Local State Feedback Controllers Research Articles

Delay-range-dependent control of nonlinear time-delay systems under input saturation

Summary This paper describes a delay-range-dependent local state feedback controller synthesis approach providing estimation of the region of stability for nonlinear time-delay systems under input saturation. By employing a Lyapunov–Krasovskii functional, properties of nonlinear functions, local sector condition and Jensen's inequality, a sufficient condition is derived for stabilization of nonlinear systems with interval delays varying within a range. Novel solutions to the delay-range-dependent and delay-dependent stabilization problems for linear and nonlinear time-delay systems, respectively, subject to input saturation are derived as specific scenarios of the proposed control strategy. Also, a delay-rate-independent condition for control of nonlinear systems in the presence of input saturation with unknown delay-derivative bound information is established. And further, a robust state feedback controller synthesis scheme ensuring L2 gain reduction from disturbance to output is devised to address the problem of the stabilization of input-constrained nonlinear time-delay systems with varying interval lags. The proposed design conditions can be solved using linear matrix inequality tools in connection with conventional cone complementary linearization algorithms. Simulation results for an unstable nonlinear time-delay network and a large-scale chemical reactor under input saturation and varying interval time-delays are analyzed to demonstrate the effectiveness of the proposed methodology. Copyright © 2015 John Wiley & Sons, Ltd.

Decentralised robust stabilisation of uncertain large-scale interconnected time-delay systems with unknown upper bounds of uncertainties

The problem of decentralised robust stabilisation is considered for a class of uncertain large-scale time-delay interconnected dynamical systems. In the paper, the upper bounds of delayed state perturbations, uncertainties, interconnection terms, and external disturbances are assumed to be completely unknown, and the delays are assumed to be any non-negative constants. For such a class of uncertain large-scale time-delay interconnected systems, a new method is presented whereby a class of adaptation-free decentralised local robust state feedback controllers can be constructed. In addition, it is also shown that the solutions of uncertain large-scale time-delay interconnected systems can be guaranteed to be uniformly ultimately bounded. Finally, as an application to the practical mechanical systems, some simulations of a numerical example are provided to demonstrate the validity of the theoretical results.

Adaptive Control of MEMS Gyroscope Based on T-S Fuzzy Model

A multi-input multioutput (MIMO) Takagi-Sugeno (T-S) fuzzy model is built on the basis of a nonlinear model of MEMS gyroscope. A reference model is adjusted so that a local linear state feedback controller could be designed for each T-S fuzzy submodel based on a parallel distributed compensation (PDC) method. A parameter estimation scheme for updating the parameters of the T-S fuzzy models is designed and analyzed based on the Lyapunov theory. A new adaptive law can be selected to be the former adaptive law plus a nonnegative in variable to guarantee that the derivative of the Lyapunov function is smaller than zero. The controller output is implemented on the nonlinear model and T-S fuzzy model, respectively, for the purpose of comparison. Numerical simulations are investigated to verify the effectiveness of the proposed control scheme and the correctness of the T-S fuzzy model.

Organically Structured Control of Large-Scale Systems with Expanding Construction Based on State Observation

This paper presents a new method on the problem of organically structured control based on state observation for a class of large-scale systems with expanding construction. This problem is to design a local state feedback controller and an observer for a new subsystem which is added to a large-scale system without changing the decentralized state feedback control laws of the original construction, so that both the new subsystem and the resulting expanded system are robustly connectively stable. Firstly, based on state observers, the mathematical model of a large-scale system with expanding construction is reestablished and analyzed. In addition, the sufficient condition for robust decentralized connective stabilization of the expanded construction of large-scale systems is deduced by taking an LMI approach, which is further relaxed by removing the square matrix condition on the output matrix. This problem is transformed into solving an LMI problem. The new design method of an organically structured controller and observer for the expanded construction is also given. Finally, the simulation examples show the effectiveness of the proposed method.

A criterion of robustness intelligent nonlinear control for multiple time-delay systems based on fuzzy Lyapunov methods

A control system with state feedback controllers, in which the fuzzy Lyapunov approach is developed for the stability criterion, is studied. The proposed intelligent design provides a systematic and effective framework for the control systems. The global nonlinear controller is constructed based on T–S (Takagi–Sugeno) fuzzy controller design techniques, blending all such local state feedback controllers. Based on this design, the stability conditions of a multiple time-delay system are derived in terms of the fuzzy Lyapunov theory. The effectiveness and the feasibility of the proposed controller design method are demonstrated through numerical simulations.

