, might act as consumers, as workers, and as voters in the model. Some macroeconomic models distinguish even more types of agents, such as workers and shoppers or commercial banks. The term ''agent'' is also used in relation to principal–agent models; in this case, it refers specifically to someone ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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State Variables
A state variable is one of the set of variables that are used to describe the mathematical "state" of a dynamical system. Intuitively, the state of a system describes enough about the system to determine its future behaviour in the absence of any external forces affecting the system. Models that consist of coupled first-order differential equations are said to be in state-variable form. Examples *In mechanical systems, the position coordinates and velocities of mechanical parts are typical state variables; knowing these, it is possible to determine the future state of the objects in the system. *In thermodynamics, a state variable is an independent variable of a state function. Examples include internal energy, enthalpy, temperature, pressure, volume and entropy. Heat and work are not state functions, but process functions. *In electronic/electrical circuits, the voltages of the nodes and the currents through components in the circuit are usually the state variables. In an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Control Valve
A control valve is a valve used to control fluid flow by varying the size of the flow passage as directed by a signal from a controller. This enables the direct control of flow rate and the consequential control of process quantities such as pressure, temperature, and liquid level. In automatic control terminology, a control valve is termed a "final control element". Operation The opening or closing of automatic control valves is usually done by electrical, hydraulic or pneumatic actuators. Normally with a modulating valve, which can be set to any position between fully open and fully closed, valve positioners are used to ensure the valve attains the desired degree of opening. Air-actuated valves are commonly used because of their simplicity, as they only require a compressed air supply, whereas electrically operated valves require additional cabling and switch gear, and hydraulically actuated valves required high pressure supply and return lines for the hydraulic fluid. Th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Equation Of Motion
In physics, equations of motion are equations that describe the behavior of a physical system in terms of its motion as a function of time. More specifically, the equations of motion describe the behavior of a physical system as a set of mathematical functions in terms of dynamic variables. These variables are usually spatial coordinates and time, but may include momentum components. The most general choice are generalized coordinates which can be any convenient variables characteristic of the physical system. The functions are defined in a Euclidean space in classical mechanics, but are replaced by curved spaces in relativity. If the dynamics of a system is known, the equations are the solutions for the differential equations describing the motion of the dynamics. Types There are two main descriptions of motion: dynamics and kinematics. Dynamics is general, since the momenta, forces and energy of the particles are taken into account. In this instance, sometimes the term ' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Sequence
In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed and order matters. Like a set, it contains members (also called ''elements'', or ''terms''). The number of elements (possibly infinite) is called the ''length'' of the sequence. Unlike a set, the same elements can appear multiple times at different positions in a sequence, and unlike a set, the order does matter. Formally, a sequence can be defined as a function from natural numbers (the positions of elements in the sequence) to the elements at each position. The notion of a sequence can be generalized to an indexed family, defined as a function from an ''arbitrary'' index set. For example, (M, A, R, Y) is a sequence of letters with the letter "M" first and "Y" last. This sequence differs from (A, R, M, Y). Also, the sequence (1, 1, 2, 3, 5, 8), which contains the number 1 at two different positions, is a valid sequence. Sequences can be '' finite'', as in these examples, or '' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Loss Function
In mathematical optimization and decision theory, a loss function or cost function (sometimes also called an error 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. An optimization problem seeks to minimize a loss function. An objective function is either a loss function or its opposite (in specific domains, variously called a reward function, a profit function, a utility function, a fitness function, etc.), in which case it is to be maximized. The loss function could include terms from several levels of the hierarchy. In statistics, typically a loss function is used for parameter estimation, and the event in question is some function of the difference between estimated and true values for an instance of data. The concept, as old as Pierre-Simon Laplace, Laplace, was reintroduced in statistics by Abraham Wald in the middle of the 20th century. In the context of economi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Open-loop Control
In control theory, an open-loop controller, also called a non-feedback controller, is a control loop part of a control system in which the control action ("input" to the system) is independent of the "process output", which is the process variable that is being controlled."Feedback and control systems" - JJ Di Steffano, AR Stubberud, IJ Williams. Schaums outline series, McGraw-Hill 1967 It does not use feedback to determine if its output has achieved the desired goal of the input command or process setpoint. There are many open- loop controls, such as on/off switching of valves, machinery, lights, motors or heaters, where the control result is known to be approximately sufficient under normal conditions without the need for feedback. The advantage of using open-loop control in these cases is the reduction in component count and complexity. However, an open-loop system cannot correct any errors that it makes or correct for outside disturbances unlike a closed-loop control syste ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Closed-loop Control
A closed-loop controller or feedback controller is a control loop which incorporates feedback, in contrast to an ''open-loop controller'' or ''non-feedback controller''. A closed-loop controller uses feedback to control states or outputs of a dynamical system. Its name comes from the information path in the system: process inputs (e.g., voltage applied to an electric motor) have an effect on the process outputs (e.g., speed or torque of the motor), which is measured with sensors and processed by the controller; the result (the control signal) is "fed back" as input to the process, closing the loop. In the case of linear feedback systems, a control loop including sensors, control algorithms, and actuators is arranged in an attempt to regulate a variable at a setpoint (SP). An everyday example is the cruise control on a road vehicle; where external influences such as hills would cause speed changes, and the driver has the ability to alter the desired set speed. The PID algorithm ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Control Loop
A control loop is the fundamental building block of control systems in general and industrial control systems in particular. It consists of the process sensor, the controller function, and the final control element (FCE) which controls the process necessary to automatically adjust the value of a measured process variable (PV) to equal the value of a desired set-point (SP). There are two common classes of control loop: open loop and closed loop. * In an open-loop control system, the control action from the controller is independent of the process variable. An example of this is a central heating boiler controlled only by a timer. The control action is the switching on or off of the boiler. The process variable is the building temperature. This controller operates the heating system for a constant time regardless of the temperature of the building. * In a closed-loop control system, the control action from the controller is dependent on the desired and actual process variable. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |