MI-MPC Controller State-Invariant Constraint Transformation
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Solution Overview
Problem
Implementing mixed-integer model predictive control (MI-MPC) on embedded control systems with limited computational resources is challenging due to the complexity of solving mixed-integer programming problems, which are NP-hard and require significant computational effort, especially for systems with discrete variables.
Innovation Solution
The solution involves transforming state constraints into state-invariant control constraints to reduce the search space and using methods like branch-and-bound to efficiently solve MI-MPC problems, including warm starting and data-based learning to reuse information across control steps and tighten the search space.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Extent of automation
If mixed-integer model predictive control (MI-MPC) is implemented on embedded control systems, then real-time control of complex systems with discrete variables is achieved, but the computational burden becomes excessive due to the NP-hard nature of solving mixed-integer programming problems
Solution Approach 1:
The patent segments the control problem by separating continuous and discrete variables, applying different solution methods to each. Continuous variables are handled through standard MPC optimization while discrete variables are addressed through specialized combinatorial optimization techniques, allowing the problem to be solved in manageable parts rather than as a single intractable mixed-integer program
Solution Approach 2:
The patent performs preliminary actions by pre-computing feasible discrete control sequences and pre-processing system models offline. This preparation work reduces the computational burden during real-time operation, allowing the embedded system to execute control decisions with limited computational resources while maintaining real-time performance
2Productivity
If the search space for solving MI-MPC problems is reduced through transformations, then computational efficiency is improved, but the complexity of constraint transformations increases
Solution Approach 1:
The patent applies parameter changes by transforming state constraints into control constraints through mathematical relationships derived from system dynamics. This transformation changes the form of the constraints while preserving their essential meaning, enabling more efficient search space exploration in the control variable domain rather than the state variable domain
3Loss of time
If warm starting and data-based learning are used to reuse information across control steps, then the number of MPC problems to be solved is minimized, but the memory requirements and initialization complexity increase
Solution Approach 1:
The patent performs preliminary action by pre-computing and storing solution information from previous control steps, including optimal control sequences and intermediate optimization results. This warm starting approach allows the solver to begin from a favorable initial position rather than from scratch, significantly reducing the time required to solve each subsequent MPC problem while using modest amounts of memory to store the pre-computed data
Data Source
AI summary
A controller for controlling a system with continuous and discrete elements of operation accepts measurements of a current state of the system, solves a mixed-integer model predictive control (MI-MPC) problem subject to state constraints on the state of the system to produce control inputs to the system, and submits the control inputs to the system thereby changing the state of the system. To solve the MI-MPC, the controller transforms the state constraints into state-invariant control constraints on the control inputs to the system, such that any combination of values for the control inputs, resulting in a sequence of values for the state variables that satisfy the state constraints, also satisfy the state-invariant control constraints, and solve the MI-MPC problem subject to the state constraints and the state-invariant control constraints.