Large-scale Nonlinear Systems Research Articles

Robust scalable stabilisability conditions for large-scale heterogeneous multi-agent systems with uncertain nonlinear interactions: towards a distributed computing architecture

ABSTRACTLarge-scale dynamic systems are becoming highly pervasive in their occurrence with applications ranging from system biology, environment monitoring, sensor networks, and power systems. They are characterised by high dimensionality, complexity, and uncertainty in the node dynamic/interactions that require more and more computational demanding methods for their analysis and control design, as well as the network size and node system/interaction complexity increase. Therefore, it is a challenging problem to find scalable computational method for distributed control design of large-scale networks. In this paper, we investigate the robust distributed stabilisation problem of large-scale nonlinear multi-agent systems (briefly MASs) composed of non-identical (heterogeneous) linear dynamical systems coupled by uncertain nonlinear time-varying interconnections. By employing Lyapunov stability theory and linear matrix inequality (LMI) technique, new conditions are given for the distributed control design of large-scale MASs that can be easily solved by the toolbox of MATLAB. The stabilisability of each node dynamic is a sufficient assumption to design a global stabilising distributed control. The proposed approach improves some of the existing LMI-based results on MAS by both overcoming their computational limits and extending the applicative scenario to large-scale nonlinear heterogeneous MASs. Additionally, the proposed LMI conditions are further reduced in terms of computational requirement in the case of weakly heterogeneous MASs, which is a common scenario in real application where the network nodes and links are affected by parameter uncertainties. One of the main advantages of the proposed approach is to allow to move from a centralised towards a distributed computing architecture so that the expensive computation workload spent to solve LMIs may be shared among processors located at the networked nodes, thus increasing the scalability of the approach than the network size. Finally, a numerical example shows the applicability of the proposed method and its advantage in terms of computational complexity when compared with the existing approaches.

Observed-Based Adaptive Fuzzy Decentralized Tracking Control for Switched Uncertain Nonlinear Large-Scale Systems With Dead Zones

In this paper, the problem of adaptive fuzzy decentralized output-feedback control design is investigated for a class of switched nonlinear large-scale systems in strict-feedback form. The considered nonlinear large-scale systems contain the unknown nonlinearities and dead zones, the switching signals with average dwell time, and without the direct requirement of the states being available for feedback. Fuzzy logic systems are utilized to approximate the unknown nonlinear functions, a fuzzy switched decentralized state observer is designed and thus via it the immeasurable states are obtained. By applying the adaptive decentralized backstepping design technique, an adaptive fuzzy decentralized output-feedback tracking control approach is developed for the switched subsystems. The stability of the whole closed-loop system is proved by using the Lyapunov function and the average dwell-time methods. Satisfactory tracking performance is achieved under the switching signals with average dwell time. The simulation example is provided to indicate the effectiveness of the proposed control method.

大規模非線形系に対する高性能振動解析手法の開発

大規模非線形系に対する高性能振動解析手法の開発

An iterative parametric estimation method for Hammerstein large-scale systems: a simulation study of hydraulic process

This paper aims at developing an iterative method which permits to estimate the parameters of single-input single-output (SISO) large-scale nonlinear systems, described by Hammerstein mathematical models. We particularly focus on the dynamic large-scale nonlinear systems, which are made up of several interconnected nonlinear monovariable subsystems. Each subsystem can operate in a stochastic environment and be described by a discrete-time Hammerstein mathematical model with known structure variables (order, delay) and unknown time-varying parameters. The problem formulation is achieved based on the prediction error method and the least-squares techniques. The convergence analysis of the recursive algorithm is provided using the differential equation approach and its performance is illustrated by treating two simulation examples.

Decentralized Robust Adaptive Output Feedback Stabilization for Interconnected Nonlinear Systems with Uncertainties

Based on adaptive nonlinear damping, a novel decentralized robust adaptive output feedback stabilization comprising a decentralized robust adaptive output feedback controller and a decentralized robust adaptive observer is proposed for a large-scale interconnected nonlinear system with general uncertainties, such as unknown nonlinear parameters, bounded disturbances, unknown nonlinearities, unmodeled dynamics, and unknown interconnections, which are nonlinear function of not only states and outputs but also unmodeled dynamics coming from other subsystems. In each subsystem, the proposed stabilization only has two adaptive parameters, and it is not needed to generate an additional dynamic signal or estimate the unknown parameters. Under certain assumptions, the proposed scheme guarantees that all the dynamic signals in the interconnected nonlinear system are bounded. Furthermore, the system states and estimate errors can approach arbitrarily small values by choosing the design parameters appropriately large. Finally, simulation results illustrated the effectiveness of the proposed scheme.

