MPC Controller Robustness Against Near Collinearity

The patent implements dynamic adjustment of control targets and move suppression factors based on real-time detection of near-collinear relationships and model uncertainty. The controller adapts its calculation approach by modifying steady-state targets and move plans when collinearity is detected, rather than using a fixed control strategy. This dynamic adaptation resolves the contradiction by making the control calculation complexity variable - simple when not needed, complex only when model uncertainty and near-collinearity are present.

The patent changes key control parameters including steady-state targets, move suppression factors, and economic objective function weights based on detected system conditions. When near-collinearity is detected, the controller modifies these parameters to avoid problematic control moves. This parameter adaptation allows the controller to maintain reliability under uncertain conditions while avoiding unnecessary complexity when conditions are favorable.

The patent performs preliminary detection of near-collinear relationships and preliminary calculation of modified steady-state targets before executing control moves. By identifying problematic directions in advance and pre-calculating alternative targets, the controller avoids oscillations without requiring complex real-time adjustments during execution. This preliminary action resolves the contradiction by shifting computational complexity to the planning phase while maintaining stable execution.

The patent introduces an intermediary detection and adjustment mechanism that identifies near-collinear relationships and mediates between the ideal control target and the practically achievable target. This intermediary layer calculates modified steady-state targets that avoid weak directional movements while maintaining overall control objectives. The intermediary resolves the contradiction by providing a computational bridge that achieves stability without excessive complexity.

The patent applies partial constraint relaxation only in specific situations where near-collinearity and model uncertainty are detected, rather than uniformly relaxing all constraints. The robustness factor is applied selectively to modify only the affected constraints, maintaining precision for unaffected constraints. This partial action resolves the contradiction by applying relaxation only where necessary to prevent violations, preserving control precision elsewhere.

The patent applies different levels of constraint strictness locally based on detected system conditions. When near-collinearity is detected in specific variable relationships, the controller applies relaxed constraints only to those affected variables while maintaining strict constraints on other variables. This local differentiation resolves the contradiction by protecting constraint satisfaction where needed while preserving control precision where possible.

The patent replaces complex mathematical detection of near-collinear relationships with a practical computational test based on the determinant of the gain matrix or a similar numerical criterion. Instead of requiring sophisticated mathematical analysis, the controller uses a straightforward computational check that is easy to implement and evaluate in real-time. This substitution resolves the contradiction by replacing difficult detection with a simple, reliable computational test.

The patent uses a simple, computationally inexpensive test for detecting near-collinearity that can be performed quickly at each control cycle. The detection mechanism is designed to be computationally lightweight, requiring minimal processing resources and time. This inexpensive detection approach resolves the contradiction by providing reliable operating point selection without significant computational burden.