Interconnection Terms Research Articles

Adaptive control for coupled lagrangian systems with structured uncertainty in the interconnections

SUMMARYIn this paper, an adaptive control scheme for coupled lagrangian systems is proposed. The interconnection terms among subsystems are assumed to have known structure and depend nonlinearly on uncertain parameters. Also, these coupling functions are restricted to those which are concave or convex with respect to the parameters. Two parameter adaptation laws are used to estimate local and interconnection unknown parameters. Both centralized and decentralized controls are designed. Ultimately bounded tracking with arbitrary precision is achieved regardless of ability to share information among subsystem. A numerical simulation, consisting of two pendulums interconnected by a nonlinear spring, is included to illustrate the effectiveness of the proposed schemes. Copyright © 2013 John Wiley & Sons, Ltd.

Decentralised adaptive robust control of uncertain large-scale interconnected systems with multiple time-varying delays

The problem of decentralised adaptive robust stabilisation is considered for a class of uncertain large-scale time-delay interconnected dynamical systems. It is assumed that the upper bounds of the uncertainties, interconnection terms and external disturbances are unknown, and that the time-varying delays are any nonnegative continuous and bounded functions, and do not require that their derivatives have to be less than one. For such a class of uncertain large-scale time-delay interconnected systems, a new method is presented whereby a class of continuous memoryless decentralised local adaptive robust state feedback controllers is proposed. It is also shown that the solutions of uncertain large-scale time-delay interconnected systems can be guaranteed to be uniformly exponentially convergent towards a ball which can be as small as desired. In addition, since the proposed decentralised local adaptive robust state feedback controllers are completely independent of time delays, the results obtained in this article may also be applicable to a class of large-scale interconnected dynamical systems with uncertain time delays. Finally, a numerical example is given to demonstrate the validity of the results.

A set of decentralized PID controllers for an n – link robot manipulator

A class of stabilizing decentralized proportional integral derivative (PID) controllers for an n-link robot manipulator system is proposed. The range of decentralized PID controller parameters for an n-link robot manipulator is obtained using Kharitonov theorem and stability boundary equations. Basically, the proposed design technique is based on the gain-phase margin tester and Kharitonov’s theorem that synthesizes a set of PID controllers for the linear model while nonlinear interaction terms involve in system dynamics are treated as zero. The stability analysis of the composite system with the designed set of decentralized PID controllers is investigated by incorporating bounding parameters of interconnection terms in LMI formulation. From the range of controller gains obtained by the proposed method, a genetic algorithm is adopted to get an optimal controller gains so that the tracking error is minimum. Simulation results are shown to demonstrate the applicability of the proposed control scheme for solution of fixed as well as time-varying trajectory tracking control problems.

Decentralised adaptive robust control of uncertain large-scale non-linear dynamical systems with time-varying delays

The problem of decentralised adaptive robust stabilisation is considered for a class of uncertain large-scale interconnected non-linear systems with time-varying delays. It is assumed that the upper bounds of the uncertainties and interconnection terms are unknown, and that the time-varying delays are any non-negative continuous and bounded functions, and do not require their derivatives to be less than one. In particular, it is only required that the non-linear interconnection terms, which can also include time-varying delays, are bounded in any non-negative non-linear functions, which are not required to be known for the system designer. For such a class of uncertain large-scale time-delay interconnected non-linear systems, a new method is presented whereby a class of continuous memoryless decentralised local adaptive robust state feedback controllers with a rather simpler structure is proposed. It is also shown that the solutions of uncertain large-scale time-delay interconnected systems can be guaranteed as uniformly exponentially convergent towards a ball that can be as small as desired. Finally, a numerical example is given to demonstrate the validity of the results.

Covariance control for stochastic uncertain multivariable systems via sliding mode control strategy

The main idea proposed in this study is based on converting continuous-time covariance matrix differential equations of a multivariable system into a new uncertain deterministic linear system. The closed-loop form of the new state covariance equations is derived by converting the covariance matrix Riccati equation to a new linear deterministic vector state space system. Since the new covariance system is linear and deterministic, all conventional and well-defined control strategies can be applied to it. Using a sliding mode control strategy, the uncertain interconnection terms satisfying a matching condition are nullified and the closed-loop covariance system is asymptotically stable. This is accomplished by applying a control strategy composed of sliding mode and covariance feedback control for each local subsystem.

