Control system with optimized periodic adjustments of system control settings using MARS-based MILP optimization
Constructing a MARS prediction model using predictor variables at a first point in time within a time horizon, including directly-controllable variables of first physical characteristics of a system and that are associated with adjustable operational control settings for directly controlling the first physical characteristic, and including controllable variables of second physical characteristics that are affected by the first physical characteristics, recursively using the prediction model to define an optimization problem for later point in time within the time horizon, transforming the optimization problem into a MILP problem, and solving the MILP problem using an optimization engine to determine, for any given one of the directly-controllable variables and corresponding to at least one of the points in time, for adjusting, using the optimized value, the adjustable operational control setting corresponding to the given directly-controllable variable and thereby control the physical characteristic associated with the directly-controllable variable.
1. A method for controlling a physical system, wherein the physical system comprises:
adjustable operational control settings, and
a plurality of physical characteristics each associated with a predictor variable,
wherein at least one of the predictor variables is a directly-controllable variable associated with one of the operational control settings and directly controls one of the plurality of physical characteristics that is associated with the respective directly-controllable variable,
wherein at least one of the predictor variables is a controllable variable associated with any of the plurality of physical characteristics that is affected by any of the plurality of physical characteristics associated with any directly-controllable variable,
the method comprising, during a predefined time horizon that includes multiple time intervals each followed by a control point:
at each of the control points:
(a) constructing a multivariate adaptive regression splines (MARS) prediction model using those of the predictor variables associated with the time interval that immediately precedes the respective control point;
(b) using the MARS prediction model to define an optimization problem for the respective control point;
(c) transforming the optimization problem into a mixed integer linear programming (MILP) problem;
(d) solving the MILP problem using an optimization engine, to determine at least one optimized value for any given one of the directly-controllable variables; and
(e) adjusting, using the at least one optimized value, the adjustable operational control setting corresponding to the given directly-controllable variable, to thereby control the physical characteristic associated with the directly-controllable variable during the time interval immediately following the respective control point.
2. The method according to claim 1 wherein the constructing comprises constructing the MARS prediction model using, as values for any of the predictor variables, real historical measurements of values of any of the plurality of physical characteristics of the physical system.
3. The method according to claim 1 wherein the constructing comprises constructing the MARS prediction model using, as values for any of the predictor variables, simulated historical measurement values of any of the plurality of physical characteristics of the physical system.
4. The method according to claim 1 wherein one or more of the predictor variables is an uncontrollable variable associated with any of the plurality of physical characteristics that is unaffected by any of the plurality of physical characteristics that are associated with any directly-controllable variable.
5. The method according to claim 1 wherein the predefined time horizon is a moving time horizon of a constant size.
6. A control system for controlling a physical system, wherein the physical system comprises:
adjustable operational control settings, and
a plurality of physical characteristics each associated with a predictor variable,
wherein at least one of the predictor variables is a directly-controllable variable associated with one of the operational control settings and directly controls one of the plurality of physical characteristics that is associated with the respective directly-controllable variable,
wherein at least one of the predictor variables is a controllable variable associated with any of the plurality of physical characteristics that is affected by any of the plurality of physical characteristics associated with any directly-controllable variable,
the control system comprising:
a multivariate adaptive regression splines (MARS) modeler;
a mixed integer linear programming (MILP) transformer; and
an optimization engine,
wherein, during a predefined time horizon that includes multiple time intervals each followed by a control point:
(a) the MARS modeler is configured to (i) construct a MARS prediction model using those of the predictor variables associated with the time interval that immediately precedes the respective control point, and (ii) use the MARS prediction model to define an optimization problem for the respective control point,
(b) the MILP transformer is configured to transform the optimization problem into a mixed integer linear programming problem,
(c) the optimization engine is configured to solve the MILP problem, to determine at least one optimized value for any given one of the directly-controllable variables, and
(d) the control system is configured to adjust, using the at least one optimized value, the adjustable operational control setting corresponding to the given directly-controllable variable, to thereby control the physical characteristic associated with the directly-controllable variable during the time interval immediately following the respective control point.
7. The control system according to claim 6 wherein the MARS modeler is configured to construct the MARS prediction model using, as values for any of the predictor variables, real historical measurements of values of any of the plurality of physical characteristics of the physical system.
8. The control system according to claim 6 wherein the MARS modeler is configured to construct the MARS prediction model using, as values for any of the predictor variables, simulated historical measurement values of any of the plurality of physical characteristics of the physical system.
9. The control system according to claim 6 wherein one or more of the predictor variables is an uncontrollable variable associated with any of the plurality of physical characteristics that is unaffected by any of the plurality of physical characteristics that are associated with any directly-controllable variable.
10. The control system according to claim 6 wherein the predefined time horizon is a moving time horizon of a constant size.
11. A computer program product for controlling a physical system, wherein the physical system comprises:
adjustable operational control settings, and
a plurality of physical characteristics each associated with a predictor variable,
wherein at least one of the predictor variables is a directly-controllable variable associated with one of the operational control settings and directly controls one of the plurality of physical characteristics that is associated with the respective directly-controllable variable,
wherein at least one of the predictor variables is a controllable variable associated with any of the plurality of physical characteristics that is affected by any of the plurality of physical characteristics associated with any directly-controllable variable,
the computer program product comprising:
a non-transitory, computer-readable storage medium; and
computer-readable program code embodied in the storage medium, wherein the computer-readable program code is configured for, during a predefined time horizon that includes multiple time intervals each followed by a control point:
at each of the control points:
(a) constructing a multivariate adaptive regression splines (MARS) prediction model using those of the predictor variables associated with the time interval that immediately precedes the respective control point,
(b) using the MARS prediction model to define an optimization problem for the respective control point,
(c) transforming the optimization problem into a mixed integer linear programming (MILP) problem,
(d) solving the MILP problem using an optimization engine, to determine at least one optimized value for any given one of the directly-controllable variables, and
(e) adjusting, using the at least one optimized value, the adjustable operational control setting corresponding to the given directly-controllable variable, to thereby control the physical characteristic associated with the directly-controllable variable during the time interval immediately following the respective control point.
12. The computer program product according to claim 11 wherein one or more of the predictor variables is an uncontrollable variable associated with any of the plurality of physical characteristics that is unaffected by any of the plurality of physical characteristics that are associated with any directly-controllable variable.