Partial Differential Equation Observer Research Articles

False Data Injection Attack in a Platoon of CACC: Real-Time Detection and Isolation With a PDE Approach

Connected vehicles are potential solutions to address some of the existing challenges in transportation systems, such as emission, traffic congestion, and fuel consumption. However, vehicular communication networks endure from reliability and security issues. Cyber-attacks with performance-disrupting purposes can lead to catastrophic collisions in connected vehicles and increase traffic congestion. To ensure safety and reliability, a monitoring system with the capability of diagnosing cyber-attacks is necessary for connected vehicles. In this study, we consider a platoon of connected vehicles equipped with cooperative adaptive cruise control (CACC) that is subjected to a specific type of cyber-attack, namely <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">“False Data Injection”</i> (FDI) attack. A smart FDI attack is modeled with ghost vehicles injection into the connected vehicles network to disrupt the performance of the whole system. To ease the analysis, we develop a partial differential equation (PDE) model for the CACC vehicle dynamics using its ordinary differential equations (ODE). Furthermore, a PDE observer is designed to detect the FDI attack and locate the attack’s injection point in the platoon. Lyapunov stability theory has been utilized to verify the observer’s convergence under no-attack scenario and study residuals’ behaviors in the presence of the attack. A non-zero constant threshold is considered to provide robustness in attack detection despite the measurement noises. Eventually, the effectiveness of the proposed algorithm is evaluated with simulation studies.

Boundary control design based on partial differential equation observer for vibration suppression and attitude control of flexible satellites with multi-section solar panels

A novel partial differential equation observer is proposed to be used in boundary attitude and vibration control of flexible satellites. Solar panels’ vibrations and attitude dynamics form a coupled partial differential equation–ordinary differential equation system which is controlled directly without discretization. Few feedback signals from boundaries are required which are estimated via a partial differential equation observer. Consequently, just satellite attitude and angular velocity should be measured and still the control system benefits information from continuous part vibrations. The closed-loop system is proved to be asymptotically stable. Simulations with a finite element technique illustrate good performance of this observer-based boundary controller.

Stabilization of Filament Production Rate for Screw Extrusion-Based Polymer Three-Dimensional-Printing

AbstractPolymer three-dimensional (3D)-printing has been commercialized rapidly during recent years; however, there remains a matter of improving the manufacturing speed. Screw extrusion has a strong potential to fasten the process through the simultaneous operation of the filament production and the deposition. This paper develops a control algorithm for screw extrusion-based 3D printing of thermoplastic materials through an observer-based output feedback design. We consider the thermodynamic model describing the time evolution of the temperature profile of an extruded polymer by means of a partial differential equation (PDE) defined on the time-varying domain. The time evolution of the spatial domain is governed by an ordinary differential equation that reflects the dynamics of the position of the phase change interface between polymer granules and molten polymer deposited as a molten filament. The steady-state profile of the distributed temperature along the extruder is obtained when the desired setpoint for the interface position is prescribed. To enhance the feasibility of our previous design, we develop a PDE observer to estimate the temperature profile via measured values of surface temperature and the interface position. An output feedback control law considering a cooling mechanism at the boundary inlet as an actuator is proposed. In extruders, the control of raw material temperature is commonly achieved using preconditioners as part of the inlet feeding mechanism. For some given screw speeds that correspond to slow and fast operating modes, numerical simulations are conducted to prove the performance of the proposed controller. The convergence of the interface position to the desired setpoint is achieved under physically reasonable temperature profiles.

Leaderless cooperative control of robotic sensor networks for monitoring dynamic pollutant plumes

In this paper, the problem of cooperative control of robotic sensor networks (RSNs) for monitoring dynamic pollutant plumes in two-dimensional (2D) space is studied. The pollutant plume propagation dynamics is governed by a 2D advection-diffusion partial differential equation (PDE), and the plume front is modelled by a level set with a pre-specified threshold value. Distributed consensus Luenberger-type PDE observers are first constructed using local concentration measurements from the RSNs for unanimous estimate of the dynamic concentration field over the entire spatial domain. With the aid of the distributed consensus observers, a leaderless cooperative control scheme is then developed for the RSNs to monitor the dynamic plume front expansion. It is proved using the Lyapunov stability method and set stability concept that the proposed cooperative control scheme guarantees tracking of the dynamic plume front expansion and coverage of the plume front. Extensive numerical simulation results demonstrate the effectiveness and merit of the proposed cooperative control scheme.

Model-Based Battery Thermal Fault Diagnostics: Algorithms, Analysis, and Experiments

Safety and reliability remain critical issues for lithium-ion (Li-ion) batteries. Out of many possible degradation modes, thermal faults constitute a significant part of critical causes that lead to battery degradation and failure. Therefore, it is extremely important to diagnose these thermal faults in real time to ensure battery safety. Motivated by this fact, we propose a partial differential equation (PDE) model-based real-time scheme in this paper for diagnosing thermal faults in Li-ion batteries. The objective of the diagnostic scheme is to detect and estimate the size of the thermal fault. We utilize a distributed parameter 1-D thermal model for cylindrical battery cells in conjunction with PDE observer-based techniques to design the scheme. Furthermore, we apply threshold-based technique to ensure robustness against modeling and measurement uncertainties. The effectiveness of the scheme is illustrated by: 1) analytical convergence verification of the PDE observers under heathy and faulty conditions utilizing Lyapunov stability theory; 2) extensive simulation case studies; 3) robustness analysis against model parametric uncertainties; and 4) experimental studies on a commercial Li-ion battery cell.