Decentralised covariance control of dynamic routing in traffic networks: a covariance feedback approach

In this study, the authors propose a novel decentralised robust routing control strategy for average and covariance of queue length in a data network. The objective is to control the transitional behaviour of the data networks in response to new traffic load. For each node, the authors design a local state feedback controller based on minimising the worst case of the queue length. The authors then propose an innovative model for covariance of the queue length in each node. To control the average of queue length, local delay-dependent robust controllers are designed based on an equivalent descriptor representation and linear matrix inequalities (LMIs). For covariance control of the queue length, the authors first show that the covariance control problem is equivalent to a standard disturbance rejection problem. Then the authors propose a covariance feedback control law. To investigate the effectiveness of the proposed methodology an example is also presented and extensive simulation results are conducted. Simulation results indicate that the proposed method significantly improves the packet loss and system response time and is able to efficiently control the transient conditions in each.

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.

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.

A Fuzzy Lyapunov LMI Criterion to a Chaotic System

Abstract In terms of the Fuzzy Lyapunov method, this work proposes stability conditions for fuzzy logic control (FLC). Their application for chaotic systems can be approximated by the Tagagi-Sugeno (T-S) fuzzy model. The fuzzy Lyapunov function is defined as a fuzzy blending of quadratic Lyapunov functions. External forces or disturbances are not considered in the controlled systems. In the design controller procedure, a parallel distributed compensation (PDC) scheme is utilized to construct a global FLC by blending all linear local state feedback controllers. The stability criteria are found not only for fuzzy modeling but also for a real chaotic system. Furthermore, this controller design problem can be reduced to a linear matrix inequality (LMI) problem by use of the Schur Complements. Efficient interior-point algorithms are now available in Matlab toolbox to solve this type of problem.

Delay Independent Criterion for Multiple Time-delay Systems

Abstract Based on the fuzzy Lyapunov method, this work addresses the stability conditions for nonlinear systems with multiple time delays to ensure the stability of building structure control systems. The delay independent conditions are derived via the traditional Lyapunov and fuzzy Lyapunov methods for multiple time-delay systems as approximated by the Tagagi-Sugeno (T-S) fuzzy model. The fuzzy Lyapunov function is defined as a fuzzy blending of quadratic Lyapunov functions. A parallel distributed compensation (PDC) scheme is utilized to construct a global fuzzy logic control (FLC) by blending all linear local state feedback controllers in the controller design procedure. Furthermore, the H infinity performance and robustness of the design for modeling errors also need to be considered in the stability conditions.

A critical review of nonlinear fuzzy multiple time-delay interconnected systems using the Lyapunov criterion

This paper reviews the development of fuzzy systems and the problem of time delay control in nonlinear systems. Based on this review, a fuzzy Lyapunov method defined in fuzzy blending quadratic Lyapunov functions is proposed from which to derive stability conditions. In the controller procedure, a parallel distributed compensation (PDC) scheme is utilized to construct a global fuzzy logic controller (FLC) by blending all linear local state feedback controllers. Furthermore, the multiple time-delay interconnected systems are considered in the nonlinear fuzzy systems. Key words: Interconnected systems, fuzzy Lyapunov method, linear matrix inequality.

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

A Coordinated Nonlinear Model Predictive Control Scheme Over Non-acknowledged Networks

This work deals with a networked model predictive coordinated control scheme for discrete-time constrained nonlinear systems characterized by mutual physical interconnections and subject to local state-feedback control policies. A centralized controller, communicating with the distributed agents through a packet-based network, is designed to guarantee the uniform boundedness of the trajectories of the overall closed-loop system. In order to cope with time-varying transmission delays, typically affecting networked control systems, a network delay compensation strategy based on the time-stamping of data packets is adopted. With respect to the existent model-based approaches for nonlinear networked control system, the proposed method eliminates the need for acknowledgment messages, by suitably modifying the finite horizon optimization problem associated to the MPC. The proposed coordinated networked policy guarantees the robust enforcement of state and input constraints even in presence of bounded model uncertainty.

Fuzzy Control for an Oceanic Structure: A Case Study in Time-delay TLP System

In this paper, a Takagi-Sugeno (T-S) fuzzy model approach combined with a parallel distributed compensation (PDC) scheme is proposed for time-delay control of the response of a tension leg platform (TLP) system subjected to an external wave force. A global PDC-based fuzzy logic controller is constructed by blending all local state feedback controllers. A fuzzy-model-based control is thereby developed which can attenuate the influence of the external wave force. The controller is evaluated in terms of stability analysis, and the linear matrix inequality (LMI) conditions guaranteeing the stability of the TLP system derived via Lyapunov theory. A simulation example is given to show the feasibility of the proposed fuzzy control approach. The example shows the concept of half-circle fuzzy number can be used in fuzzy control and the proposed control method can be employed in practical engineering problems of oceanic structure.

