Large-scale Nonlinear Systems Research Articles

A New Robust Adaptive Decentralized Tube Model Predictive Control of Continuous Time Uncertain Nonlinear Large-Scale Systems

In this paper, a new decentralized model predictive control has been proposed for continuous-time nonlinear large-scale systems made of multiple interconnected subsystems and uncertain systems with...

Plug-and-Play Fault Detection and Isolation for Large-Scale Nonlinear Systems With Stochastic Uncertainties

This paper proposes a novel scalable model-based fault detection and isolation approach for the monitoring of nonlinear large-scale systems, consisting of a network of interconnected subsystems. The fault diagnosis architecture is designed to automatically manage the possible plug-in of novel subsystems and unplugging of existing ones. The reconfiguration procedure involves only local operations and communication with neighboring subsystems, thus, yielding a distributed and scalable architecture. In particular, the proposed fault diagnosis methodology allows the unplugging of faulty subsystems in order to possibly avoid the propagation of faults in the interconnected large-scale system. Measurement and process uncertainties are characterized in a probabilistic way leading to the computation, at each time-step, of stochastic time-varying detection thresholds with guaranteed false-alarms probability levels. To achieve this goal, we develop a distributed state estimation scheme, using a consensus-like approach for the estimation of variables shared among more than one subsystem; the time-varying consensus weights are designed to allow plug-in and unplugging operations and to minimize the variance of the uncertainty of the fault diagnosis thresholds. Convergence results of the distributed estimation scheme are provided. A novel fault isolation method is then proposed, based on a generalized observer scheme and providing guaranteed error probabilities of the fault exclusion task. Detectability and isolability conditions are provided. Simulation results on a power network model comprising 15 generation areas show the effectiveness of the proposed methodology.

Development of a High-Performance Method of Vibration Analysis for a Large-Scale Nonlinear System

Development of a High-Performance Method of Vibration Analysis for a Large-Scale Nonlinear System

Fuzzy Adaptive Control Design Strategy of Nonlinear Switched Large-Scale Systems

The decentralized adaptive fuzzy control problem for switched nonstrict-feedback nonlinear large-scale systems is investigated in this paper. Fuzzy logic systems are adopted to identify the unknown nonlinear system functions and unknown interconnected nonlinearities. A linear state observer is designed to solve the problem of unmeasured states, and a new observer-based output-feedback decentralized control scheme is developed based on adaptive fuzzy control principle and bacsktepping design technique. The proposed control strategy not only solves the control design problem of more general form nonlinear switched systems in nonstrict-feedback form, but also does not require the switched signals to meet the restriction of average dwell time. The stability of fuzzy control systems under arbitrary switchings is proven based on the common Lyapunov function method. Simulation results of numerical examples are presented to further demonstrate the effectiveness of the proposed control strategy.

Finite-Time Filter Decentralized Control for Nonstrict-Feedback Nonlinear Large-Scale Systems

This paper solves the finite-time decentralized control problem for uncertain nonlinear large-scale systems in nonstrict-feedback form. The considered controlled plants are different from the previous results of finite-time control systems, which are the nonstrict-feedback large-scale systems with the unknown functions consisting of all states, interactions, and immeasurable states. Fuzzy logic systems and a filter-based state observer are utilized to model uncertain systems and deal with the immeasurable states, respectively. By combining the backstepping recursive design with Lyapunov function theory, a finite-time adaptive fuzzy decentralized control approach is raised. It is testified that the developed control strategy can guarantee that the closed-loop signals are bounded, and the outputs of systems have satisfactory tracking performance in a finite time. A quadruple-tank process system is given to testify the effectiveness and applicability of the proposed approach.

Synchronization in large-scale nonlinear network systems with uncertain links

In this paper, we study the problem of synchronization over a network, with nonlinear components dynamics modeled in Lure form, and linear stochastic interaction among the components. To study this problem we utilize the stochastic version of Positive Real Lemma (PRL), which is used to provide a sufficient condition for synchronization of stochastic network systems. This sufficiency condition is a function of nominal (mean coupling) Laplacian eigenvalues, and the statistics of link uncertainty in the form of coefficient of dispersion (CoD). Robust control-based small-gain interpretation is provided for the derived sufficiency condition which allows us to define the margin of synchronization. The margin of synchronization is used to understand the important tradeoff between the component dynamics, network topology, and uncertainty characteristics for network synchronization. Our results indicate that significant role played by both the largest and the second smallest eigenvalue of the nominal Laplacian in synchronization of stochastic networks. Furthermore, for a special class of network system connected over torus topology we provide an analytical expression for the tradeoff between the number of neighbors and the dimension of the torus. Similarly, by exploiting the identical nature of component dynamics computationally efficient sufficient condition, independent of network size, is provided for general class of network system. Simulation results for network of coupled oscillators with stochastic link uncertainty are presented to verify the developed theoretical framework.

