Large-scale Nonlinear Systems Research Articles

Advanced-multi-step moving horizon estimation for large-scale nonlinear systems

Nonlinear Model Predictive Control (NMPC) is an optimization-based control strategy that directly incorporates nonlinear dynamic models and has desirable stability and robustness properties. State estimation is an essential counterpart to NMPC and Moving Horizon Estimation (MHE) is also an optimization-based strategy that directly incorporates the nonlinear dynamics and constraints. However, NMPC and MHE are challenged by the computational expense of solving NLPs at each time step. For NMPC, this is avoided by advanced-step and advanced-multi-step approaches, which solve the detailed optimization off-line (possibly over multiple sampling times) and perform sensitivity-based corrections to the optimal solution on-line, with over two orders of magnitude less computation. This work complements advanced-multi-step NMPC with an advanced-multi-step MHE approach. The development solves rigorous optimization problems in background along with detailed updates to the arrival cost. On-line corrections are enabled by fast sensitivity-based NLP. The amsMHE approach is demonstrated on two large-scale distillation case studies with hundreds of state variables, and shows that nonlinear state estimation for large-scale systems can be implemented with negligible on-line computation.

A multigroup fault detection and diagnosis framework for large-scale industrial systems using nonlinear multivariate analysis

In a large-scale industrial system with numerous variables, the relations among variables are often nonlinear and very complicated, due to material, energy and information flows throughout the entire system. In such systems, fault detection and diagnosis (FDD) suffer from the strong interference of fault-free variables and hence become more difficult, especially for minor faults. To achieve high-performance FDD in large-scale nonlinear industrial systems, a multigroup FDD framework is proposed in this paper. In this framework, system variables are divided into groups firstly, and then FDD are implemented in the form of variable groups. The whole framework consists of three components: a variable grouping method based on mutual information (MI), intra-group FDD methods based on gradKPCA, and inter-group FDD methods based on gradKCCA. The MI-based variable grouping method obtains optimal variable groups by maximizing the MI of variables in every group. The gradKPCA and gradKCCA are used for extracting nonlinear variable relations within each group and between groups, respectively. Except for the ability to cope with nonlinear variable relations, this multigroup FDD framework also has other advantages, such as the improved detection ability to minor faults and the ability to reveal fault transfers between variables and groups. These advantages are demonstrated with a numerical example and an industrial case study.

Decentralized adaptive neural two-bit-triggered control for nonstrict-feedback nonlinear systems with actuator failures

This article studies the adaptive neural decentralized two-bit-triggered control problem for interconnected large-scale nonlinear systems in nonstrict-feedback forms (NFF) with actuator failures. Since actuator failures occur frequently in practical systems, it will affect the stability of the interconnected large-scale systems under consideration. Combining radial basis function neural networks (RBF NNs) and a command filter, an adaptive decentralized two-bit-triggered (TBT) control method based on backstepping recursive design is presented to deal with this problem. Different from the traditional event-triggered control, the problem of control signal transmission bit is further considered to save system transmission resources. The proposed control scheme can guarantee that all signals are bounded and have good tracking performance. Finally, two simulation examples are provided to verify the validity of the presented control scheme.

Removing the feasibility conditions on adaptive fuzzy decentralized tracking control of large-scale nonlinear systems with full-state constraints

This work is dedicated to solving the adaptive fuzzy decentralized tracking control issue of large-scale nonlinear systems with full-state constraints. Different with barrier Lyapunov function, the main difference is that a novel nonlinear state-dependent function (NSDF) is introduced to prevent the state constraints being overstepped. Based on NSDF, the necessary feasibility conditions for virtual controllers are completely removed. Then, the prior knowledge of the unknown virtual control coefficients is no longer required since the original system is transformed via the new affine variable. Under the control strategy, three objectives on system performance are achieved: (a) all signals of the closed-loop system are bounded; (b) the subsystem output closely tracks the reference trajectory and original error is ultimately uniformly bounded; (c) the full-state constraints are not violated for all the time. At the end, two simulation examples are shown to verify the effectiveness of the control method.