Distributed attitude tracking for multiple flexible spacecraft described by partial differential equations

In this study, two distributed control strategies without or with a Partial Differential Equation (PDE) observer are proposed for a team of flexible spacecraft to track the attitude of a virtual leader under an undirected and connected graph. The PDE is used to describe the dynamics of each spacecraft with an appendage, which is simplified as a hub-beam system. It is assumed that both the hub and the free tip of the beam are actuated directly. The desired attitude angle, i.e., the state of the virtual leader, is only available for one spacecraft in the team. A distributed controller with the state measurements of the hub and the free tip of the beam is proposed first. Then a PDE observer is presented to estimate the states of the whole beam from the information of the hub only. A novel distributed controller with such a PDE observer is developed to drive the team to track the virtual leader. It is indicated by rigorous proof that the two controllers can actuate the team to the desired attitude without any residual vibration asymptotically. Finally, two numerical examples are given to demonstrate the effectiveness of the proposed controllers.

Backstepping boundary observer based-control for hyperbolic PDE in rotary drilling system

It is well known that torsional vibrations in oil well system affect the drilling directions and may be inherent for drilling systems. The drill pipe model is described by second order hyperbolic Partial Differential Equation (PDE) with mixed boundary conditions in which a sliding velocity is considered at the top end. In this paper, we consider the problem of boundary observer design for one-dimensional PDE with the usually neglected damping term. The main purpose is the construction of a control law which stabilizes the damped wave PDE, using only boundary measurements. From the Lyapunov theory, we show an exponentially vibration stability of the partially equipped oil well drilling system. The observer-based control law is found using the backstepping approach for second-order hyperbolic PDE. The numerical simulations confirm the effectiveness of the proposed PDE observer based controller.

A spatial domain decomposition approach to distributed H∞ observer design of a linear unstable parabolic distributed parameter system with spatially discrete sensors

ABSTRACTThis paper discusses the design problem of distributed H∞ Luenberger-type partial differential equation (PDE) observer for state estimation of a linear unstable parabolic distributed parameter system (DPS) with external disturbance and measurement disturbance. Both pointwise measurement in space and local piecewise uniform measurement in space are considered; that is, sensors are only active at some specified points or applied at part thereof of the spatial domain. The spatial domain is decomposed into multiple subdomains according to the location of the sensors such that only one sensor is located at each subdomain. By using Lyapunov technique, Wirtinger's inequality at each subdomain, and integration by parts, a Lyapunov-based design of Luenberger-type PDE observer is developed such that the resulting estimation error system is exponentially stable with an H∞ performance constraint, and presented in terms of standard linear matrix inequalities (LMIs). For the case of local piecewise uniform measurement in space, the first mean value theorem for integrals is utilised in the observer design development. Moreover, the problem of optimal H∞ observer design is also addressed in the sense of minimising the attenuation level. Numerical simulation results are presented to show the satisfactory performance of the proposed design method.

Modeling and vibration control for a flexible pendulum inverted system based on a PDE observer

ABSTRACTThis study addresses the problem of trajectory control of a flexible pendulum inverted system on the basis of the partial differential equation (PDE) and ordinary differential equation (ODE) dynamic model. One of the key contributions of this study is that a new model is proposed to simplify the complex system. In addition, this study proposed a nonlinear PDE observer to estimate distributed positions and velocities along flexible pendulum. Singular perturbation method is proposed to solve the coupling system of nonlinear PDE observer. The nonlinear PDE observer is divided into a fast subsystem and a slow subsystem by the use of the singular perturbation method. To stabilise this fast subsystem, a boundary controller is proposed at the free end of the beam. The sliding-mode control method is proposed to design controller for slow subsystems. The asymptotic stability of both the proposed nonlinear PDE observer and controller is validated by theoretical analysis. The results are illustrated by simulation.

Observer-based partial differential equation boundary control for a flexible two-link manipulator in task space

This study addresses the problem of trajectory control of a flexible two-link manipulator on the basis of the partial differential equation (PDE) dynamic model. One of the key contributions of this study is that a novel non-linear PDE observer is proposed to estimate distributed positions and velocities along flexible links, which cannot be achieved by the typical ordinary differential equation observer. In addition, the rigidity-flexibility coupling dynamics is decomposed using the singular perturbation approach, thus providing convenience for control design. Based on the proposed observer and the decoupled PDE model, a boundary control scheme is designed to regulate the end effector along reference trajectory in task space and suppress vibration simultaneously. The asymptotic stability of both the proposed observer and the control algorithm is validated by theoretical analysis and demonstrated by simulation results, respectively.