Piecewise continuous control of groundwater remediation
First Claim
1. An apparatus comprising:
- a processing unit;
a memory system, said memory system being connected to said processing unit; and
a program stored in said memory system for execution on said processing unit, said program including;
an optimization mechanism that optimizes remediation of a contaminated groundwater site by a minimization of a groundwater remediation design objective J with respect to a groundwater remediation design vector v(t), wherein t denotes time, wherein v(t) is a piecewise continuous function of t, wherein J is functionally dependent on both v(t) and a state vector x(t), and wherein dx(t)/dt and v(t) are functionally related by a differential equation of;
dx/dt=T(x(t),v(t),t) subject to the condition of x(t0)=xinitial.
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Abstract
A piecewise continuous-time dynamic control method and apparatus for optimizing remediation of groundwater is disclosed. The piece-wise continuous control process is used to generate efficient designs for rededication systems based on differentiable groundwater models. The remediation strategies generated are characterized by piece-wise continuous functions of time which dictate the operation of remediation devices. The piece-wise continuous functions may change discontinuity at the end of each management period, or optionally, a finite number of times during each management period. The duration and number of management periods covering a groundwater cleanup may be selected by the user of the invention to maximize the contamination removal efficiency and reflect the mechanical limitations of the specific rededication devices chosen. The continuous-time property of piece-wise continuous control requires simpler (usually sparse) derivatives of a groundwater model than the derivatives required by static and discrete-time control of groundwater remediation.
28 Citations
8 Claims
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1. An apparatus comprising:
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a processing unit; a memory system, said memory system being connected to said processing unit; and a program stored in said memory system for execution on said processing unit, said program including; an optimization mechanism that optimizes remediation of a contaminated groundwater site by a minimization of a groundwater remediation design objective J with respect to a groundwater remediation design vector v(t), wherein t denotes time, wherein v(t) is a piecewise continuous function of t, wherein J is functionally dependent on both v(t) and a state vector x(t), and wherein dx(t)/dt and v(t) are functionally related by a differential equation of;
dx/dt=T(x(t),v(t),t) subject to the condition of x(t0)=xinitial. - View Dependent Claims (2, 3, 4, 5, 7, 8)
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6. A program product comprising:
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a recordable media; and a program recorded on said recordable media by a computer system for execution on a central processing unit, said program having; an optimization mechanism that optimizes remediation of a contaminated groundwater site by a minimization of a groundwater remediation design objective J with respect to a groundwater remediation design vector v(t), wherein t denotes time, wherein v(t) is a piecewise continuous function of t, wherein J is functionally dependent on both v(t) and a state vector x(t), and wherein dx(t)/dt and v(t) are functionally related by a differential equation of;
dx/dt=T(x(t),v(t),t) subject to the condition of x(t0)=xinitial.
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Specification