Asynchronous Decentralized Fuzzy Observer-Based Output Feedback Control of Nonlinear Large-Scale Systems

This paper is concerned with the problem of decentralized robust $${{\mathscr {H}}}_{\infty }$$ output feedback control for a class of continuous-time nonlinear large-scale systems based on T–S fuzzy affine models. Based on a common quadratic Lyapunov function and piecewise quadratic Lyapunov functions, some new results are proposed to the asynchronous observer-based controller synthesis for T–S fuzzy affine large-scale systems with unmeasurable premise variables. The observer and controller gains can be attained through solving a set of linear matrix inequalities. Finally, two simulation examples are presented to verify the effectiveness of the proposed approaches.

Decentralized Control for Large-Scale Nonlinear Systems With Unknown Mismatched Interconnections via Policy Iteration

In this paper, the decentralized control problem is solved based on a policy iteration algorithm for large-scale nonlinear systems with unknown mismatched interconnections. The unknown interconnection is approximated by a neural network with local states of isolated subsystem and substituted reference states of coupled subsystems. Then, an adaptive estimation term is utilized to construct the improved local performance index function that reflects the substitution error. Hereafter, the closed-loop large-scale nonlinear system is guaranteed to be ultimately uniformly bounded by the implementation of a set of developed decentralized optimal control policies. Two simulation examples are given to verify the effectiveness of the presented scheme. The significant contribution of this scheme lies in that it removes the common assumptions on satisfying matching condition and upper boundedness of interconnections, when designing the decentralized optimal control for large-scale nonlinear systems.

Adaptive Fuzzy Robust Fault-Tolerant Optimal Control for Nonlinear Large-Scale Systems

The problem of adaptive fuzzy decentralized fault-tolerant optimal control is investigated for nonlinear large-scale systems with actuator faults in this paper. Fuzzy logic systems are utilized to approximate the unknown nonlinear functions and learn cost functions. Filtered signals are adopted to circumvent the problems of an algebraic loop on designing the decentralized controllers. Based on the backstepping technique and fault-tolerant control technique, a decentralized feedforward control strategy is designed. Based on the adaptive critic technique, a decentralized feedback optimal control strategy is designed. By combining the feedforward control strategy with the feedback optimal control strategy, a novel adaptive fuzzy decentralized fault-tolerant optimal control scheme is established. The stability of the closed-loop system is proved by using the Lyapunov stability theory. The effectiveness of the proposed decentralized control approach is confirmed via a simulation example.

Robustly stable adaptive horizon nonlinear model predictive control

We present a new method for adaptively updating nonlinear model predictive control (NMPC) horizon lengths online via nonlinear programming (NLP) sensitivity calculations. This approach depends on approximation of the infinite horizon problem via selection of terminal conditions, and therefore calculation of non-conservative terminal conditions is key. For this, we also present a new method for calculating terminal regions and costs based on the quasi-infinite horizon framework that extends to large-scale nonlinear systems. This is accomplished via bounds found through simulations under linear quadratic regulator (LQR) control. We show that the resulting controller is Input-to-State practically Stable (ISpS) with a stability constant that depends on the level of nonlinearity in the terminal region. Finally, we demonstrate this approach on a quad-tank system and a large-scale distillation application. Simulation results reveal that the proposed approach is able to achieve significant reduction in average computation time without much loss in the performance with reference to fixed horizon NMPC.