Decentralized Event-Triggered Adaptive Fuzzy Control for Nonlinear Switched Large-Scale Systems With Input Delay Via Command-Filtered Backstepping

This article presents a decentralized fuzzy adaptive event-triggered command-filtered control scheme for switched large-scale nonlinear systems with input delay. Fuzzy logic systems are employed to approximate uncertain nonlinearities and a novel observer is constructed to estimate unmeasured states. The “explosion of complexity” defect inherent in the backstepping approach is overcome by employing command filter technology. An auxiliary system is designed to compensate for the effect of input delay, and a novel event-triggered decentralized controller is derived based on the common Lyapunov function method. This article shows that the presented strategy guarantees that all closed-loop variables are semiglobally uniformly ultimately bounded. Finally, simulation results are shown to further confirm the presented strategy’s validity.

An Overview on Modelling of Complex Interconnected Nonlinear Systems

This paper proposes new mathematical models of representation, which can describe the dynamic behavior of large-scale nonlinear systems, such as an extended mathematical model of Volterra series, interconnected Hammerstein structures, and interconnected Wiener structures. In this research, we focus on the class of large-scale nonlinear systems, which are composed of several interconnected nonlinear subsystems. In this context, a discrete nonlinear mathematical model with unknown time-varying parameters, mono-variable, characterizes each interconnected subsystem operating in a deterministic or stochastic environment. An illustrative numerical simulation example of two interconnected nonlinear processes is provided to prove the validity and the performance of the developed theoretical results.

Adaptive decentralized prescribed performance control for a class of large-scale nonlinear systems subject to nonsymmetric input saturations

Adaptive decentralized prescribed performance control for a class of large-scale nonlinear systems subject to nonsymmetric input saturations

Adaptive output feedback control of large-scale nonlinear time-delay systems with uncertain output equations

For a class of large-scale nonlinear time-delay systems with uncertain output equations, the problem of global state asymptotic regulation is addressed by output feedback. The class of systems under consideration are subject to feedforward growth conditions with unknown growth rate and time delays in inputs and outputs. To deal with the system uncertainties and the unknown delays, a novel low-gain observer with adaptive gain is firstly proposed; next, an adaptive output feedback delay-free controller is constructed by combining Lyapunov-Krasovskii functional with backstepping algorithm. Compared with the existing results, the controllers proposed are capable of handling both the uncertain output functions and the unknown time delays in inputs and outputs. With the help of dynamic scaling technique, it is shown that the closed-loop states converge asymptotically to zero, while the adaptive gain is bounded globally. Finally, the effectiveness of our control schemes are illustrated by three examples.

Sensitivity matrices as keys to local structural system properties of large-scale nonlinear systems

Sensitivities are shown to play a key role in a highly efficient algorithm, presented in this paper, to establish three fundamental structural system properties: local structural identifiability, local observability, and local strong accessibility. Sensitivities have the advantageous property to be governed by linear dynamics, also if the system itself is nonlinear. By integrating their linear dynamics over a short time period, and by sampling the result, a sensitivity matrix is obtained. If this sensitivity matrix satisfies a rank condition, then the local structural system property under investigation holds. This rank condition will be referred to in this paper as the sensitivity rank condition (SERC). Applying a singular value decomposition (SVD) to the sensitivity matrix not only determines its rank but also pinpoints exactly the system components causing a possible failure to satisfy the local structural system property. The algorithm is highly efficient because integration of linear systems over short time-periods and computation of an SVD are computationally cheap. Therefore, it allows for the handling of large-scale systems in the order of seconds, as opposed to conventional algorithms that mostly rely on Lie series expansions and a corresponding Lie algebraic rank condition (LARC). The SERC and LARC algorithms are mathematically and computationally compared through a series of examples.

Adaptive neural smooth finite-time controller for large-scale stochastic nonlinear state-constrained systems with feasibility removal and time delays

This paper studies the adaptive smooth finite-time neural controller design for large-scale stochastic nonlinear systems subject to command filter and time-delay interactions. The main features are (1) the communication interconnection has the output delay between subsystems; (2) the smooth finite time strategy is given for stochastic disturbances; (3) all states are confined in the constrained space without feasibility conditions. First, the state time-delay interactions are tackled by the appropriate establishment of Lyapunov–Krasovskii functionals. Second, for full-state constraints, state-related mappings are employed to remove the feasibility. Then, by constructing the switching virtual control signals, the smooth fast finite-time feature is attached to the controller. Finally, based on finite-time stability theory in probability, command filter, and backstepping technique, the smooth fast finite-time neural controller is constructed to make that all system states converge in finite time, all closed-loop variables are bounded in probability, and full-state constraints are satisfied. Simulation results are provided to test the correctness of the method.

