Approach to Boolean Controller Design by Algebraic Relaxation for Heating Systems

The paper proposes a relaxation for a special class of Boolean controller design problems which are relevant in optimization of heating systems for buildings. The controller design problem can be formulated as a discrete optimization problem which is hard to solve because of its exponential complexity. It is shown how Zhegalkin polynomials can be used as algebraic normal forms of the Boolean controller functions to relax the optimization problem to a continuous one. This has been successfully applied to a real heating system with 1.8 MW thermal power and the improvement is discussed.