Minimal-Approximation-Based Decentralized Backstepping Control of Interconnected Time-Delay Systems.

A decentralized adaptive backstepping control design using minimal function approximators is proposed for nonlinear large-scale systems with unknown unmatched time-varying delayed interactions and unknown backlash-like hysteresis nonlinearities. Compared with existing decentralized backstepping methods, the contribution of this paper is to design a simple local control law for each subsystem, consisting of an actual control with one adaptive function approximator, without requiring the use of multiple function approximators and regardless of the order of each subsystem. The virtual controllers for each subsystem are used as intermediate signals for designing a local actual control at the last step. For each subsystem, a lumped unknown function including the unknown nonlinear terms and the hysteresis nonlinearities is derived at the last step and is estimated by one function approximator. Thus, the proposed approach only uses one function approximator to implement each local controller, while existing decentralized backstepping control methods require the number of function approximators equal to the order of each subsystem and a calculation of virtual controllers to implement each local actual controller. The stability of the total controlled closed-loop system is analyzed using the Lyapunov stability theorem.

Adaptive decentralised dynamic surface control for non‐linear large‐scale systems against actuator failures

This study presents an adaptive decentralised dynamic surface control (DSC) approach for a class of large-scale non-linear systems with unknown non-linear functions, unknown control gains, time-varying delays and in the presence of unknown actuator failures. The considered actuator failures are modelled to cover both loss of effectiveness and stuck at some time-varying values where the values, patterns and time occurrences of the failures are unknown. With the help of neural networks to approximate the unknown non-linear functions, a novel adaptive actuator failure compensation controller is developed based on the backstepping method and the DSC approach. The appropriate Lyapunov–Krasovskii functionals are introduced to design new adaptive laws to compensate the unknown actuator failures as well as uncertainties from unknown non-linearities and time delays. The proposed design method does not require a priori knowledge of the bounds of the unknown time delays and actuator failures. The boundedness of all the closed-loop signals is guaranteed and the tracking errors are proved to converge to a small neighbourhood of the origin. The proposed approach is employed for a double inverted pendulums benchmark and a chemical reactor system. The simulation results show the effectiveness of the proposed method.

Robust Decentralized Static Output-Feedback Control Design for Large-Scale Nonlinear Systems Using Takagi-Sugeno Fuzzy Models

This paper is concerned with the problem of robust decentralized output-feedback control for a class of continuous-time large-scale nonlinear systems. Each nonlinear subsystem, described by a Takagi–Sugeno model, involves in the interconnections and parametric uncertainties of the large-scale systems. The main focus of this paper is to design a robust decentralized static output-feedback (SOF) fuzzy controller, such that the resulting closed-loop system is asymptotically stable with a prescribed $ \mathscr {H}_{\infty } $ disturbance attenuation level. Based on some matrix inequality linearization techniques and the descriptor system approach, sufficient conditions for the existence of a robust decentralized SOF $ \mathscr {H}_{\infty }$ fuzzy controller are presented in terms of linear matrix inequalities. From different perspectives, the desired controller is designed to analyze the degree of conservatism induced by considering various limitations. The effectiveness and superiority of the proposed method are finally demonstrated by two numerical examples.

Decentralized adaptive fuzzy fault-tolerant tracking control of large-scale nonlinear systems with actuator failures

This study is concerned with the problem of decentralized adaptive fault-tolerant control for a class of large-scale non-affine and nonlinear systems with external disturbances and actuator failures including loss of effectiveness and bias. Based on fuzzy logic systems (FLSs) to approximate the appropriate nonlinear functions, a novel decentralized adaptive fuzzy fault-tolerant control scheme is developed via direct adaptive control technique. To tackle the non-affine term with actuator failures, with the help of a non-affine compensation term, the corresponding adaptive mechanism that depends on the unknown upper bound of a defined compounded disturbance is introduced. Meanwhile, by utilizing the on-line estimating information of the unknown upper bound and the unknown parameters of necessary FLSs, a new adaptive fuzzy fault-tolerant controller with the adjustable parameter updated laws is designed to achieve robust tracking performance. Furthermore, it is shown that all the closed-loop signals of the interconnected subsystems are uniformly bounded and the tracking errors asymptotically converge to zero via Lyapunov stability analysis. Finally, numerical simulation results are provided to demonstrate the efficiency of the presented decentralized adaptive fuzzy fault-tolerant tracking design scheme.

