System and method for exploiting a good starting guess for binding constraints in quadratic programming with an infeasible and inconsistent starting guess for the solution
First Claim
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1. A method for controlling a multivariable system including the steps of:
- a) receiving a plurality of sensor signals indicating current conditions of the system;
b) receiving a plurality of commands;
c) determining the desired dynamic response of the system based upon the commands and the sensor signals;
d) in each of a plurality of time steps, formulating a problem of controlling the system to achieve the desired dynamic response as a solution to a quadratic programming problem;
e) solving the quadratic programming problem in each time step using an iterative algorithm which searches for an optimal active set, wherein the active set comprises a set of constraints that are binding at an optimized solution; and
f) in each subsequent time step of the plurality of time steps;
g) solving the quadratic programming problem based on a final active set of a prior time step of the plurality of time steps to obtain xf;
h) initializing a search for the optimal active set based on the final active set of the prior time step of the plurality of time steps and based upon the assumption that xf is feasible.
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Abstract
The present invention provides an algorithm that does not relax the problem at the very onset, even if xf is infeasible. Instead, it solves the EQP with the initial guess for the active set without relaxing the problem. If this solution to the first EQP is not optimal, but nevertheless feasible, we can use this as our guess for the feasible point. This has the advantage of being a feasible point that is consistent with the initial active set, whereas the initial guess used in the previous method is not necessarily so.
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Citations
15 Claims
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1. A method for controlling a multivariable system including the steps of:
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a) receiving a plurality of sensor signals indicating current conditions of the system; b) receiving a plurality of commands; c) determining the desired dynamic response of the system based upon the commands and the sensor signals; d) in each of a plurality of time steps, formulating a problem of controlling the system to achieve the desired dynamic response as a solution to a quadratic programming problem; e) solving the quadratic programming problem in each time step using an iterative algorithm which searches for an optimal active set, wherein the active set comprises a set of constraints that are binding at an optimized solution; and f) in each subsequent time step of the plurality of time steps; g) solving the quadratic programming problem based on a final active set of a prior time step of the plurality of time steps to obtain xf; h) initializing a search for the optimal active set based on the final active set of the prior time step of the plurality of time steps and based upon the assumption that xf is feasible. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8)
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9. A control system comprising:
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a desired trajectory generator for creating a desired trajectory; a linearization module deriving a linearized model about the desired trajectory; a quadratic programming module in each of a plurality of time steps, formulating a problem of controlling the system to achieve the desired dynamic response as a solution to a quadratic programming problem; a quadratic programming solver for solving an optimization problem established by the quadratic programming module to generate a profile of optimal controls, the quadratic programming solver solving the quadratic programming problem in each time step using an iterative algorithm which searches for an optimal active set and in each subsequent time step of the plurality of time steps, the quadratic programming solver in each subsequent time step of the plurality of time steps solving the quadratic programming problem based on a final active set of a prior time step of the plurality of time steps to obtain xf, the quadratic programming solver initializing a search for the optimal active set based on the final active set of the prior time step of the plurality of time steps and based upon the assumption that xf is feasible. - View Dependent Claims (10, 11, 12, 13, 14, 15)
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Specification