Dissipativity/Passivity Based Control Design for Symmetric and Switched Systems with Application to Medical Robotics

This dissertation studies the concept of dissipativity and passivity, in theory, in practice, and in design of control systems. To this end, the passivity-based approach is applied to the control of various types of challenging problems in control systems such as symmetric systems, switched systems, and the automatic cycle-rider systems. Dissipativity/passivity-based control approaches, referred to as energy-based control approaches, play an important role in the analysis and synthesis of dynamical control systems. In these approaches, the manner of energy exchange between different components of the system is analyzed. In addition to the direct connection of the passivity and stability concepts, the passivity and dissipativity-based approaches provide numerous advantages including conserved passivity of interconnected systems and guaranteed stability of closed loop systems. This dissertation contains three major topics all linked to the dissipativity/passivity concept.

The stability and dissipativity of multi-agent systems connected in different symmetry configurations are studied from a theoretical point of view. The concept of symmetry is employed as a powerful tool to overcome the complexity of multi-agent systems by reducing the number of multiple interconnections. Both, stability conditions and passivity properties of cyclic and star-shaped symmetric systems are explored.

In addition, we employ energy-based approaches using an enhanced passivation method in the design of switched controllers to circumvent the challenges of traditional methods. Moreover, to guarantee the desirable performance and stability for switched controllers, our approach provides new insights in extending the notion of passivity to hybrid systems.

In practical applications, motion cycling system is considered. Combination of learnability and passivity concepts are applied to the state-dependent switched cycle-rider system, induced by functional electrical stimulation (FES) of lower muscles with the assistance of an electric motor. The FES cycling exercise has therapeutic applications in the rehabilitation of people who suffer from paraplegia due to the stroke, or spinal cord-injury. In this novel approach, the iterative learning control (ILC) scheme is utilized which benefits from the passivity property of the closed-loop dynamics to reject the nonlinearity and uncertainty of the dynamics and to achieve the desired tracking performance after certain cycling trials.

Overall, this dissertation considers energy-based control methods to address both theoretical (symmetric and hybrid systems) and practical (functional electrical stimulation) problems and makes important contributions to the stability and performance of nonlinear control systems.