Initial Sampling of Ensemble for Steam-Assisted-Gravity-Drainage-Reservoir History Matching

Summary History matching of a steam-assisted-gravity-drainage (SAGD) reservoir requires a large ensemble size for proper uncertainty assessment, which ultimately results in high computational cost. Therefore, it is necessary to reduce the number of realizations for SAGD-reservoir simulation purposes. In this paper, a novel sampling method (based on the probability-distance-minimization method) to generate an initial ensemble of reduced size is discussed. This method considers multiple static measurements and geological properties and uses Kantorovich distance to quantify the probability distance between the original ensemble and the reduced ensemble, which is later optimized by use of the mixed-integer linear-optimization (MILP) technique. To show the effectiveness of the method, we have shown history matching of an SAGD reservoir using the smaller size initial ensemble derived from the proposed method and compared with the original ensemble. For history matching, the ensemble Kalman filter (EnKF) has been used because of its ability to assimilate data for large-scale nonlinear systems. Results are compared with several other methods, such as importance sampling, kernel K-means clustering, and sampling by use of orthogonal ensemble members. The robustness and usefulness of each method for generating an improved initial ensemble of reduced size are analyzed on the basis of two criteria: (1) Does the smaller ensemble retain the same statistical distribution characteristics as the original ensemble, and (2) does the smaller ensemble improve the performance of history matching? In general, we conclude that the improved, smaller initial ensemble created by use of the proposed method retains the best statistical characteristics of the original ensemble. Also, it provides better performance compared with other ranking methods in sampling and history matching using EnKF. Finally, the proposed method can reduce the computing cost significantly without compromising uncertainty in the forecast model, which allows for real-time updating at smaller time intervals.

Decentralised H ∞ fuzzy filter for non‐linear large‐scale systems under imperfect premise matching

This study presents a decentralised H∞ filter design problem for non-linear large-scale systems that are represented based on the Takagi–Sugeno fuzzy model. To enhance the design flexibility of the fuzzy filter for non-linear large-scale systems, the imperfect premise matching problem is adopted in the filter design procedure. In the sense of fuzzy Lyapunov, sufficient conditions for both asymptotic stability of the error system and a prescribed level of the H∞ norm are ensured to guarantee the H∞ fuzzy filter performance. The sufficient conditions are formulated in terms of linear matrix inequalities, which can be solved efficiently using convex optimisation algorithms. Finally, simulation examples are provided to verify the feasibility of the proposed approach.

Adaptive fuzzy decentralized control for uncertain large-scale nonlinear time-delay systems with virtual control functions

In this paper, the adaptive fuzzy decentralized tracking control problem is investigated for a class of uncertain large-scale nonlinear systems, interacted through their outputs with completed unknown time-varying delays. The novel contribution is to remove the common assumptions on the unknown time delays by the proposed delay replacement technique, so that the controller design is not dependent on these assumptions any more, and thus, added flexibility in decentralized control design is achieved. Furthermore, the approximation and replacement errors are handled by the adaptive technique. All closed-loop signals are proved to be semiglobal uniform ultimate boundedness, and the tracking errors are guaranteed to converge to a small residual set around the origin. The simulation studies illustrate the effectiveness of the control scheme.

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

This paper addresses a novel constrained decentralized shaping control problem for a class of nonlinear large-scale interconnected distribution systems. Such systems are generated by multiple output conditional probability density functions (PDFs) and exist in multi-channel non-Gaussian stochastic processes. Following a decoupled B-spline approximation to the output conditional PDFs, the large-scale interconnected weight systems are introduced to characterize the correlation in different weight vectors and further to describe the dynamic relation between the control input and weight vectors. The decentralized PI controller with delay dependent analysis is designed to ensure the system stability and convergence of the dynamic tracking error to zero. Moreover, the L2−L∞ norm from the disturbance to the controlled output is reduced to a prescribed level and the state constraint requirement can also be guaranteed. The effectiveness of the developed algorithm is verified by simulations of paper making process.

Delay-dependent decentralized control for nonlinear similar interconnected large-scale 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.

New results onH∞filtering for nonlinear large-scale systems with interconnected time-varying delays

Summary This paper proposes a new design method of H∞ filtering for nonlinear large-scale systems with interconnected time-varying delays. The interaction terms with interval time-varying delays are bounded by nonlinear bounding functions including all states of the subsystems. A stable linear filter is designed to ensure that the filtering error system is exponentially stable with a prescribed convergence rate. By constructing a set of improved Lyapunov functions and using generalized Jensen inequality, new delay-dependent conditions for designing H∞ filter are obtained in terms of linear matrix inequalities. Finally, an example is provided to illustrate the effectiveness of the proposed result. Copyright © 2015 John Wiley & Sons, Ltd.

