Distributed controller design for a class of sparse singular systems with privacy constraints

Extreme UltraViolet (EUV) lithography is a new technology for production of integrated circuits. In EUV lithographic machines, optical elements are heated by absorption of exposure energy. Heating induces thermoelastic deformations of optical elements and consequently, it creates wavefront aberrations. These Thermally Induced Wavefront Aberrations (TIWA) can significantly degrade the resolution of EUV lithographic machines. One of the ways to correct TIWA and consequently, to improve the resolution of EUV lithographic machines, is to use the Adaptive Optics (AO) technique and predictive control algorithms. However, the predictive control of TIWA is a challenging problem, mainly because the dynamical behavior of TIWA is described by thermoelastic Partial Differential Equations (PDEs). By discretizing the thermoelastic equations using the finite difference or finite element methods, large-scale state-space models can be obtained. A striking feature of these state-space models is that they have sparse (multi) banded matrices. Consequently, these state-space models can be interpreted as large-scale networks of local subsystems. All this implies that the problem of correcting TIWA can be placed in a much more general context of identifying, estimating and controlling large-scale interconnected (distributed) systems. However, currently used estimation and control algorithms are not computationally feasible for large-scale systems. For this reason, this thesis focuses on the development of computationally efficient identification, estimation and control algorithms for large-scale interconnected systems. In this thesis, we prove that the inverses of (finite-time) Gramians of large-scale interconnected systems, obtained by discretizing PDEs, belong to a class of off-diagonally decaying matrices. Consequently, these inverses can be approximated by sparse (multi) banded matrices with O(N) complexity, where N is the number of local subsystems. To compute the approximate inverses, the Chebyshev approximation method and the Newton iteration are used. On the basis of these theoretical results, we develop novel estimation and identification algorithms for large-scale interconnected systems. The computational and memory complexity of these methods scale with O(N). This is the main advantage over the traditional estimation and identification methods, which complexity is O(N^3). Furthermore, in this thesis we develop and experimentally verify AO control algorithms for predictive correction of TIWA. The experimental results give a good first indication for a possible implementation of the developed predictive control algorithms in EUV lithographic machines. Finally, we develop and experimentally test an iterative learning control algorithm for high performance correction of wavefront aberrations.

Distributed control of large-scale dynamical systems poses a new challenge to the field of control driven by the technological advances of modern communication networks. A particular challenge is the distributed design of such control systems. Here, a distributed iterative controller synthesis method for continuous time linear systems using a gradient descent method is presented. One of the main contributions is the determination of the step size according to a distributed Barzilai-Borwein (BB) method. As the control objective, we treat the finite horizon linear quadratic cost functional. The gradient approach uses communication only with direct neighbors and is based on the forward simulation of the system states and the backwards simulation of adjoint states. The effectiveness of the approach is shown by means of numerical simulations.

This paper deals with a novel Plug-and-Play (PnP) architecture for the control and monitoring of Large-Scale Systems (LSSs). The proposed approach integrates a distributed Model Predictive Control (MPC) strategy with a distributed Fault Detection (FD) architecture and methodology in a PnP framework. The basic concept is to use the FD scheme as an autonomous decision support system: once a fault is detected, the faulty subsystem can be unplugged to avoid the propagation of the fault in the interconnected LSS. Analogously, once the issue has been solved, the disconnected subsystem can be re-plugged-in. PnP design of local controllers and detectors allow these operations to be performed safely, i.e., without spoiling stability and constraint satisfaction for the whole LSS. The PnP distributed MPC is derived for a class of nonlinear LSSs and an integrated PnP distributed FD architecture is proposed. Simulation results in two paradigmatic examples show the effectiveness and the potential of the general methodology.

Hybrid decentralized maximum entropy control for large-scale dynamical systems

Decentralized adaptive neural control of nonlinear interconnected large-scale systems with unknown time delays and input saturation

This paper deals with the problem of iterative learning control for large-scale interconnected linear systems in the presence of fixed initial shifts. According to the characteristics of the systems, iterative learning control laws are proposed for such large-scale interconnected linear systems based on the PD-type learning schemes. The proposed controller of each subsystem only relies on local output variables without any information exchanges with other subsystems. Using the contraction mapping method, we show that the schemes can guarantee the output of the system converges uniformly to the corresponding output limiting trajectory over the whole time interval along the iteration axis. Simulation examples illustrate the effectiveness of the proposed method.

In analysis and control of large-scale nonlinear dynamical systems, a distributed approach is often an attractive option due to its computational tractability and usually low communication requirements. Success of the distributed control design relies on the separability of the network into weakly interacting subsystems such that minimal information exchange between subsystems is sufficient to achieve satisfactory control performance. While distributed analysis and control design for dynamical network have been well studied, decomposition of nonlinear networks into weakly interacting subsystems has not received as much attention. In this article we propose a vector Lyapunov functions based approach to quantify the energy-flow in a dynamical network via a model of a comparison system. Introducing a notion of power and energy flow in a dynamical network, we use sum-of-squares programming tools to partition polynomial networks into weakly interacting subsystems. Examples are provided to illustrate the proposed method of decomposition.

Efficient decentralized iterative learning tracker for unknown sampled-data interconnected large-scale state-delay system with closed-loop decoupling property

Delay-dependent robust and reliable [formula omitted] fuzzy hyperbolic decentralized control for uncertain nonlinear interconnected systems

Decentralized PI tracking control for non-Gaussian large-scale interconnected distribution systems

In recent years, research on speed cruise control for high-speed trains has primarily focused on control design based on multi-body models, leading to significant achievements in various aspects. However, these control methods adopt a single-system approach for the entire train, referred to as the typical method in this paper. Yet, a malfunction in one car can impact the control laws and controller design of other cars. To address this limitation, this paper proposes a large-scale system control, which decouples the control laws and controller design for each car. The control law of an individual car is based solely on its own position and velocity, with separate processes for solving the controllers for each car. Additionally, the speed cruise control for high-speed trains considers both <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\mathcal {H}}_{2}$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\mathcal {H}}_{\infty } $ </tex-math></inline-formula> performance in the presence of uncertain parameters. This study validates the feasibility of such decoupled methods in this domain through simulation-based comparative analysis. This study aims to verify the effectiveness of large-scale system control methods in normal train operations and to lay the foundation for more complex fault-tolerant and model-switching challenges. In these areas, large-scale system control has greater potential for application and offers significant advantages.

Secure administration of cryptographic role-based access control for large-scale cloud storage systems

Predefined-time adaptive neural network decentralized control for large-scale interconnected systems with input hysteresis.

This paper presents a new design algorithm for the decentralized output feedback control problem of large-scale interconnected systems. Each subsystem is composed of a linear (possibly unstable) time-invariant part and an uncertain additive nonlinearity which is a discontinuous function of time and state of the overall system. The nonlinear function is assumed to be bounded by a quadratic inequality, and a decentralized estimated state feedback controller and a decentralized observer are designed for each subsystem, based on linear matrix inequalities. Sufficient conditions for the synthesis of feedback action are provided, under which the proposed controllers and observers can achieve robust stabilization of the overall large-scale system. An attractive feature of the proposed scheme is that it guarantees connective stability of the overall system and requires no intersubsystem communication. The controller design is evaluated on a natural circulation drum boiler, where the nonlinear model describes the key dynamical properties of the drum, the risers, the downcomers, and the turbine-generator unit. The linearized system has two poles at origin, one associated with water dynamics and the other with generator dynamics. Simulation results are presented that show the effectiveness of the proposed control against instabilities following sudden load variations. The control is also effective for steady-state operation.

Toolkit for large-scale systems controller design in the frequency-domain