Stabilization in Dynamic Systems with Varying Equilibrium

System design often explores optimality of performance. What is optimal is, however, often not predefined or static in most cases, because it is affected by the context of operation, such as the environment or external system inputs. In this paper, we formulate the maintenance of optimality of performance in dynamical systems in terms of the standard notion of stabilization. For systems with observable external inputs and computable optimality, stabilization may be achieved by adding a stabilizing input estimator to the system. But environments and external inputs are often unobservable. To overcome this difficulty, we present two alternative methods, one based on a game-theoretic MinMax strategy that leads to Nash equilibrium, and the other based on a feedback control mechanism that adds a stabilizing output transformer to the system. We exemplify these two approaches with a pursuit-evasion application and a MAC layer duty cycle adaptation protocol, respectively.