28,044 research outputs found
Delay-Adaptive Boundary Control of Coupled Hyperbolic PDE-ODE Cascade Systems
This paper presents a delay-adaptive boundary control scheme for a coupled linear hyperbolic PDE-ODE cascade system with an unknown and
arbitrarily long input delay. To construct a nominal delay-compensated control
law, assuming a known input delay, a three-step backstepping design is used.
Based on the certainty equivalence principle, the nominal control action is fed
with the estimate of the unknown delay, which is generated from a batch
least-squares identifier that is updated by an event-triggering mechanism that
evaluates the growth of the norm of the system states. As a result of the
closed-loop system, the actuator and plant states can be regulated
exponentially while avoiding Zeno occurrences. A finite-time exact
identification of the unknown delay is also achieved except for the case that
all initial states of the plant are zero. As far as we know, this is the first
delay-adaptive control result for systems governed by heterodirectional
hyperbolic PDEs. The effectiveness of the proposed design is demonstrated in
the control application of a deep-sea construction vessel with cable-payload
oscillations and subject to input delay
Safe Adaptive Control of Hyperbolic PDE-ODE Cascades
Adaptive safe control employing conventional continuous infinite-time
adaptation requires that the initial conditions be restricted to a subset of
the safe set due to parametric uncertainty, where the safe set is shrunk in
inverse proportion to the adaptation gain. The recent regulation-triggered
adaptive control approach with batch least-squares identification (BaLSI,
pronounced ``ballsy'') completes perfect parameter identification in finite
time and offers a previously unforeseen advantage in adaptive safe control,
which we elucidate in this paper. Since the true challenge of safe control is
exhibited for CBF of a high relative degree, we undertake a safe BaLSI design
in this paper for a class of systems that possess a particularly extreme
relative degree: ODE-PDE-ODE sandwich systems. Such sandwich systems arise in
various applications, including delivery UAV with a cable-suspended load.
Collision avoidance of the payload with the surrounding environment is
required. The considered class of plants is hyperbolic PDEs
sandwiched by a strict-feedback nonlinear ODE and a linear ODE, where the
unknown coefficients, whose bounds are known and arbitrary, are associated with
the PDE in-domain coupling terms that can cause instability and with the input
signal of the distal ODE. This is the first safe adaptive control design for
PDEs, where we introduce the concept of PDE CBF whose non-negativity as well as
the ODE CBF's non-negativity are ensured with a backstepping-based safety
filter. Our safe adaptive controller is explicit and operates in the entire
original safe set
Boundary Control of Coupled Reaction-Advection-Diffusion Systems with Spatially-Varying Coefficients
Recently, the problem of boundary stabilization for unstable linear
constant-coefficient coupled reaction-diffusion systems was solved by means of
the backstepping method. The extension of this result to systems with advection
terms and spatially-varying coefficients is challenging due to complex boundary
conditions that appear in the equations verified by the control kernels. In
this paper we address this issue by showing that these equations are
essentially equivalent to those verified by the control kernels for first-order
hyperbolic coupled systems, which were recently found to be well-posed. The
result therefore applies in this case, allowing us to prove H^1 stability for
the closed-loop system. It also shows an interesting connection between
backstepping kernels for coupled parabolic and hyperbolic problems.Comment: Submitted to IEEE Transactions on Automatic Contro
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