Adaptive fuzzy decentralized control for a class of MIMO large-scale nonlinear state delay systems with unmodeled dynamics subject to unknown input saturation and infinite number of actuator failures

This paper addresses design of an adaptive fuzzy decentralized fault-tolerant controller for a class of uncertain multi-input multi-output (MIMO) large-scale nonlinear systems with unmodeled dynamics subject to unknown state time-varying delay, external disturbances, unknown input saturation and actuator faults. It is shown that the proposed fault-tolerant control (FTC) scheme can handle infinite number of actuator failures including partial and total loss of effectiveness. System uncertainties have been approximated by the fuzzy logic systems (FLSs). To cope with the unknown state time-varying delay, the Razumikhin lemma has been utilized and unmodeled dynamics has been tackled by introducing a dynamical signal. To avoid high computational burden, the dynamic surface control (DSC) technique has been used and the number of adaption laws has been reduced by updating the maximum norm of fuzzy weight vectors of each subsystem. It has been shown that all closed-loop signals are semi-globally uniformly ultimately bounded (SGUUB) and the output tracking errors converge to a small neighborhood of the origin by choosing the design parameters appropriately. Simulation results demonstrate the effectiveness of the proposed control scheme.

Decentralized reliable guaranteed cost control for large-scale nonlinear systems using actor-critic network

Abstract In this paper, the decentralized reliable guaranteed cost control problem of large-scale nonlinear systems with mismatched interconnection and time-varying actuator fault is investigated. The unknown actuator fault is assumed to be with known upper bounds. Under the case that the interconnection term is unknown and mismatched, the guaranteed cost control problem for a class of large-scale nonlinear systems can be transformed into design an optimal control strategy of the isolated system, which is necessary to solve the HJB (Hamilton–Jacobi–Bellman) equations by using adaptive dynamic programming (ADP) of actor-critic networks. The convergence property of the neural network weights and the stability of the closed-loop system have been strictly proved even if time-varying actuator faults and unknown interconnection coexist. Finally, simulation examples are given to show the effectiveness of the proposed approach.

Integral reinforcement learning based decentralized optimal tracking control of unknown nonlinear large-scale interconnected systems with constrained-input

Abstract This paper deals with the decentralized optimal tracking control problem of large-scale interconnected systems with constrained-input. The large-scale interconnected systems are firstly transformed to several nominal isolated subsystems. Then, nominal isolated subsystems tracking problem is solved via integral reinforcement learning (IRL) method. It is proved that the solved optimal controllers ensure the boundedness of the original systems tracking error. The actor-critic neural network (NN) technique is used to approximate the critic cost and control policy to implement the IRL algorithm. The least squares approach is employed to solve the weights of actor-critic NN by using only system data. A simulation example is provided to verify the effectiveness of the controllers by comparing with the controllers without considering constrained-input.

Partitioning for distributed model predictive control of nonlinear processes

A distributed model predictive control (DMPC) strategy brings interesting features of topology, flexibility and maintenance to large-scale nonlinear systems. This work presents contributions in the study of distributed controllers for nonlinear and large-scale systems. Two types of distributed predictive control based on model (DMPC) are proposed: non-cooperative locally linearized DMPC and cooperative locally linearized DMPC. The decomposition is performed based on a local linearized version of the process model by using local matrices representing interactions between controlled outputs, states and inputs. The proposed strategy was successfully evaluated and compared to the centralized control strategy.

A derivative-free three-term projection algorithm involving spectral quotient for solving nonlinear monotone equations

ABSTRACTIn this paper, we develop a three-term conjugate gradient method involving spectral quotient, which always satisfies the famous Dai-Liao conjugacy condition and quasi-Newton secant equation, independently of any line search. This new three-term conjugate gradient method can be regarded as a variant of the memoryless Broyden-Fletcher-Goldfarb-Shanno quasi-Newton method with regard to spectral quotient. By combining this method with the projection technique proposed by Solodov and Svaiter in 1998, we establish a derivative-free three-term projection algorithm for dealing with large-scale nonlinear monotone system of equations. We prove the global convergence of the algorithm and obtain the R-linear convergence rate under some mild conditions. Numerical results show that our projection algorithm is effective and robust, and is more competitive with the TTDFP algorithm proposed Liu and Li [A three-term derivative-free projection method for nonlinear monotone system of equations. Calcolo. 2016;53:427–450].

Order reduction of hierarchical interconnected dynamical systems

Abstract. The simulation of large scale nonlinear dynamical interconnected systems, as they arise in all modern engineering disciplines, is a usual task. Due to the high complexity of the considered systems, the principle of thinking in hierarchical structures is essential and common among engineers. Therefore, this contribution proposes an approach for the numerical simulation of large systems, which keeps the hierarchical system structure alive during the entire simulation process while simultaneously exploiting it for order reduction purposes. This is accomplished by embedding the trajectory piecewise linear order reduction scheme in a modified variant of the component connection modeling for building interconnected system structures. The application of this concept is demonstrated by means of a widely used benchmark example and a modified variant of it.

