Estimate-to-State Stability for Hybrid Human-Prosthesis Systems

Control methods for lower-limb powered prostheses remain mostly model-independent and cannot always guarantee stability. Model-dependent prosthesis control methods yield a wider range of stability properties, but require knowledge of the interaction force between the human and prosthesis. Any error in force estimation compromise the formal guarantees. This paper addresses this uncertainty by formalizing the stability of the human-prosthesis system subject to force estimation error. A novel notion of estimate-to-state stability is introduced and provides a means to guarantee exponential convergence of the prosthesis to a set when the controller's model contains estimation error. Conditions are established to ensure input-to-state stability for the human's hybrid periodic orbits when subject to disturbances from the prosthesis control action deviating from its nominal control law. A class of estimate-to-state stable prosthesis controllers is proposed and implemented in simulation, demonstrating how the human-prosthesis system converges to a tube around the desired trajectory resulting in stable walking.