A Lattice-Theoretic Algorithm forFeasible-State Optimization in Sensor-Driven Cyber-Physical Systems

Abstract

Controllers for industrial systems now function within heterogeneous sensing processes, disjoint operating intervals, safety zones, and preferences over partial orders. Scalar threshold-based controller systems tend to have high interpretability but low robustness when approaching their boundaries. On the other hand, pure continuous optimization approaches fail to convey the feasibility of the problem if the technical state space is non-continuous or naturally discreet. In this research paper, a lattice interval-based approach to optimizing the technical state of industrial assets is proposed. The multisensor inputs form the basis of technical states that are ordered using finite product lattices. Utility on the feasible interval accounts for throughput, stability, safety margin, energy consumption, and actuator effort. Extremum selection subsequently selects the most useful feasible state when operating in production mode and the least risky state when operating in protective mode. Meet and join provide safe conflict resolution and merge heterogeneous readings from multiple sensors into an admissible result. Properties guarantee finite completion, feasibility maintenance, and deterministic tie breaking. Reproducible testing on a synthetic benchmark of a compressor skid is conducted to compare the algorithm against thresholdbased and weighted scalar approaches. The findings indicate that the proposed algorithm does not violate hard constraints and makes fewer actuator adjustments than the baselines.