United Technologies Corporation

Indraneel Das

James W Fuller

Gonzalo J Rey

The present invention provides an algorithm that does not relax the problem at the very onset, even if xis 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.

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

Real-time control of a dynamical system is provided by determining control variables that get as close as possible to producing a desired response. Additional consideration of physical limitations leads to a convex Quadratic Program with inequality constraints that needs to be solved in real-time. A new active set algorithm is described to solve the convex Quadratic Program efficiently that meets real-time requirements. Based on the key observation that the physical limitations of the system translate to optimal active sets that remain relatively unchanged over time (even though the actual optimal controls may be varying), starting guesses for the active set obtained from the final iterate in the previous time period greatly reduces the number of iterations and hence allows the Quadratic Programs to be solved to convergence in real-time.

Real-time quadratic programming for control of dynamical systems

An active set algorithm exploits a 'hot start' for the set of binding constraints at optimality along with efficient linear algebra to make rapid progress towards the solution. The linear algebra is designed to deal with degenerate constraints as the required factorizations are performed and as degeneracy emerges, and not via a mostly unnecessary pre-process step. Combined together, these novel approaches enable solution of the control problem in real-time.

System and method of accelerated active set search for quadratic programming in real-time model predictive control

A method of controlling a multivariable system includes the step of receiving a plurality of sensor signals indicating current conditions of the system and receiving a plurality of commands. The desired dynamic response of the system is then determined based upon the commands and the sensor signals. The problem of controlling the system to achieve the desired dynamic response without violating numerous actuator and physical constraints is then formulated as a quadratic programming problem. By solving the quadratic programming problem, the effector commands are determined and the physical constraints are enforced.

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Vernon, CT, United States of America

Indraneel Das