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

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.

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

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

In this chapter, by using neural network (NN)-based online learning optimal control approach, a decentralized control strategy is developed to stabilize a class of continuous-time large-scale interconnected nonlinear systems . It is proven that the decentralized control strategy of the overall system can be established by adding appropriate feedback gains to the optimal control laws of the isolated subsystems . Then, an online policy iteration (PI) algorithm is developed to solve the Hamilton–Jacobi–Bellman equations related to the optimal control problem. By constructing a set of critic NNs, the cost functions can be obtained by NN approximation, followed by the control laws. Furthermore, as a generalization, an NN-based decentralized control law is developed to stabilize the large-scale interconnected nonlinear systems using an online model-free integral PI algorithm. The model-free PI approach can solve the decentralized control problem for large-scale interconnected nonlinear systems with unknown dynamics. Finally, two simulation examples are provided to illustrate the effectiveness of the present decentralized control scheme.

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

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.

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

In this paper, the problem of delay-dependent decentralized control for a class of nonlinear large-scale interconnected systems with similar structure is investigated, where the linear state vectors, the nonlinear state vectors and the nonlinear interconnections involve time delays. The new similar structure is presented via memory feedback. Based on which, by exploiting the structure of interconnected systems, the new integral inequalities, constrained Lyapunov equations and LMI method, a decentralized memory derivative feedback control strategy is proposed to stabilize the resulting interconnected systems uniformly asymptotically, in addition, the stability domain is estimated. Finally, simulation results show the effectiveness of the proposed approach.

This paper studies the problem of global decentralized control by applying time-varying output feedback for large-scale uncertain systems whose subsystems are interconnected not only by their outputs but also by their unmeasurable states. We show that under a linear growth condition, there is a decentralized output feedback controller rendering the closed-loop systems globally exponentially stable. This is accomplished by extending and output feedback domination design which requires little information about the nonlinear systems. Furthermore, we apply our results to a multi-vehicle system to demonstrate the use of our time-varying output feedback controller.

We present a novel decentralized tracking control scheme for a class of large-scale nonlinear systems with partial state constraints. For the first time, backstepping design with the newly proposed BLF is incorporated to effectively deal with the control problem of nonlinear systems with interconnected constraints. To prevent the states of each subsystem from violating the constraints, we employ a special barrier Lyapunov function (BLF), which grows to infinity whenever its argument approaches some finite limits. By ensuring boundedness of the barrier Lyapunov function in the closed loop, we ensure that those limits are not transgressed. Asymptotic tracking is achieved without violation of the constraints, and all closed-loop signals remain bounded. In the end, an illustrative example is presented to demonstrate the performance of the proposed control.

In this paper, a novel cooperative constrained distributed model predictive control algorithm is proposed to control the nonlinear interconnected constrained large-scale systems. In this algorithm, a novel reduced-order cooperative optimisation approach is proposed which is its main contribution that reconstructs and improves the global cost function of any local controller. In proposed algorithm, each local controller computes its optimal control by minimising the corresponding global cost function which is a combination of its own and its neighbouring subsystems’ cost functions. The sufficient conditions are derived to guarantee the recursive feasibility and closed-loop stability specifications to ensure the convergence of the overall states into the positive region which is the neighbourhood of origin. The performance of the proposed algorithm is illustrated via simulation results of a nonlinear large-scale cart-spring-damper system.

To the problem of this interconnected large-scale system, which is characteristic of unmatched nonlinear interconnection functions that are unknown but quadratically bounded in the overall system state, decentralized feedback control method based on BMI is presented. The proposed control method can determine whether the overall system is asymptotical stable by judging whether the deduced linear matrix inequality groups have feasible solutions after offsetting the interaction of nonlinear interconnected function to the subsystem itself by virtue of the known inequality and converting the qualification to Lyapunov stability into bilinear matrix inequality via Schur complement formula. Whatpsilas more, the algorithms for calculating the decentralized feedback matrices are proposed by using the method of bilinear matrix inequalities. In additional, the simulation of a two-machine infinite bus power system has been done here. The simulation results of this power system show that this method is feasible and valid.

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

This paper is concerned with the analysis of large-scale interconnected systems constructed from positive subsystems and a nonnegative interconnection matrix. We first show that the interconnected system is admissible and stable if and only if a Metzler matrix built from the coefficient matrices of the positive subsystems and the interconnection matrix is Hurwitz stable. By means of this key lemma, we further provide several results that characterize the admissibility and stability of interconnected systems in terms of the weighted L1-induced norm of each positive subsystem and the Frobenius eigenvalue of the interconnection matrix. Moreover, in the case where every subsystem is SISO, we provide explicit conditions under which the interconnected system has the property of persistence, i.e., the state of the interconnected system converges to a unique strictly positive vector (up to a strictly positive constant multiplicative factor) irrespective of nonnegative and nonzero initial states. We illustrate the effectiveness of the persistence results via formation control of multi-agent systems.

The problem of decentralized impulse controllability/observability for large-scale interconnected descriptor systems with two subsystems by derivative feedback is studied. Necessary conditions for the existence of a derivative feedback controller for the first subsystem of the large-scale interconnected descriptor systems ensuring the second subsystem to be impulse controllable and impulse observable are derived, respectively. Based on the results, a derivative feedback controller for the first subsystem of the large-scale interconnected descriptor systems is constructed easily such that the second subsystem is impulse controllable or impulse observable. Finally, examples are given to illustrate the effectiveness of the results obtained in this paper.