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Control of items in a complex system by using fluid models and solving continuous linear programs

  • US 7,433,742 B2
  • Filed: 05/02/2005
  • Issued: 10/07/2008
  • Est. Priority Date: 07/26/2002
  • Status: Expired due to Fees
First Claim
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1. An apparatus for optimizing the performance of a controlled system over a plurality of times, said apparatus comprising:

  • a plurality of process control devices for controlling said controlled system in response to control signals from the apparatus,a plurality of sensors for sensing variable conditions of the controlled system by the apparatus,a means for modeling said controlled system by a conceptual fluid-model,a means for calculating optimal control signals for the control of said controlled system,wherein said controlled system comprises a plurality of discrete items, a plurality of actions, and a plurality of resources, where at each of said times each of said items is in one of a plurality of classes, and where application of one of said actions to one of said items in one of said classes at one of said times will change the class of the item, and where said application of one of said actions to one of said items at one of said times will consume some of said resources, and wherein the control of the said controlled system comprises the timing of said actions and the allocation of said resources to said actions, and wherein said means of the apparatus for modeling said controlled system by a conceptual fluid-model comprise;

    a plurality of state functions that denote levels of fluids in buffers as a function of time, where the fluid in a buffer at time t approximates the number of items in a corresponding class in the controlled system around the time t, anda plurality of control functions that denote flow rates as a function of time, where a flow rate at time t represents the number of applications of a corresponding action in the controlled system system around the time t, anda linear relationship between the flow rates and the rates of change of the state of the fluid-model system at time t, anda linear relationship between the flow rates of the fluid-model system at time t and the rate of consumption of resources,and wherein said means of the apparatus for calculating optimal control signals comprise an algorithm for a solution of separated continuous linear programming problems, and wherein the operation of the apparatus comprises the repeated applications of the steps;

    (a) setting current-time to 0, and setting time-horizon to a predetermined value T, and using the apparatus sensing devices tosensing current-state of the controlled system, andsensing the predicted exogenous inputs into the controlled system over the time horizon, andsensing the predicted levels of available resources over the time horizon, and sensing the predicted rates of reward, per item in each class, and per action, over the time horizon,and formulating a separated continuous linear programming optimization problem for the fluid-model system from the sensed data of the controlled system,(b) solving said separated continuous linear programming optimization problem, by an algorithm comprising a sequence of iterations, each of said iterations comprisinga current solution valid in a current validity range, andan updated solution valid in an updated validity range, anda calculation of the updated solution from the current solution, said calculation comprising the steps of;

    solving a linear programming problem relating to rates, anddetermining if a need for solving a sub-problem exists, andif the need exists then;

    formulating the sub-problem, andsolving the sub-problem by a recursive call to a version of the algorithm,to obtain a fluid solution, comprising the optimal values of the controls of the fluid system and the optimal values of the states of the fluid system for all the times from 0 to T,(d) producing control signals for controlling the real system in accordance with the optimal solution of the fluid-model system,where the repeated application of the steps (a), (b), and (c) is performed at a plurality of predetermined decision times.

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