Nonlinear MPC Discretization for Stable and Controllable Models
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Solution Overview
Problem
Nonlinear model predictive controllers face challenges in ensuring the stability and controllability of discrete time models derived from continuous time nonlinear dynamical systems, as discretization can render the models unstable and uncontrollable.
Innovation Solution
The system automatically discretizes a continuous time model to produce a discrete time model, checks the parameters by sweeping through a predetermined operational range to identify stable and controllable regions in the parameter space, and configures the nonlinear model predictive controller with parameters within these regions to ensure stability and controllability.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If automatic discretization is used to convert continuous time model to discrete time model, then productivity is improved, but stability and controllability of the model deteriorate
Solution Approach 1:
The system performs preliminary stability and controllability checks on discretization parameters before final model deployment. By预先 checking parameter validity and performing stability analysis on the discrete-time model, the system prevents unstable configurations from being used in control operations, thus maintaining reliability while preserving automation efficiency
Solution Approach 2:
The system implements feedback mechanisms where stability and controllability are verified after discretization. The parameter checking module continuously monitors discretization parameters and provides feedback to adjust parameters that fall outside stable regions, ensuring the discrete-time model maintains reliability while benefiting from automatic discretization
2Reliability
If parameter checking is performed by sweeping through operational range, then model reliability is improved, but computational time increases
Solution Approach 1:
The parameter checking process is segmented into distinct phases: initial stability region identification, parameter validation checks, and runtime verification. By dividing the comprehensive parameter checking into manageable segments, the system ensures thorough reliability verification while avoiding unnecessary computational overhead in real-time operations
Solution Approach 2:
Stability and controllability analysis is performed preliminarily during system setup and parameter definition phases. By pre-identifying stable parameter regions and validating parameters before control operations begin, the system minimizes runtime computational burden while maintaining high reliability standards
Data Source
AI summary
Systems and methods for automatically ensuring the stability and controllability of a nonlinear control system are disclosed herein. In one embodiment, a system receives, at a nonlinear model predictive controller, optimal control problem code representing an optimal control problem that includes a continuous time model representing a nonlinear dynamical system. The system discretizes automatically the continuous time model to produce a discrete time model that includes one or more parameters. The system also checks automatically the one or more parameters to identify one or more regions in a parameter space in which the discrete time model is both stable and controllable when used by the nonlinear model predictive controller. The system also controls, at least in part, operation of the nonlinear dynamical system using the nonlinear model predictive controller configured with values of the one or more parameters that lie within the one or more stable and controllable regions.