Stability and robustness of adaptive controllers for underactuated Lagrangian systems and robotic networks

This dissertation studies the stability and robustness of an adaptive control framework for underactuated Lagrangian systems and robotic networks. In particular, an adaptive control framework is designed for a manipulator, which operates on an underactuated dynamic platform. The framework promotes the use of a filter in the control input to improve the system robustness. The characteristics of the controller are represented by two decoupled indicators. First, the adaptation gain determines the rate of adaptation, as well as the deviation between the adaptive control system and a nonadaptive reference system governing the ideal response. Second, the filter bandwidth determines the tracking performance, as well as the system robustness. The ability of the control scheme to tolerate time delay in the control loop, which is an indicator of robustness, is explored using numerical simulations, estimation of the time-delay margin of an equivalent linear, time-invariant system, and parameter continuation for Hopf bifurcation analysis.;This dissertation also performs theoretical study of the delay robustness of the control framework. The analysis shows that the controller has a positive lower bound for the time-delay margin by exploring a number of properties of delay systems, especially the continuity of their solutions in the delay, uniformly in time. In particular, if the input delay is below the lower bound, then the state and control input of the closed-loop system follow those of a nonadaptive, robust reference system closely. A method for computing the lower bound for the delay robustness using a Pade approximant is proposed. The results show that the minimum delay that destabilizes the system, which may also be estimated by forward simulation, is always larger than the value computed by the proposed method.;The control framework is extended to the synchronization and consensus of networked manipulators operating on an underactuated dynamic platform in the presence of communication delays. The theoretical analysis based on input-output maps of functional differential equations shows that the adaptive control system's behavior matches closely that of a nonadaptive reference system. The tracking-synchronization objective is achieved despite the effects of communication delays and unknown dynamics of the platform. When there is no desired trajectory common to the networked manipulators, a modified controller drives all robots to a consensus configuration. A further modification is proposed that allows for the control of the constant and time-varying consensus values using a leader-follower scheme. Simulation results illustrate the performance of the proposed control algorithms.