Constraint Transformation and Controller Synthesis

Abstract

The mathematical tools and propositions of the previous chapter provide the backbone for the control synthesis procedures presented here. In section 5.1, two techniques are introduced for generating transformations of linear constraints that will meet the conditions of Theorem 4.12. Methods for characterizing all admissible constraints for plants with uncontrollable and unobservable transitions are developed in section 5.2. These techniques are then employed in sections 5.3 and 5.4 for the synthesis of controllers that enforce the disjunctions of linear inequalities allowing for a high degree of plant freedom. The technique for enforcing nonconvex constraints in section 5.4 requires a modification of the controller net’s transition enabling rule, however this modification does not decrease the computational efficiency of the closed loop system model, and it leaves many of the analytical results and tools intact.