Composite adaptive fuzzy output feedback dynamic surface control design for stochastic large-scale nonlinear systems with unknown dead zone

In this paper, a composite adaptive fuzzy output feedback decentralized control problem is investigated for a class of nonlinear stochastic large-scale systems. The nonlinear large-scale systems under study have unknown nonlinear functions, unknown dead-zone and immeasurable states. Fuzzy logic systems are used to approximate the unknown nonlinear functions, a fuzzy adaptive state observer is designed to estimate the unmeasured states. By utilizing the designed fuzzy state observer, a serial-parallel estimation model is established. Based on adaptive backstepping dynamic surface control technique and the prediction error between the system states observer model and the serial-parallel estimation model, an adaptive output feedback controller is constructed. The designed fuzzy controller with the composite parameters adaptive laws ensures that all the variables of closed-loop system are bounded in probability, and tracking error converges to a small neighborhood of zero. A numerical example is provided to verify the effectiveness of the proposed approach.

Fuzzy Finite-Time Dynamic Surface Control for Nonlinear Large-Scale Systems

In this paper, a new finite-time dynamic surface control (DSC) method is proposed to enhance the convergence rate and robustness of a DSC system on the basis of the traditional infinite-time stability viewpoint for application to nonlinear large-scale systems. By defining a novel recursive finite-time virtual error variable, a virtual controlled stabilizing functions are derived, and the finite-time control performance is ensured by means of the finite-time-based Lyapunov stability theorem. An adaptive fuzzy logic system is adopted to approximate the unknown functions. The applicability of the proposed control strategy is verified by simulation and an experiment for a mobile manipulator and an articulated manipulator.

Distributed memoryless detection and accommodation of unknown time-delayed interaction faults in a class of interconnected nonlinear systems

This paper addresses a memoryless design problem for the distributed fault detection and accommodation (FDA) of a class of large-scale nonlinear systems in the presence of nonlinear interaction faults with unknown time delays. Existing works designed distributed FDA schemes without considering interaction delays. However, we consider these delays, design distributed memoryless detection estimators and time-varying thresholds for detecting unknown time-delayed interaction faults, and analyze the distributed fault detectability. Then, an approximation-based distributed fault accommodation scheme which is independent of time delays is constructed via Lyapunov stability theorem. Thus, it is shown that all signals of the total controlled closed-loop system are uniformly ultimately bounded and tracking errors of subsystems converge to an adjustable neighborhood of the origin. Finally, a simulation example is presented to show the effectiveness of the proposed methodology.

A three-term derivative-free projection method for nonlinear monotone system of equations

In this paper, we propose a three-term conjugate gradient method, which has two attractive properties that the search direction is descent and satisfies the famous D-L conjugacy condition without any line search. Moreover, this new three-term conjugate gradient method can be viewed as a modification of the memoryless BFGS method. By combining this new three-term conjugate gradient method with the projection technique proposed by Solodov and Svailter in 1998, we establish a three-term derivative-free projection method for solving nonlinear monotone system of equations. Due to maintain some nice properties of conjugate gradient method such as the simplicity and the low storage, the proposed projection method is very suitable to solve large-scale nonlinear monotone system of equations. The global convergence and R-linear convergence rate of the proposed projection method are proved under some appropriate conditions. The preliminary numerical results are also given to indicate that the proposed projection method is effective and robust.

Decentralized Adaptive Fuzzy Output-Feedback Control of Switched Large-Scale Nonlinear Systems

In this paper, a decentralized adaptive fuzzy output-feedback control problem is discussed for a class of switched large-scale nonlinear systems without the measurements of the system states. Fuzzy logic systems are used to approximate the unknown nonlinear functions, and a switched observer is designed to avoid the conservativeness caused by adoption of a common observer for all subsystems. A common coordinate transformation of all subsystems is constructed to get rid of individual coordinate transformations for subsystems that are required when applying the backstepping recursive design scheme. Meanwhile, since the exponential decline property of Lyapunov functions for individual subsystems is no longer satisfied in this paper, the classical average dwell time method cannot be directly applied. Based on this, a switched observer-based decentralized adaptive fuzzy output-feedback control technique is set up by exploiting the average dwell time method and backstepping. It is proved that all the signals of the resulting closed-loop system are semiglobally uniformly ultimately bounded under a class of switching signals with average dwell time, while the tracking errors converge to a small neighborhood of the origin. The effectiveness of the proposed control scheme is illustrated by its applications to a two-inverted-pendulum system and a quadruple-tank process system.