Preconditioner for Continuation Model Predictive Control
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Solution Overview
Problem
Continuation model predictive control (CNMPC) for nonlinear dynamical systems faces inefficiencies due to the complexity of computing the coefficient matrix and the need for matrix-vector multiplications, leading to slow convergence and reduced control quality in real-time calculations.
Innovation Solution
The method involves determining and using a preconditioner by explicitly calculating the coefficient matrix, either partially or fully, using approximate and exact coefficient functions, allowing for flexible partitioning and updating of matrix entries across time, space, and accuracy levels, and utilizing this preconditioner in iterative methods to reduce the number of iterations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the coefficient matrix is computed using exact coefficient functions, then the accuracy of the control solution is improved, but the computational time and complexity increase
Solution Approach 1:
The patent applies partial action by computing only the necessary portion of the coefficient matrix (partial coefficient matrix) rather than the complete matrix. This selective computation reduces the computational burden while maintaining sufficient accuracy for the control application, directly addressing the trade-off between accuracy and computational time.
Solution Approach 2:
The patent pre-computes and stores the partial coefficient matrix in advance before it is needed for the control calculation. This preliminary action allows the matrix to be readily available during real-time control operations, reducing the computational time required during critical control moments while maintaining accuracy through the use of exact coefficient functions for the pre-computed portion.
2Productivity
If the coefficient matrix is computed using approximate coefficient functions, then the computational speed is improved, but the accuracy of the control solution deteriorates
Solution Approach 1:
The patent computes only a partial coefficient matrix rather than the full matrix, which reduces computational speed requirements while maintaining adequate accuracy. This partial computation approach allows the system to achieve sufficient control accuracy without the full computational burden of exact matrix computation.
3Reliability
If the complete coefficient matrix is computed and stored, then the quality of the control signal is improved, but the memory requirements and device complexity increase
Solution Approach 1:
The patent extracts and uses only the essential portion of the coefficient matrix (partial coefficient matrix) that is necessary for achieving acceptable control quality. By taking out only the needed elements rather than storing the complete matrix, the system reduces memory requirements and device complexity while maintaining sufficient control signal quality.
Data Source
AI summary
A method for a continuation model predictive control (CMPC) of a system determines at least a part of a preconditioner using an approximate coefficient function and determines a solution vector by solving a matrix equation of the CMPC with a coefficient matrix defined by an exact coefficient function at a current time step of a control using an iterative method with the preconditioner. The approximate coefficient function applied to a vector approximates a result of an application of the exact coefficient function to the vector. A control signal for controlling the system is generated using the solution vector.