Can thermodynamics be used to design control systems?

Thermodynamics is a physical branch of science that governs the thermal behavior of dynamical systems. The laws of thermodynamics involving conservation of energy and nonconservation of entropy are two of the most useful and general laws in all sciences. In particular, the second law of thermodynamics is intimately connected to the irreversibility of dynamical processes, that is, the status quo cannot be restored everywhere. This gives rise to an interesting quantity known as entropy. Entropy permeates the whole of nature, and unlike energy, which describes the state of a dynamical system, entropy is a measure of change in the status quo of a dynamical system. Motivated by this observation, in this paper we use the entropy function for deterministic systems as a benchmark to design a semistable controller that minimizes the time-averaging of the "heat" of the dynamical system. We present both state feedback control and output feedback control based on the dissipative systems. Furthermore, we convert the control design into an optimization problem with two linear matrix inequalities.