Operational Flexibility Analysis of High-Dimensional Systems via Cylindrical Algebraic Decomposition

The cylindrical algebraic decomposition (CAD) method has been proposed for flexibility analysis to derive analytical expressions of a feasible region. Due to the heavy computational burden caused by symbolic computation, this method can only handle small-scale problems currently. To overcome this limitation, a novel method is proposed for high-dimensional systems with a number of equalities and limited inequalities. A surrogate model is first built to correlate the inequality constraints based on an initial sample set. Then, the flexibility region is obtained with explicit expressions via the CAD method. Next, for any violation, a refinement will be activated by taking an iterative process of boundary check, surrogate modeling, region deriving, and underestimation check, until the termination condition is satisfied. The case studies show the proposed method can effectively describe the flexibility region for both the convex and nonconvex systems.