Consensus-based control for a network of diffusion PDEs with boundary local interaction

In this paper the problem of driving the state of a network of identical agents, modeled by boundary-controlled heat equations, towards a common steady-state profile is addressed. Decentralized consensus protocols are proposed to address two distinct problems. The first problem is that of steering the states of all agents towards the same constant steady-state profile which corresponds to the spatial average of the agents initial condition. A linear local interaction rule addressing this requirement is given. The second problem deals with the case where the controlled boundaries of the agents dynamics are corrupted by additive persistent disturbances. To achieve synchronization between agents, while completely rejecting the effect of the boundary disturbances, a nonlinear sliding-mode based consensus protocol is proposed. Performance of the proposed local interaction rules are analyzed by applying a Lyapunov-based approach. Simulation results are presented to support the effectiveness of the proposed algorithms

Model based fault diagnosis and prognosis of class of linear and nonlinear distributed parameter systems modeled by partial differential equations

With the rapid development of modern control systems, a significant number of industrial systems may suffer from component failures. An accurate yet faster fault prognosis and resilience can improve system availability and reduce unscheduled downtime. Therefore, in this dissertation, model-based prognosis and resilience control schemes have been developed for online prediction and accommodation of faults for distributed parameter systems (DPS). First, a novel fault detection, estimation and prediction framework is introduced utilizing a novel observer for a class of linear DPS with bounded disturbance by modeling the DPS as a set of partial differential equations. To relax the state measurability in DPS, filters are introduced to redesign the detection observer. Upon detecting a fault, an adaptive term is activated to estimate the multiplicative fault and a tuning law is derived to tune the fault parameter magnitude. Then based on this estimated fault parameter together with its failure limit, time-to-failure (TTF) is derived for prognosis. A novel fault accommodation scheme is developed to handle actuator and sensor faults with boundary measurements. Next, a fault isolation scheme is presented to differentiate actuator, sensor and state faults with a limited number of measurements for a class of linear and nonlinear DPS. Subsequently, actuator and sensor fault detection and prediction for a class of nonlinear DPS are considered with bounded disturbance by using a Luenberger observer. Finally, a novel resilient control scheme is proposed for nonlinear DPS once an actuator fault is detected by using an additional boundary measurement. In all the above methods, Lyapunov analysis is utilized to show the boundedness of the closed-loop signals during fault detection, prediction and resilience under mild assumptions --Abstract, page iv

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

Model based fault diagnosis and prognosis of nonlinear systems

Rapid technological advances have led to more and more complex industrial systems with significantly higher risk of failures. Therefore, in this dissertation, a model-based fault diagnosis and prognosis framework has been developed for fast and reliable detection of faults and prediction of failures in nonlinear systems. In the first paper, a unified model-based fault diagnosis scheme capable of detecting both additive system faults and multiplicative actuator faults, as well as approximating the fault dynamics, performing fault type determination and time-to-failure determination, is designed. Stability of the observer and online approximator is guaranteed via an adaptive update law. Since outliers can degrade the performance of fault diagnostics, the second paper introduces an online neural network (NN) based outlier identification and removal scheme which is then combined with a fault detection scheme to enhance its performance. Outliers are detected based on the estimation error and a novel tuning law prevents the NN weights from being affected by outliers. In the third paper, in contrast to papers I and II, fault diagnosis of large-scale interconnected systems is investigated. A decentralized fault prognosis scheme is developed for such systems by using a network of local fault detectors (LFD) where each LFD only requires the local measurements. The online approximators in each LFD learn the unknown interconnection functions and the fault dynamics. Derivation of robust detection thresholds and detectability conditions are also included. The fourth paper extends the decentralized fault detection from paper III and develops an accommodation scheme for nonlinear continuous-time systems. By using both detection and accommodation online approximators, the control inputs are adjusted in order to minimize the fault effects. Finally in the fifth paper, the model-based fault diagnosis of distributed parameter systems (DPS) with parabolic PDE representation in continuous-time is discussed where a PDE-based observer is designed to perform fault detection as well as estimating the unavailable system states. An adaptive online approximator is incorporated in the observer to identify unknown fault parameters. Adaptive update law guarantees the convergence of estimations and allows determination of remaining useful life --Abstract, page iv

Observation and control of PDE with disturbances

In this Thesis, the problem of controlling and Observing some classes of distributed parameter systems is addressed. The particularity of this work is to consider partial differential equations (PDE) under the effect of external unknown disturbances. We consider generalized forms of two popular parabolic and hyperbolic infinite dimensional dynamics, the heat and wave equations. Sliding-mode control is used to achieve the control goals, exploiting the robustness properties of this robust control technique against persistent disturbances and parameter uncertainties

Observation and control of PDE with disturbances

In this Thesis, the problem of controlling and Observing some classes of distributed parameter systems is addressed. The particularity of this work is to consider partial differential equations (PDE) under the effect of external unknown disturbances. We consider generalized forms of two popular parabolic and hyperbolic infinite dimensional dynamics, the heat and wave equations. Sliding-mode control is used to achieve the control goals, exploiting the robustness properties of this robust control technique against persistent disturbances and parameter uncertainties

Boundary second-order sliding-mode control of an uncertain heat process with unbounded matched perturbation

n/

Sliding Mode Observers for Distributed Parameter Systems: Theory and Applications

Many processes in nature and industry can be described by partial differential equations. PDEs employ quantities such as density, temperature, velocity, etc. and their partial derivatives to model these phenomena. However, in the case of distributed parameter systems, it is not always possible to have access to the states of the systems due to technical difficulties such as lack of sensors. Therefore, there is the need for state observers to estimate the states of the system only having the output of the system available. In this research, the theory of sliding mode and variable structure systems are employed in order to design observers for different classes of distributed parameter systems such as advection equation, Burgers’ equation, Euler equations, etc. Some contributions of this research are: suggesting the state transformation which allows the arbitrary design of sliding manifold in sliding mode observer, developing some formulae for observer gain, discussing the shock wave situation and its properties and solutions, designing sliding mode observer and anomaly detection system for a system of advection equations

Polynomial Fuzzy Observer-Based Feedback Control for Nonlinear Hyperbolic PDEs Systems

This article explores the observer-based feedback control problem for a nonlinear hyperbolic partial differential equations (PDEs) system. Initially, the polynomial fuzzy hyperbolic PDEs (PFHPDEs) model is established through the utilization of the fuzzy identification approach, derived from the nonlinear hyperbolic PDEs model. Various types of state estimation and controller design problems for the polynomial fuzzy PDEs system are discussed concerning the state estimation problem. To investigate the relaxed stability problem, Euler’s homogeneous theorem, Lyapunov–Krasovskii functional with polynomial matrices (LKFPM), and the sum-of-squares (SOSs) approach are adopted. The exponential stabilization condition is formulated in terms of the spatial-derivative-SOSs (SD-SOSs). Additionally, a segmental algorithm is developed to find the feasible solution for the SD-SOS condition. Finally, a hyperbolic PDEs system and several numerical examples are provided to illustrate the validity and effectiveness of the proposed results