Right now, the world is looking towards machine learning and algorithms that exploit 'big data' for the required advancements in autonomy, but in safety-critical settings, we cannot rely on black-box algorithms without insight into their internal workings or safety/stability guarantees. Further, designing learned systems that function in the real world typically requires massive training sets. So, instead we are turning towards classic input-output stability theory to see how it can help us tackle the challenges of modern autonomy. In particular, we have used it to confront issues in networked systems (large scale, heterogeneous agents, communication delays, changing interconnections), have found that it can establish stability and reduce data requirements in imitation learning, and have confronted longstanding issues in the analysis and control of nonlinear systems.
Dissipativity augmented imitation learning
Imitation learning enables synthesis of controllers for systems with complex objectives and uncertain plant models. However, ensuring an imitation learned controller is stable requires copious amounts of data and/or a known plant model. We've explored an input-output stability approach to imitation learning, which achieves stability with sparse data sets while only requiring coarse knowledge of the energy characteristics of the plant.
Systematic dissipativity analysis for nonlinear systems
When studying input-output stability theory, an elephant in the room has loomed, barely acknowledged for six decades: we've developed input-output stability for nonlinear systems, and yet have no systematic way to establish input-output properties for general nonlinear systems. While Hamilton Jacobi Inequalities (HJIs) establishing input-output stability have long been known, the problem is that nobody knows how to solve them. Important strides have been made, developing SOS methods, but these only apply to polynomial systems, and data-driven techniques using delta covering and probablistic strategies, which entail either untenable sample complexity or lack error estimates. We have been expanding this field by solving HJIs for more general input-affine systems, and providing error-estimates that motivate new sampling strategies for data-driven methods.