Secure filtering under adaptive event-triggering protocols with memory mechanisms

The paper investigates secure filtering of nonlinear large-scale systems suffering from randomly occurring DoS attacks. By introducing an adjustable parameter, an adaptive event-triggering mechanism is proposed for the sake of decreasing the transmission burden of signals, where the memory is utilized to reflect the influence of past triggered information. The main objective is to design an event-based secure filter to ensure that the dynamics of filtering errors is input-to-state stable in the mean square. Using the constructed Lyapunov function, a sufficient condition is derived where some element matrix inequalities are utilized to handle the inherent coupling of subsystems. Furthermore, the desired filter gains are parameterized by resorting to the feasibility of matrix inequalities. Finally, a numerical simulation about a power system is provided to verify the effectiveness of the developed secure filtering algorithm.

A Polynomial Decentralized Controller Design for a Large-Scale Nonlinear System: SOS Approach

This paper proposes a novel approach for designing a decentralized controller to stabilize the large-scale nonlinear system. Unlike the previous studies, the polynomial system framework is employed to model the nonlinear large-scale system to decrease not only the modeling error but also the complexity and computational load significantly. Especially, in case the large-scale nonlinear systems consist of non-polynomial forms (such as sine, cosine, and so on), synthesizing the controller for this system becomes much more challenging. By putting non-polynomial terms inside the matrices, a new approach for designing a decentralized polynomial controller is presented to eliminate the impacts of nonlinear terms and stabilize the system. Based on Lyapunov methodology, the conditions for synthesizing a decentralized polynomial controller expressed under the framework of Sum-of-Square (SOS) are derived in the main theorems. Finally, the effectiveness and superiority of the proposed method are demonstrated in two illustrative examples.

Extending a sensitivity based algorithm to detect local structural identifiability

Output sensitivities to parameters underly a highly efficient sensitivity based algorithm to compute local structural identifiability of possibly large-scale nonlinear dynamic systems. By means of simple examples, this paper explores exceptional cases where this algorithm fails. That is, if one applies the common definition of local structural identifiability. As also shown in this paper, when applying a closely related definition of identifiability, based on sensitivities, the sensitivity based algorithm always provides the correct answer. The subtle difference between these two definitions, that seems to have been overlooked in the literature, is further explored and explained in this paper. For the common definition of local structural identifiability, an extension of the sensitivity based algorithm is presented that approximately doubles the computation time. This extension is shown to work along non-singular trajectories.

Adaptive Decentralized Asymptotic Tracking Control for Large-Scale Nonlinear Systems With Unknown Strong Interconnections

An adaptive decentralized asymptotic tracking control scheme is developed in this paper for a class of large-scale nonlinear systems with unknown strong interconnections, unknown time-varying parameters, and disturbances. First, by employing the intrinsic properties of Gaussian functions for the interconnection terms for the first time, all extra signals in the framework of decentralized control are filtered out, thereby removing all additional assumptions imposed on the interconnections, such as upper bounding functions and matching conditions. Second, by introducing two integral bounded functions, asymptotic tracking control is realized. Moreover, the nonlinear filters with the compensation terms are introduced to circumvent the issue of “explosion of complexity”. It is shown that all the closed-loop signals are bounded and the tracking errors converge to zero asymptotically. In the end, a simulation example is carried out to demonstrate the effectiveness of the proposed approach.

All state constrained decentralized adaptive implicit inversion control for a class of large scale nonlinear hysteretic systems with time-delays

This paper proposes an all state constrained decentralized adaptive implicit inversion control scheme for a class of large scale nonlinear systems with unknown time delays and asymmetric saturated hysteresis. First, to address the states constrained problem, the asymmetric barrier Lyapunov function is introduced to keep the error surface within an appropriate range from the view of engineering practice to ensure the performance and safety, such as for attitude tracking of rigid spacecraft, for spacecraft approach and intersection. Second, the transmission delays between different subsystems are considered and approximated through the incorporation of the neural-network approximators and the finite coverage lemma. Third, a new hysteresis implicit inverse algorithm is designed to effectively mitigate asymmetric and saturated hysteresis nonlinearities. It should be noted that the implicit inverse implies that the analytical inverse of the asymmetric and saturated hysteresis is not required. Instead, the decoupling algorithms are designed to extract the actual control signal from the temporarily hysteretic control signal , which reduces the preliminary work of the control algorithm. Finally, all of the signals in the closed-loop system are proved to be semi-globally ultimately uniformly bounded and the tracking errors converge to an arbitrarily small residual set. The experimental results on two-machine excitation power systems in the hardware-in-loop system are presented to illustrate the effectiveness of the proposed scheme.