Approximate Dynamic Programming Based Control of Proppant Concentration in Hydraulic Fracturing

Hydraulic fracturing has played a crucial role in enhancing the extraction of oil and gas from deep underground sources. The two main objectives of hydraulic fracturing are to produce fractures with a desired fracture geometry and to achieve the target proppant concentration inside the fracture. Recently, some efforts have been made to accomplish these objectives by the model predictive control (MPC) theory based on the assumption that the rock mechanical properties such as the Young’s modulus are known and spatially homogenous. However, this approach may not be optimal if there is an uncertainty in the rock mechanical properties. Furthermore, the computational requirements associated with the MPC approach to calculate the control moves at each sampling time can be significantly high when the underlying process dynamics is described by a nonlinear large-scale system. To address these issues, the current work proposes an approximate dynamic programming (ADP) based approach for the closed-loop control of hydraulic fracturing to achieve the target proppant concentration at the end of pumping. ADP is a model-based control technique which combines a high-fidelity simulation and function approximator to alleviate the “curse-of-dimensionality” associated with the traditional dynamic programming (DP) approach. A series of simulations results is provided to demonstrate the performance of the ADP-based controller in achieving the target proppant concentration at the end of pumping at a fraction of the computational cost required by MPC while handling the uncertainty in the Young’s modulus of the rock formation.

A scheme for comprehensive computational cost reduction in proper orthogonal decomposition

Abstract This paper addresses the issue of offline and online computational cost reduction of the proper orthogonal decomposition (POD) which is a popular nonlinear model order reduction (MOR) technique. Online computational cost is reduced by using the discrete empirical interpolation method (DEIM), which reduces the complexity of evaluating the nonlinear term of the reduced model to a cost proportional to the number of reduced variables obtained by POD: this is the POD-DEIM approach. Offline computational cost is reduced by generating an approximate snapshot-ensemble of the nonlinear dynamical system, consequently, completely avoiding the need to simulate the full-order system. Two snapshot ensembles: one of the states and the other of the nonlinear function are obtained by simulating the successive linearization of the original nonlinear system. The proposed technique is applied to two benchmark large-scale nonlinear dynamical systems and clearly demonstrates comprehensive savings in computational cost and time with insignificant or no deterioration in performance.

Finite-time decentralized adaptive neural constrained control for interconnected nonlinear time-delay systems with dynamics couplings among subsystems

The problem of finite-time decentralized neural adaptive constrained control is studied for large-scale nonlinear time-delay systems in the non-affine form. The main features of the considered system are that 1) unknown unmatched time-delay interactions are considered, 2) the couplings among the nested subsystems are involved in uncertain nonlinear systems, 3) based on finite-time stability approach, asymmetric saturation actuators and output constraints are studied in large-scale systems. First, the smooth asymmetric saturation nonlinearity and barrier Lyapunov functions are used to achieve the input and output constraints. Second, the appropriately designed Lyapunov-Krasovskii functional and the property of hyperbolic tangent functions are used to deal with the unknown unmatched time-delay interactions, and the neural networks are employed to approximate the unknown nonlinearities. Note that, due to unknown time-delay interactions and the couplings among subsystems, the controller design is more meaningful and challenging. At last, based on finite-time stability theory and Lyapunov stability theory, a decentralized adaptive controller is proposed, which decreases the number of learning parameters. It is shown that the designed controller can ensure that all closed-loop signals are bounded and the tracking error converges to a small neighborhood of the origin. The simulation studies are presented to show the effectiveness of the proposed method.

Reduced Order Optimization of Large-Scale Nonlinear Systems with Nonlinear Inequality Constraints Using Steady State Simulators

Technological advances have led to the widespread use of computational models of increasing complexity, in both industry and everyday life. This helps to improve the design, analysis and operation of complex systems. Many computational models in the field of engineering consist of systems of coupled nonlinear partial differential equations (PDEs). As a result, optimization problems involving such models may lead to computational issues because of the large number of variables arising from the spatiotemporal discretization of the PDEs. In this work, we present a methodology for steady-state optimization, with nonlinear inequality constraints of complex large-scale systems, for which only an input/output steady-state simulator is available. The proposed method is efficient for dissipative systems and is based on model reduction. This framework employs a two-step projection scheme followed by three different approaches for handling the nonlinear inequality constraints. In the first approach, partial reductio...