Symbiotic autonomous systems (SAS) are advanced intelligent and cognitive systems that exhibit autonomous collective intelligence enabled by coherent symbiosis of human-machine interactions in hybrid societies. Basic research in the emerging field of SAS has triggered advanced general-AI technologies that either function without human intervention or synergize humans and intelligent machines in coherent cognitive systems. This work presents a theoretical framework of SAS underpinned by the latest advances in intelligence, cognition, computer, and system sciences. SAS are characterized by the composition of autonomous and symbiotic systems that adopt bio-brain-social-inspired and heterogeneously synergized structures and autonomous behaviours. This paper explores the cognitive and mathematical foundations of SAS. The challenges to seamless human-machine interactions in a hybrid environment are addressed. SAS-based collective intelligence is explored in order to augment human capability by autonomous machine intelligence towards the next generation of general AI, cognitive computers, and trustworthy mission-critical intelligent systems. Emerging paradigms and engineering applications of SAS are elaborated via autonomous knowledge learning systems that symbiotically work between humans and cognitive robots. This article is part of the theme issue 'Towards symbiotic autonomous systems'.
Keywords: autonomous systems; brain-inspired systems; cognitive cybernetics; cognitive systems; intelligence science; symbiotic autonomous systems.