Adaptive Bounded Bilinear Control of a Parallel-Flow Heat Exchanger

Abstract

This work investigates the adaptive constrained control design for a parallel-flow heat exchanger represented by a system of two coupled linear first-order hyperbolic partial differential equations (PDEs). This system incorporates structured uncertainty involving unknown in-domain parameters that characterize neglected dynamics in the heat exchanger model. These parameters may encompass unmodeled heat transfer phenomena, variations in fluid properties, and modeling simplifications. The objective is to regulate the internal fluid outlet temperature to track a desired reference trajectory by adjusting the external fluid velocity. Due to inherent physical constraints, this manipulated variable is upper and lower-bounded. Accordingly, the control problem is bounded and bilinear. Using the set-invariance principle and an energy-like framework, we first develop a bounded state-feedback controller. Then, since the measurements are considered only at the boundaries, we propose an adaptive boundary observer using a swapping scheme and a recursive least squares identifier. The proposed adaptive observer provides online estimates of the distributed state and the unknown parameters. Next, the state-feedback controller is associated with the boundary observer and parameter identifier, and the exponential stability of the closed-loop system is guaranteed using Lyapunov's stability theory. Finally, we provide numerical simulations to demonstrate the efficiency of the proposed control scheme.