Symbiotic Control of Uncertain Dynamical Systems: Harnessing Synergy Between Fixed-Gain Control and Adaptive Learning Architectures

Both fixed-gain control and adaptive learning architectures aim to mitigate the effects of uncertainties. In particular, fixed-gain control offers more predictable closed-loop system behavior but requires the knowledge of uncertainty bounds. In contrast, while adaptive learning does not necessarily require such knowledge, it often results in less predictable closed-loop system behavior compared to fixed-gain control. To this end, this paper presents a novel symbiotic control framework that offers the strengths of fixed-gain control and adaptive learning architectures. Specifically, this framework synergistically integrates these architectures to mitigate the effects of uncertainties in a more predictable manner as compared to adaptive learning alone and it does not require any knowledge on such uncertainties. Both parametric and nonparametric uncertainties are considered, where we utilize neural networks to approximate the unknown uncertainty basis for the latter case. Counterintuitively, the proposed framework has the ability to achieve a desired level of closed-loop system behavior even with an insufficient number of neurons (e.g., when the neural network approximation error is large) or in the face of injudiciously selected adaptive learning parameters (e.g., high leakage term parameters).