Global decentralized control for uncertain large-scale feedforward nonlinear time-delay systems via output feedback

Abstract In this paper, the problem of global decentralized output feedback control is addressed for a class of large-scale nonlinear systems with zero dynamics and unknown time-varying delay. System disturbance nonlinearities are subject to feedforward growth restrictions with unknown growth rate. In the spirit of dynamic scaling change technique, a novel pair of time-varying-gain observer and controller is proposed. Compared with the existing results, the controller proposed is capable of handling the difficulties caused by the zero-dynamics, the uncertainties and the unknown time-varying delay. With the help of the Razumikhin theorem, it is shown that the closed-loop states asymptotically converge to zero. Finally, the effectiveness of the proposed control scheme is illustrated by a numerical example.

Fuzzy Elman Wavelet Network: Applications to function approximation, system identification, and power system control

Fuzzy Wavelet Neural Networks (FWNNs) have recently gained popularity as a powerful tool for various applications. Although the literature contains several effective FWNNs, there is still scope for improvement. This research proposes and implements a novel modification called the Fuzzy Elman Wavelet Network (FEWN), which combines the appealing properties of Elman Neural Networks (ENNs), wavelet functions, and fuzzy membership functions (MFs). The integration suggests the use of interval type-2 fuzzy MFs and wavelet functions with self-recurrent and ENN's cross-coupled feedback loops to handle system uncertainties while accurately representing the intrinsic cross-coupled interferences of real dynamic nonlinear systems. However, it is worth noting that the proposed integration has no detrimental effect on the computational network load, which is critical for online applications.Furthermore, a thorough stability analysis is conducted, and the novel network is implemented and tested in various applications. Finally, the effectiveness of the proposed novel network is evaluated through extensive simulation studies using well-known benchmark functions and dynamic systems. These studies demonstrate the proposed FEWN's efficacy in function approximation, system identification, and as a damping controller for two benchmark large-scale nonlinear power systems.

On the derivative-free quasi-Newton-type algorithm for separable systems of nonlinear equations

A derivative-free quasi-Newton-type algorithm in which its search direction is a product of a positive definite diagonal matrix and a residual vector is presented. The algorithm is simple to implement and has the ability to solve large-scale nonlinear systems of equations with separable functions. The diagonal matrix is simply obtained in a quasi-Newton manner at each iteration. Under some suitable conditions, the global and R-linear convergence result of the algorithm are presented. Numerical test on some benchmark separable nonlinear equations problems reveal the robustness and efficiency of the algorithm.

Observer-based decentralized adaptive control for large-scale nonlinear systems with mixed dynamic interaction

The problem of decentralized adaptive control is investigated for a class of large-scale nonstrict-feedback nonlinear systems subject to dynamic interaction and unmeasurable states, where the dynamic interaction is related to both input and output items. First, the fuzzy logic system is utilized to tackle unknown nonlinear function with nonstrict-feedback structure. Then, by combining adaptive and backstepping technology, the proper output feedback controller is designed. Meanwhile, a fuzzy state observer is proposed to estimate the unmeasurable states. The proposed controller could guarantee that all the signals of the resulting closed-loop systems are bounded. Finally, the applicability of the proposed controller is well carried out by a simulation example.

Robust Adaptive Fuzzy Control via State-Dependent Function for Nonlinear Stochastic Large-Scale Systems Subject to Dead Zones

This paper concentrates on the adaptive fuzzy control problem for stochastic nonlinear large-scale systems with constraints and unknown dead zones. By introducing the state-dependent function, the constrained closed-loop system is transformed into a brand-new system without constraints, which can realize the same control objective. Then, fuzzy logic systems (FLSs) are used to identify the unknown nonlinear functions, the dead zone inverse technique is utilized to compensate for the dead zone effect, and a robust adaptive fuzzy control scheme is developed under the backstepping frame. Based on the Lyapunov stability theory, it is proved ultimately that all signals in the closed-loop system are bounded and the tracking errors converge to a small neighborhood of the origin. Finally, an example based on an actual system is given to verify the effectiveness of the proposed control scheme.