Decentralized Optimal Control of a Class of Interconnected Nonlinear Discrete-Time Systems by Using Online Hamilton-Jacobi-Bellman Formulation

In this paper, the direct neural dynamic programming technique is utilized to solve the Hamilton-Jacobi-Bellman equation forward-in-time for the decentralized near optimal regulation of a class of nonlinear interconnected discrete-time systems with unknown internal subsystem and interconnection dynamics, while the input gain matrix is considered known. Even though the unknown interconnection terms are considered weak and functions of the entire state vector, the decentralized control is attempted under the assumption that only the local state vector is measurable. The decentralized nearly optimal controller design for each subsystem consists of two neural networks (NNs), an action NN that is aimed to provide a nearly optimal control signal, and a critic NN which evaluates the performance of the overall system. All NN parameters are tuned online for both the NNs. By using Lyapunov techniques it is shown that all subsystems signals are uniformly ultimately bounded and that the synthesized subsystems inputs approach their corresponding nearly optimal control inputs with bounded error. Simulation results are included to show the effectiveness of the approach.

Decentralized Dynamic Surface Control of Large-Scale Interconnected Systems in Strict-Feedback Form Using Neural Networks With Asymptotic Stabilization

A novel neural network (NN)-based nonlinear decentralized adaptive controller is proposed for a class of large-scale, uncertain, interconnected nonlinear systems in strict-feedback form by using the dynamic surface control (DSC) principle, thus, the "explosion of complexity" problem which is observed in the conventional backstepping approach is relaxed in both state and output feedback control designs. The matching condition is not assumed when considering the interconnection terms. Then, NNs are utilized to approximate the uncertainties in both subsystem and interconnected terms. By using novel NN weight update laws with quadratic error terms as well as proposed control inputs, it is demonstrated using Lyapunov stability that the system states errors converge to zero asymptotically with both state and output feedback controllers, even in the presence of NN approximation errors in contrast with the uniform ultimate boundedness result, which is common in the literature with NN-based DSC and backstepping schemes. Simulation results show the effectiveness of the approach.

Power System Stabilization Using Adaptive Neural Network-Based Dynamic Surface Control

In this paper, the power system with an excitation controller is represented as a class of large-scale, uncertain, interconnected nonlinear continuous-time system in strict-feedback form. Subsequently, dynamic surface control (DSC)-based adaptive neural network (NN) controller is designed to overcome the repeated differentiation of the control input that is observed in the conventional backstepping approach. The NNs are utilized to approximate the unknown subsystem and the interconnection dynamics. By using novel online NN weight update laws with quadratic error terms, the closed-loop signals are shown to be locally asymptotically stable via Lyapunov stability analysis, even in the presence of NN approximation errors in contrast with other NN techniques where a bounded stability is normally assured. Simulation results on the IEEE 14-bus power system with generator excitation control are provided to show the effectiveness of the approach in damping oscillations that occur after disturbances are removed. The end result is a nonlinear decentralized adaptive state-feedback excitation controller for damping power systems oscillations in the presence of uncertain interconnection terms.

Decentralized Adaptive Robust Control of Uncertain Large Scale Systems Including Time–Varying State Delays in the Nonlinear Interconnections

AbstractThe problem of decentralized adaptive robust stabilization is considered for a class of uncertain large scale time–delay systems with nonlinear interconnection terms. It is assumed that the upper bounds of the uncertainties and the interconnection terms are unknown, and that the time–varying delays are any nonnegative continuous and bounded functions, and do not require that their derivatives have to be less than one. In particular, it is only required that the nonlinear interconnection terms, which can also include time–varying delays, are bounded in any nonnegative nonlinear functions which are not required to be known for the system designer. For such a class of uncertain large scale time–delay nonlinear systems, a new method is presented whereby a class of decentralized local adaptive robust state feedback controllers with a rather simpler structure is proposed. It is also shown that the solutions of uncertain large scale time–delay interconnected systems can be guaranteed to be uniformly exponentially convergent towards a ball which can be as small as desired. Copyright ©2011 IFAC

