1 research outputs found
Nonlinear Bilateral Output-Feedback Control for a Class of Viscous Hamilton-Jacobi PDEs
We tackle the boundary control and estimation problems for a class of viscous
Hamilton-Jacobi PDEs, considering bilateral actuation and sensing, i.e., at the
two boundaries of a 1-D spatial domain. First, we solve the nonlinear
trajectory generation problem for this type of PDEs, providing the necessary
feedforward actions at both boundaries. Second, in order to guarantee
trajectory tracking with an arbitrary decay rate, we construct nonlinear,
full-state feedback laws employed at the two boundary ends. Third, a nonlinear
observer is constructed, using measurements from both boundaries, which is
combined with the full-state feedback designs into an observer-based
output-feedback law. All of our designs are explicit since they are constructed
interlacing a feedback linearizing transformation (which we introduce) with
backstepping. Due to the fact that the linearizing transformation is locally
invertible, only regional stability results are established, which are,
nevertheless, accompanied with region of attraction estimates. Our stability
proofs are based on the utilization of the linearizing transformation together
with the employment of backstepping transformations, suitably formulated to
handle the case of bilateral actuation and sensing. We illustrate the developed
methodologies via application to traffic flow control and we present consistent
simulation results.Comment: Submitted to Automatica on March 8, 201