Modeling and Fuzzy PDC Control and Its Application to an Oscillatory TLP Structure

An analytical solution is derived to describe the wave‐induced flow field and surge motion of a deformable platform structure controlled with fuzzy controllers in an oceanic environment. In the controller design procedure, a parallel distributed compensation (PDC) scheme is utilized to construct a global fuzzy logic controller by blending all local state feedback controllers. The Lyapunov method is used to carry out stability analysis of a real system structure. The corresponding boundary value problems are then incorporated into scattering and radiation problems. These are analytically solved, based on the separation of variables, to obtain a series of solutions showing the harmonic incident wave motion and surge motion. The dependence of the wave‐induced flow field and its resonant frequency on wave characteristics and structural properties including platform width, thickness and mass can thus be drawn with a parametric approach. The wave‐induced displacement of the surge motion is determined from these mathematical models. The vibration of the floating structure and mechanical motion caused by the wave force are also discussed analytically based on fuzzy logic theory and the mathematical framework to find the decay in amplitude of the surge motion in the tension leg platform (TLP) system. The expected effects of the damping in amplitude of the surge motion due to the control force on the structural response are obvious.

The stability of an oceanic structure with T–S fuzzy models

In this study we construct and derive analytical solutions for a mathematical model of an oceanic environment in which wave-induced flow fields cause structural surge motion after which a fuzzy control technique is developed to alleviate structural vibration. Specifically the Takagi–Sugeno (T–S) fuzzy model is employed to approximate the oceanic structure and a parallel-distributed-compensation (PDC) scheme is utilized in a control procedure designed to reduce the structural response. All local state feedback controllers are integrated to construct a global fuzzy logic controller. The Lyapunov method is used to achieve structural stability. The interaction between the wave motion and the structural response is explained using the separation of variables method. The surge motion is related to the characteristics of the wave and the structure. A parametric approach is utilized to show these effects. Other parameters remain constant. In an oceanic structural system, platform migration is often caused by the wave force. The stability of an oceanic structure can be proven theoretically based on stability analysis. The decay of the displacement and velocity due to the use of the proposed fuzzy controllers is demonstrated by a numerical simulation.

Decentralized guaranteed cost control for uncertain large‐scale systems using additive control gain

AbstractThis paper investigates an application of additive control gain to the guaranteed cost control (GCC) problem of decentralized robust control for a class of discrete‐time uncertain large‐scale systems. Based on the Linear Matrix Inequality (LMI) design approach, a class of decentralized local fixed state feedback controllers with additive control gain is established. The novel contribution of this paper is that multiobjective control is attained by using the additive control gain. Although the additive control gain is included in the uncertain large‐scale systems, the closed‐loop system is asymptotically stable. In order to demonstrate the efficiency of our proposed controller, using the fuzzy logic control as the additive control gain, the simple numerical example is given. © 2009 Wiley Periodicals, Inc. Electr Eng Jpn, 169(3): 18–32, 2009; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/eej.20726

The guaranteed cost control for uncertain nonlinear large-scale stochastic systems via state and static output feedback

The guaranteed cost control (GCC) problem involved in decentralized robust control of a class of uncertain nonlinear large-scale stochastic systems with high-order interconnections is considered. After determining the appropriate conditions for the stochastic GCC controller, a class of decentralized local state feedback controllers is derived using the linear matrix inequality (LMI). The extension of the result of the study to the static output feedback control problem is discussed by considering the Karush–Kuhn–Tucker (KKT) conditions. The efficiency of the proposed design method is demonstrated on the basis of simulation results.

Decentralised adaptive controllers for robust tracking and model following of uncertain large scale systems

The problem of decentralised robust tracking and model following is considered for a class of uncertain large scale interconnected systems. In this article, it is assumed that the upper bounds of the uncertainties and external disturbances are unknown. A modified adaptation law with σ-modification is introduced to estimate such unknown bounds, and on the basis of the updated values of these unknown bounds, a class of decentralised local state feedback controllers is constructed for robust tracking of dynamical signals. The proposed decentralised adaptive robust tracking controllers can guarantee that the tracking errors between each subsystem and the corresponding local reference model decrease uniformly asymptotically to zero. Finally, a numerical example is given to demonstrate the validity of the results.

Decentralized Adaptive Robust Tracking Controllers of Uncertain Large Scale Systems with Time Delays

The problem of decentralized robust tracking and model following is considered for a class of uncertain large scale systems including delayed state perturbations in the interconnections. In this paper, it is assumed that the upper bounds of the delayed state perturbations, uncertainties, and external disturbances are unknown. A modified adaptation law with σ–modification is introduced to estimate such unknown bounds, and on the basis of the updated values of these unknown bounds, a class of decentralized local memoryless state feedback controllers is constructed for robust tracking of dynamical signals. The proposed decentralized adaptive robust tracking controllers can guarantee that the tracking errors between each time–delay subsystem and the corresponding local reference model without time–delay decrease uniformly asymptotically to zero.