Lyapunov-based switched systems control

Switched systems theory consists of tools developed for systems containing a combination of continuous and discrete dynamics. The focus in this dissertation is the further development and application of switched systems methods for uncertain nonlinear networked systems. Specifically, control methods are developed in this dissertation when the discontinuities are due to the dynamics or network connections.;In Chapter 2, the discontinuities are due to the dynamics of the system. Specifically, an output feedback (OFB), time-dependent, switched controller is developed for an Euler-Lagrange system with parametric uncertainty and exogenous disturbances. This controller is motivated by the fact that Euler-Lagrange (EL) dynamics model many practical systems with nonlinear dynamics and hybrid behaviors (e.g., a bouncing ball, humanoid robot during walking). In this chapter, a time-dependent switching signal is designed using an average dwell-time scheme based on a multiple Lyapunov functions (MLFs) approach where the switched system achieves semi-global uniformly ultimately bounded (UUB) tracking with arbitrary switching sequences.;In Chapter 3 and 4, the discontinuities in the system are due to the fact that sensing occurs within a network. In Chapter 3, a decentralized switched controller is developed to enable dynamic agents to perform global formation configuration convergence while maintaining network connectivity and avoiding collision within agents and between stationary obstacles using only local feedback under limited and intermittent sensing. In a multi-agent network system, an individual robot reacts according to information (e.g., relative location) from its neighboring agents. In practice, sensors have limited abilities (e.g., limitation in field-of-view, malfunction) that can lead to intermittent sensing. As a result, constant position feedback for agents may not be available all the time, and these inevitable behaviors might lead to a disconnected network or collisions between agents. Furthermore, these hybrid dynamics motivate the need for switched system analysis. Using a navigation function framework, a decentralized switched controller is developed in Chapter 3 to navigate the agents to the desired positions while ensuring network maintenance and collision avoidance. Simulations are provided to support the development.;In Chapter 4, a decentralized controller that uses event-triggered scheduling is developed for the leader-follower consensus problem under fixed and switching communication topologies. To eliminate continuous inter-agent communication, state estimates of neighboring agents are designed for control feedback and are updated by scheduled communication to reset growing estimate errors. Since the estimate error is associated with a neighbor's control input, when the true state is unknown until the next communication, the state estimate is updated to avoid system instability. The communication event times are based on an event-triggered approach, which considers the interplay between system performance and minimal communication bandwidth and requires no communication for event detection. Since the control strategy produces switched dynamics, analysis is provided to show that Zeno behavior is avoided by developing a positive constant lower bound on the minimum inter-event interval. A Lyapunov-based convergence analysis is also provided to indicate asymptotic convergence of the developed control methodology. Simulation results are provided to demonstrate the effectiveness of the developed control strategy.;In Chapter 5, the decentralized event-triggered control scheme developed in Chapter 4 is extended to a containment control problem, where multiple leaders exist in the networked system and only a subset of followers can communicate to some of the leaders. The estimate-based decentralized controller, requiring only local feedback from neighboring follower agents, is designed for each follower agent so that communication can be intermittent to reduce communication while achieving a global objective. To avoid the Zeno behavior induced from the event-triggered approach, a positive constant lower bound on the inter-event interval is developed. A Lyapunov-based convergence analysis is provided to indicate asymptotic convergence of the developed strategy. Simulation results are provided to demonstrate the effectiveness of the developed control strategy.