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Weak Variations Optimal Boundary Control of Hyperbolic PDEs with Application to Traffic Flow and Delay Systems

  • Author(s): Moura, Scott J
  • et al.
Abstract

We investigate optimal boundary control of firstorder hyperbolic PDEs. These equations are ubiquitous in engineered systems, such as traffic flows, fluid flows, heat exchangers, chemical reactors, and oil production systems. We derive linear quadratic regulator (LQR) results using a weak variations approach, recently developed for parabolic PDEs. The distinguishing characteristic of this approach is that it provides a systematic procedure for deriving LQR control laws without semi-group theoretic concepts. Ultimately, these control laws are given by the solution of an associated Riccati PDE. We demonstrate the applicability of these results on two case studies: traffic flow control and input-delayed systems. Finally, we extend the LQR results to solve the output reference tracking problem. Unlike motion planning, these reference tracking equations do not require state trajectory generation.

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