430 research outputs found
Delay-Adaptive Control of First-order Hyperbolic PIDEs
We develop a delay-adaptive controller for a class of first-order hyperbolic
partial integro-differential equations (PIDEs) with an unknown input delay. By
employing a transport PDE to represent delayed actuator states, the system is
transformed into a transport partial differential equation (PDE) with unknown
propagation speed cascaded with a PIDE. A parameter update law is designed
using a Lyapunov argument and the infinite-dimensional backstepping technique
to establish global stability results. Furthermore, the well-posedness of the
closed-loop system is analyzed. Finally, the effectiveness of the proposed
method was validated through numerical simulation
Robust stabilization of first-order hyperbolic PDEs with uncertain input delay
A backstepping-based compensator design is developed for a system of
first-order linear hyperbolic partial differential equations (PDE)
in the presence of an uncertain long input delay at boundary. We introduce a
transport PDE to represent the delayed input, which leads to three coupled
first-order hyperbolic PDEs. A novel backstepping transformation, composed of
two Volterra transformations and an affine Volterra transformation, is
introduced for the predictive control design. The resulting kernel equations
from the affine Volterra transformation are two coupled first-order PDEs and
each with two boundary conditions, which brings challenges to the
well-posedness analysis. We solve the challenge by using the method of
characteristics and the successive approximation. To analyze the sensitivity of
the closed-loop system to uncertain input delay, we introduce a neutral system
which captures the control effect resulted from the delay uncertainty. It is
proved that the proposed control is robust to small delay variations. Numerical
examples illustrate the performance of the proposed compensator
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
Delay-robust stabilization of an n + m hyperbolic PDE-ODE system
International audienceIn this paper, we study the problem of stabilizing a linear ordinary differential equation through a system of an n + m (hetero-directional) coupled hyperbolic equations in the actuating path. The method relies on the use of a backstepping transform to construct a first feedback to tackle in-domain couplings present in the PDE system and then on a predictive tracking controller used to stabilize the ODE. The proposed control law is robust with respect to small delays in the control signal
An adaptive observer for hyperbolic systems with application to UnderBalanced Drilling
International audienceWe present an adaptive observer design for a first-order hyperbolic system of Partial Differential Equations with uncertain boundary parameters. The design relies on boundary measurements only, and is based on a backstepping approach. Using a Gradient Descent technique, we prove exponential convergence of the distributed system and estimation of the parameter. This method is applied to the estimation of uncertain parameters during the process of oil well drilling
Mean-square Exponential Stabilization of Mixed-autonomy Traffic PDE System
Control of mixed-autonomy traffic where Human-driven Vehicles (HVs) and
Autonomous Vehicles (AVs) coexist on the road have gained increasing attention
over the recent decades. This paper addresses the boundary stabilization
problem for mixed traffic on freeways. The traffic dynamics are described by
uncertain coupled hyperbolic partial differential equations (PDEs) with Markov
jumping parameters, which aim to address the distinctive driving strategies
between AVs and HVs. Considering the spacing policies of AVs vary in the mixed
traffic, the stochastic impact area of AVs is governed by a continuous Markov
chain. The interactions between HVs and AVs such as overtaking or lane changing
are mainly induced by the impact areas. Using backstepping design, we develop a
full-state feedback boundary control law to stabilize the deterministic system
(nominal system). Applying Lyapunov analysis, we demonstrate that the nominal
backstepping control law is able to stabilize the traffic system with Markov
jumping parameters, provided the nominal parameters are sufficiently close to
the stochastic ones on average. The mean-square exponential stability
conditions are derived, and the results are validated by numerical simulations
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