MPC Quadratic Program Solver Using Variable-Ordered Factor Updates

Solution Overview

Problem

Existing quadratic programming solvers for model predictive control face challenges with high computational complexity and memory requirements, particularly in embedded systems with limited CPU power and memory, due to the rapid growth of possible factors with the number of optimization variables, which limits their effectiveness in solving small to medium-sized QP problems efficiently.

Innovation Solution

The system employs a factorization module with a memory containing saved factors and a factor search mechanism to find the nearest stored factor for updating, using variable ordering to reduce the number of factors stored and allowing updates at zero floating-point operations per unit time, thereby reducing computational complexity and memory needs.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Measurement precision

If standard quadratic programming solvers are used for model predictive control, then solution accuracy is maintained, but computational complexity and memory requirements grow rapidly with the number of optimization variables

Engineering Contradiction:

Improvesolution accuracyVSAvoidcomputational complexity

Core Design Contradiction:

Measurement precisionVSDevice complexity

Solution Approach 1:

The patent precomputes and stores factors of the Hessian matrix offline before the online control phase. By performing the computationally intensive factorization in advance when the system is not time-constrained, the online solver only needs to retrieve and use precomputed factors, dramatically reducing online computational complexity while maintaining solution accuracy.

Inventive Principle:

Principle #10Preliminary action

Solution Approach 2:

The patent segments the solution process into offline factor computation and online factor retrieval/application phases. The Hessian matrix factorization is separated from the online QP solving, allowing the complex computational task to be performed once offline rather than repeatedly online, thus reducing the burden on embedded systems with limited computational resources.

Inventive Principle:

Principle #1Segmentation

2Measurement precision

If standard quadratic programming solvers are used for model predictive control, then solution accuracy is maintained, but memory requirements increase with the number of optimization variables

Engineering Contradiction:

Improvesolution accuracyVSAvoidmemory requirements

Core Design Contradiction:

Measurement precisionVSQuantity of substance

Solution Approach 1:

The patent precomputes and stores factors of the Hessian matrix offline before the online control phase. By performing the computationally intensive factorization in advance when the system is not time-constrained, the online solver only needs to retrieve and use precomputed factors, dramatically reducing online computational complexity while maintaining solution accuracy.

Inventive Principle:

Principle #10Preliminary action

Solution Approach 2:

The patent creates and stores copies of the Hessian matrix factors offline. These precomputed factor copies are saved in memory and reused during online operation, eliminating the need to store and recompute the full Hessian matrix repeatedly. This copying approach reduces online memory access requirements and computational overhead.

Inventive Principle:

Principle #26Copying

3Adaptability or versatility

If the number of optimization variables increases, then problem modeling capability is improved, but the number of factors that need to be stored increases rapidly

Engineering Contradiction:

Improveproblem modeling capabilityVSAvoidnumber of factors to store

Core Design Contradiction:

Adaptability or versatilityVSQuantity of substance

Solution Approach 1:

The patent precomputes and stores factors of the Hessian matrix offline before the online control phase. By performing the computationally intensive factorization in advance when the system is not time-constrained, the online solver only needs to retrieve and use precomputed factors, dramatically reducing online computational complexity while maintaining solution accuracy.

Inventive Principle:

Principle #10Preliminary action

Solution Approach 2:

The patent changes the computational parameters by precomputing factors offline rather than during online operation. This parameter change in when and how factorization is performed allows the system to handle larger numbers of optimization variables by shifting the computational burden to offline time, enabling the system to scale to more complex problems without proportionally increasing online memory and computational requirements.

Inventive Principle:

Principle #35Parameter changes

Data Source

PatentUS11144017B2Quadratic program solver for MPC using variable ordering

Publication Date: 2021.10.12 GARRETT TRANSPORTATION I INC

AI summary

A system and approach for storing factors in a quadratic programming solver of an embedded model predictive control platform. The solver may be connected to an optimization model which may be connected to a factorization module. The factorization module may incorporate a memory containing saved factors that may be connected to a factor search mechanism to find a nearest stored factor in the memory. A factor update unit may be connected to the factor search mechanism to obtain the nearest stored factor to perform a factor update. The factorization module may provide variable ordering to reduce a number of factors that need to be stored to permit the factors to be updated at zero floating point operations per unit of time.