Model Predictive Control With Iterative Uncertainty Updates
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Solution Overview
Problem
Model predictive control (MPC) systems face challenges in handling uncertainty, leading to suboptimal performance or instability when applied to partially unknown or uncertain models, as they typically rely on linear assumptions and lack efficient methods for updating parameters in real-time.
Innovation Solution
The system employs model predictive control with parameters of uncertainty that are updated iteratively using model-free optimization methods, such as extremum seeking or reinforcement learning, to improve performance by analyzing real-time changes and previous outputs, allowing for simultaneous identification and control of systems with time-varying or constant uncertainties.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If model predictive control is applied to uncertain models, then the system can handle real-world variability, but the performance becomes suboptimal or unstable
Solution Approach 1:
The patent implements iterative updating of uncertain parameters using feedback from actual system outputs. The controller compares predicted outputs with actual measurements and adjusts the uncertain parameters accordingly, creating a closed-loop system that adapts to real-world variations while maintaining stability through continuous correction
Solution Approach 2:
The patent transforms static uncertain parameters into dynamic, time-varying parameters that are continuously updated. By allowing parameters to evolve iteratively based on system performance, the controller adapts to changing conditions while maintaining reliable operation through real-time adjustment
2Productivity
If linear assumptions are used in MPC, then the control problem becomes computationally tractable, but the system cannot capture nonlinear behaviors
Solution Approach 1:
The patent changes the nature of parameters from fixed linear values to dynamically updated parameters that can capture nonlinear behaviors. By iteratively adjusting parameters based on system responses, the linear MPC framework adapts to represent nonlinear system characteristics without requiring computationally intensive nonlinear solvers
3Measurement precision
If parameters of uncertainty are updated iteratively, then the accuracy of control inputs improves, but the computational complexity increases
Solution Approach 1:
The patent applies partial updating of parameters by focusing computational effort on updating only the uncertain parameters rather than the entire control policy. This selective approach improves accuracy of control inputs by refining specific parameter values while avoiding the computational burden of complete re-optimization at each step
Data Source
AI summary
A method controls a system for a multiple control steps according to the reference trajectory of a task of the operation to produce an actual trajectory of the system completing the task of the operation. For each control step, a control input to the system is determined using a model predictive control (MPC) having at least one parameter of uncertainty. The method determines a value of a learning cost function of a distance between the reference trajectory and the actual trajectory and determines, using a model free optimization, a value of the parameter of uncertainty reducing the value of the learning cost function. Next, the method determines a set of control inputs for completing the task according to the reference trajectory using the MPC with the updated parameter of uncertainty.