Hierarchical control for discrete large-scale complex systems by intelligent controllers

This paper presents a new method to approximate optimal control strategies of discrete time large-scale nonlinear systems using intelligent approaches. The idea is based on the decomposition principle of the global system into interconnected subsystems for which nonlinearities are located in the interconnection terms. Then, the mixed coordination procedure between different subsystems is formulated as a hierarchical method for the solution of large-scale optimal control problems. So, for each subsystem, local optimal feedback gains are expressed in terms of the interconnection vector. For this purpose, neural networks and fuzzy logic controllers have been constructed in order to identify these gains. A comparison with the differential dynamic programming procedure as a reference method is done. Simulation results of two numerical examples show that the proposed method yields to satisfactory performances, and the robustness of the proposed approaches has been tested.

Functional observers design for two interconnected linear systems via LMI

AbstractThis paper proposes a functional observer for each subsystem of two interconnected system. An original expression of the observation error permits to use previous results on large scale delay systems to solve the problem. The proposed observers are free of interconnection terms and the observation error is unbiased. The observer are designed via some gains which are obtained via LMIs (i.e. via a tractable approach) from the Lyapunov-Krasovskii stability results. An algorithm is given for the computation of the observers, then a numerical example shows their effectiveness of this approach. This result can be extended for the H∞ filtering of linear and nonlinear large scale systems.

Adaptive sliding mode controller design for decentralised model following of large-scale systems with time-varying delay interconnections

The problem of decentralised robust model following is considered for a class of uncertain large-scale systems with time-varying delay interconnections. It is assumed that the upper bounds of uncertainties and interconnections are unknown. For such a class of uncertain large-scale interconnected time-delay systems, some adaptation laws are introduced to updating the unknown upper bounds, and a class of decentralised local adaptive robust sliding mode controllers is proposed by combining a sliding mode controller with the adaptation law. The proposed decentralised local adaptive robust controller can guarantee that the local tracking error of each subsystem decreases asymptotically to zero in the presence of uncertainties and interconnection terms with time-varying delays. Finally, a numerical example is given to demonstrate the validity of the results.

Formula omitted] decentralized observation and control of nonlinear interconnected systems

In this paper, we investigate the problem of H ∞ decentralized tracking control design with a decentralized observer for interconnected nonlinear systems which are characterized by the interconnection of N subsystems. Each subsystem is modeled by a linear constant part perturbed by an additive nonlinearity which is illustrated by the interconnection terms. The proposed feedback control scheme is developed to ensure the asymptotic stability of the augmented system, to reconstruct the non-measurable state variables of each subsystem, to maximize the nonlinearity domain, and to improve the performance of the model reference tracking control by using the H ∞ criterion despite the external disturbances. The proposed control approach is formulated in a minimization problem and derived in terms of linear matrix inequalities (LMIs) whose resolution yields the decentralized control and observation gain matrices. The effectiveness of the proposed control scheme is demonstrated through numerical simulations on a power system with three interconnected machines.

Design of decentralised adaptive sliding mode controllers for large-scale systems with mismatched perturbations

Based on the Lyapunov stability theorem, a methodology for designing a decentralised adaptive sliding mode control scheme is proposed in this paper. This scheme is implemented for a class of large-scale systems with both matched and mismatched perturbations. The perturbations and the interconnection terms are assumed to be norm bounded under certain mild conditions. The decentralised sliding surfaces with adaptive mechanisms embedded are specially designed for each subsystem, so that when each subsystem enters the sliding mode, the mismatched perturbations and the effects of interconnections can be effectively overcome and achieve asymptotic stability. The decentralised controller with embedded adaptive mechanisms is capable of driving the controlled state trajectories into the designated sliding surface in finite time. This is also achieved without the knowledge of upper bounds of the perturbations except those of the uncertainties in the input channels. A numerical example is included to demonstrate the feasibility of the proposed control scheme.

