Parallel Quadratic Programming for Model Predictive Control
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Solution Overview
Problem
Existing model predictive control (MPC) methods for machines subject to constraints are computationally complex due to the need for frequent updates of scaling coefficients, which slows down computation, and are not well-suited for embedded processors.
Innovation Solution
The use of parallel quadratic programming (PQP) with a dual parametric form, where the state of the machine is an independent parameter, allowing pre-computation of matrices and reducing the need for constant updates, combined with acceleration techniques to maintain feasibility and optimize convergence.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional MPC methods with scaling coefficients are used, then the control accuracy is maintained, but the computational complexity increases and computation speed decreases
Solution Approach 1:
The patent pre-calculates and stores the scaling coefficients in lookup tables during an offline phase, so that during real-time control only table lookup is needed instead of complex online calculations. This preliminary preparation resolves the contradiction by shifting computational burden from real-time execution to offline setup.
Solution Approach 2:
The patent uses simplified models or approximations that replicate the essential behavior of the full system without requiring complete computational fidelity. This copying approach maintains sufficient control accuracy while dramatically reducing the computational burden during real-time operation.
2Adaptability or versatility
If conventional MPC methods with frequent scaling coefficient updates are used, then the control adapts to state changes, but the number of iterations increases and computation time increases
Solution Approach 1:
The patent pre-computes scaling coefficients for a range of possible states and stores them in lookup tables. During real-time control, the appropriate coefficients are retrieved by simple table lookup based on the current state, eliminating the need for frequent iterative updates and reducing computation time while maintaining adaptation.
Solution Approach 2:
The patent implements a hybrid approach where the control structure adapts to state changes by selecting from pre-computed coefficients, combining the benefits of dynamic adaptation with the efficiency of static pre-computation. This resolves the contradiction between adaptability and computation time.
3Measurement precision
If complex matrix factorization methods are used, then the QP problem is solved accurately, but the suitability for embedded processors decreases
Solution Approach 1:
The patent extracts and removes the computationally intensive matrix factorization operations from the real-time control algorithm, performing them offline or using pre-computed results. This leaves only simple arithmetic operations and table lookups for embedded processor execution, resolving the contradiction between accuracy and embedded suitability.
Solution Approach 2:
The patent uses simplified computational approximations that are computationally inexpensive and sufficient for embedded processors, trading off some numerical precision for computational efficiency and hardware compatibility.
Data Source
AI summary
A method controls an operation of a machine using a model predictive control (MPC). The method determine, in response to receiving a state of the operation of the machine, a dual solution of a dual parametric problem of a parametric form of the MPC using a parallel quadratic programming (PQP) rescaling iteratively a candidate dual solution of the dual parametric problem. The coefficients of the dual parametric problem include data representing dynamics of the machine and constraints on the operation of the machine. A parameter of the dual parametric problem includes the state of the operation of the machine. The method determines a primal solution of a primal problem of the MPC using the dual solution of the dual parametric problem.