Fast model predictive ellipsoid control process

Claim 2

A model predictive control process for controlling a physical process through actuators that have a polytopic defined constraint set defining the operational limitations of the actuators, the process comprising: periodically sampling one or more sensors whose outputs characterize operational results of the physical process; computing a desired set of manipulated variables, by conducting an off-line computation which approximates the constraint set as an ellipsoid; conducting an on-line scaling to scale the ellipsoid approximation to the constraint set and implement a selected control algorithm; and adjusting the actuators according to the scaling.

Claim 3

The model predictive control process of claim 1, wherein the step of conducting an on-line scaling comprises computation of a solution via bisection of the ellipsoid from the off-line computation.

Claim 4

The model predictive control process of claim 1, wherein said computation of said solution is first conducted as an unconstrained solution before conducting a scaling, and the unconstrained solution is accepted if it conforms to the constraint set.

Claim 5

The model predictive control process of claim 3, wherein said computation of said solution is conducted via said scaling as a constrained solution if the unconstrained solution fails to conform to the constraint set.

Claim 6

The model predictive control process of claim 4, wherein said constrained solution is iteratively scaled until the constrained solution yields an active constraint.

Claim 7

The model predictive control process of claim 1, wherein the physical process is defined as the constrained quadratic: ##EQU22## and the constraint set is represented as Fz≦α.

Claim 8

The model predictive control process of claim 6, wherein said off-line computation approximates the constraint set as an ellipsoid as: Φ=VΛ.sub.Φ V.sup.T. 8.

Claim 9

A model predictive control process having a constraint set approximated by the finite polytope: u(k)ε≡{u(k)|Au(k)≦b} and having a control move determined by computing u k as a solution to a quadratic program of the form: ##EQU23## subject to ##EQU24## where r(k+j) is the desired profile W y and W u are positive semi-definite weighting matrices, and p is the control horizon, the process comprising the steps of: approximating the finite polytope with an ellipsoid of the form: (u(k)-u.sub.m).sup.T Φ(u(k)-u.sub.m)≦α, where u m is the center and Φ defines the direction and relative length of the axes of an ellipsoid, and α is a scaling parameter, the matrix Φ is selected to have the form Φ=VΛ.sub.Φ V.sup.T, where Λ.sub.Φ is a real diagonal matrix whose diagonal elements are nonnegative; computing an optimal unconstrained actuator move of the form: ##EQU25## where the subscript x i denotes the ith element of the vector x and X ii denotes the ith diagonal element of the matrix X; and, if the unconstrained solution fails to satisfy the constraints imposed by the polytope, computing an optimal constrained actuator move by solving the following system of algebraic equations: ##EQU26## making a control move according to the optimal unconstrained actuator move if the unconstrained solution satisfied the constraints imposed by the polytope, otherwise, making the optimal constrained actuator move.

Claim 10

A model predictive control process having a constraint set approximated by the finite polytope: u(k)ε≡{u(k)|Au(k)≦b} and having a control move determined by computing u k as a solution to a quadratic program of the form: ##EQU23## subject to ##EQU24## where r(k+j) is the desired profile W y and W u are positive semi-definite weighting matrices, and p is the control horizon, the process comprising the steps of: approximating the finite polytope with an ellipsoid of the form: (u(k)-u.sub.m).sup.T Φ(u(k)-u.sub.m)≦α, where u m is the center and Φ defines the direction and relative length of the axes of an ellipsoid, and α is a scaling parameter, the matrix Φ is selected to have the form Φ=VΛ.sub.Φ V.sup.T, where Λ.sub.Φ is a real diagonal matrix whose diagonal elements are nonnegative; computing an optimal unconstrained actuator move of the form: ##EQU25## where the subscript x i denotes the ith element of the vector x and X ii denotes the ith diagonal element of the matrix X; and, if the unconstrained solution fails to satisfy the constraints imposed by the polytope, computing an optimal constrained actuator move by solving the following system of algebraic equations: ##EQU26## making a control move according to the optimal unconstrained actuator move if the unconstrained solution satisfied the constraints imposed by the polytope, otherwise, making the optimal constrained actuator move.