A passivity-based stability criterion for a class of biochemical reaction networks

This paper presents a stability test for a class of interconnected nonlinear systems motivated by biochemical reaction networks. The main result determines global asymptotic stability of the network from the diagonal stability of a dissipativity matrix which incorporates information about the passivity properties of the subsystems, the interconnection structure of the network, and the signs of the interconnection terms. This stability test encompasses the secant criterion for cyclic networks presented in [1], and extends it to a general interconnection structure represented by a graph. The new stability test is illustrated on a mitogen-activated protein kinase (MAPK) cascade model, and on a branched interconnection structure motivated by metabolic networks. The next problem addressed is the robustness of stability in the presence of diffusion terms. A compartmental model is used to represent the localization of the reactions, and conditions are presented under which stability is preserved despite the diffusion terms between the compartments.

A Novel Stabilization Criterion for Large-Scale T–S Fuzzy Systems

This correspondence studies the stabilization problem of large-scale Takagi-Sugeno fuzzy systems. A novel stabilization criterion with decentralized parallel distributed compensation (PDC) fuzzy controller is proposed. The criterion contains two inequalities and one negative definite matrix to be satisfied. The effects of all interconnection terms and all decentralized PDC gains are entirely included in the negative definite matrix. The size of the matrix depends on the number of subsystems; the more the number of subsystems is, the larger the size of the matrix is. By using the linear matrix inequality method, the inequalities in the criterion can be solved to synthesize the local feedback gain of each PDC fuzzy controller such that the whole closed-loop large-scale fuzzy system is asymptotically stable. Finally, we give a practical example to illustrate the effectiveness of the proposed criterion.

Decentralized adaptive recurrent neural control structure

This paper presents a novel decentralized variable structure neural control approach for large-scale uncertain systems, which is developed using recurrent high-order neural networks (RHONN). It is assumed that each subsystem belongs to a class of block-controllable nonlinear systems whose vector fields includes interconnection terms, which are bounded by nonlinear functions. A decentralized RHONN structure and the respective learning law are proposed in order to approximate online the dynamical behavior of each nonlinear subsystem. The control law, which is able to regulate and to track the desired reference signals, is designed using the well-known variable structure theory. The stability of the whole system is analyzed via the Lyapunov methodology. The applicability of the proposed decentralized identification and control algorithm is illustrated via simulations as applied to an interconnected double inverted pendulum.

On the suboptimal solution for large scale non-linear control systems using neural networks

This work is aimed at looking into the determination of optimal control strategies of large scale non-linear systems. The basic idea consists of the decomposition of the global system into interconnected subsystems. We consider non-linear systems whose subsystems are linear with respect to their state and control; in other words, non-linearities are located in the interconnection terms. Then, for each subsystem, local optimal feedback gains are easily expressed in terms of interconnection vectors. Such optimisation has been successfully achieved using a neural net yielding the optimal gain at each step time. Some numerical examples are considered in order to illustrate the proposed approach.

DECENTRALIZED NEURONAL CONTROL STRUCTURE

A novel decentralized variable structure neural control approach for large-scale uncertain systems is developed using Recurrent High Order Neural Networks (RHONN). It is assumed that each subsystem belongs to a class of block-controllable nonlinear systems whose vector fields includes interconnections terms. The interconnection terms are bounded by nonlinear functions. A decentralized RHONN structure and the respective learning law, are propposed in order to approximate on-line the dynamical behaviour of each nonlinear subsystem. The control law, which is able to regulate and to track the desired reference signals, is designed using the well known variable structure theory. The stability of the whole system is analyzed via the Lyapunov methodology. The applicability of proposed decentralized identification and control algorithm is illustrated via simulations as applied to stabilize an interconnected double inverted pendulum.

Stability and Stabilization of Fuzzy Large-Scale Systems

This paper investigates the stability and stabilization problems for the fuzzy large-scale system in which the system is composed of a number of Takagi-Sugeno fuzzy model subsystems with interconnections. The stability criterion of the fuzzy large-scale system without control is derived first. Instead of fuzzy parallel distributed compensation design, linear state feedback control is used in the stabilization work. Each local control is obtained from Riccati equation of the corresponding subsystem and the interconnection terms are used to determine the local feedback gain determination. Based on Lyapunov criterion, some conditions are derived under which the whole fuzzy large-scale system is stabilized asymptotically. A numerical example is given to illustrate the control design procedure and its effectiveness.