Asymptotic stabilization of some finite and infinite dimensional systems by means of dynamic event-triggered output feedbacks

Abstract

The problem of designing dynamic sampling routines for output feedback stabilization of controlled plants is considered. Instead of the more conventional periodic sampling, our approach is based on using event-triggered conditions for sampling, which potentially allow for reduced rate of communication between the plant and the controller. Several classes of control systems, from finite dimensional to infinite dimensional, are considered in this chapter, each within its own problem setup. Within the setup of finite dimensional systems, we consider plants comprising linear and nonlinear ordinary differential equations, and controlled via dynamic output feedback controllers. For such systems, we provide (different) event-based dynamic algorithms to determine sampling times for outputs and control inputs. In the linear case, it is further shown that the proposed algorithms are robust with respect to communication errors due to quantization, and if the parameters of the quantizers are updated appropriately, then the state of the closed-loop system converges asymptotically to the equilibrium. For the plants modeled as hyperbolic system of conservation laws, an event-triggered sampling algorithm of the boundary control results in state converging to the origin. Together with the asymptotic stabilization of the closed-loop system, it is also shown that there exists a minimum inter-sampling time and thus Zeno solutions are avoided in the closed-loop system despite the state-dependent occurrence of discrete dynamics. For all the considered control problems, Lyapunov functions are instrumental to define the sampling sequences, the desired robustness properties of the controller are formalized using input-to-state stability notion, and the tools from stability of cascaded systems and certainty equivalence principle are essential for analysis carried out in our work.