  In this paper, we expand recently introduced observer-based periodic
event-triggered control (PETC) and self-triggered control (STC) schemes for
reaction-diffusion PDEs to boundary control of $2\times2$ coupled hyperbolic
PDEs in canonical form and with anti-collocated measurement and actuation
processes. The class of problem under study governs transport phenomena arising
in water management systems, oil drilling, and traffic flow, to name a few.
Relative to the state of the art in observer-based event-triggered control of
hyperbolic PDEs, our contribution goes two steps further by proposing
observer-based PETC and STC for the considered class of systems. These designs
arise from a non-trivial redesign of an existing continuous-time
event-triggered control (CETC) scheme. PETC and STC eliminate the need for
constant monitoring of an event-triggering function as in CETC; PETC requires
only periodic evaluations of the triggering function for event detection,
whereas STC is a predictor-feedback that anticipates the next event time at the
current event exploiting continuously accessible output measurements. The
introduced resource-aware designs act as input holding mechanisms allowing for
the update of the input signal only at events. Subject to the designed boundary
output feedback PETC and STC control laws characterized by a set of
event-trigger design parameters, the resulting closed-loop systems, which are
inherently Zeno-free by design, achieve exponential convergence to zero in the
spatial $L^2$ norm. We illustrate the feasibility of the approach by applying
the control laws to the linearized Saint-Venant model, which describes the
dynamics of shallow water waves in a canal and is used to design flow
stabilizer feedback laws via gate actuation. The provided simulation results
illustrate the proposed theory.
