An Improved Robust Model Predictive Control Approach to Systems with Linear Fractional Transformation Perturbations

In this paper, a robust model predictive control approach is proposed for a class of uncertain systems with time-varying, linear fractional transformation perturbations. By adopting a sequence of feedback control laws instead of a single one, the control performance can be improved and the region of attraction can be enlarged compared with the existing model predictive control （MPC） approaches. Moreover, a synthesis approach of MPC is developed to achieve high performance with lower on-line computational burden. The effectiveness of the proposed approach is verified by simulation examples.

Robust model-reference control for descriptor linear systems subject to parameter uncertainties

Robust model-reference control for descriptor linear systems with structural parameter uncertainties is investigated. A sufficient condition for existing a model-reference zero-error asymptotic tracking controller is given. It is shown that the robust model reference control problem can be decomposed into two subproblems： a robust state feedback stabilization problem for descriptor systems subject to parameter uncertainties and a robust compensation problem. The latter aims to find three coefficient matrices which satisfy four matrix equations and simultaneously minimize the effect of the uncertainties to the tracking error. Based on a complete parametric solution to a class of generalized Sylvester matrix equations, the robust compensation problem is converted into a minimization problem with quadratic cost and linear constraints. A numerical example shows the effect of the proposed approach.

Adaptive nonlinear model predictive control design of a flexible-link manipulator with uncertain parameters

This paper presents a novel adaptive nonlinear model predictive control design for trajectory tracking of flexible-link manipulators consisting of feedback linearization, linear model predictive control, and unscented Kalman filtering. Reducing the nonlinear system to a linear system by feedback linearization simplifies the optimization problem of the model predictive controller significantly, which, however, is no longer linear in the presence of parameter uncertainties and can potentially lead to an undesired dynamical behaviour. An unscented Kalman filter is used to approximate the dynamics of the prediction model by an online parameter estimation, which leads to an adaptation of the optimization problem in each time step and thus to a better prediction and an improved input action. Finally, a detailed fuzzy-arithmetic analysis is performed in order to quantify the effect of the uncertainties on the control structure and to derive robustness assessments. The control structure is applied to a serial manipulator with two flexible links containing uncertain model parameters and acting in three-dimensional space.

Load Frequency Control of Small Hydropower Plants Using One-Input Fuzzy PI Controller with Linear and Non-Linear Plant Model

This study presents an intelligent approach for load frequency control (LFC) of small hydropower plants (SHPs). The approach which is based on fuzzy logic (FL), takes into account the non-linearity of SHPs—something which is not possible using traditional controllers. Most intelligent methods use two- input fuzzy controllers, but because such controllers are expensive, there is economic interest in the relatively cheaper single-input controllers. A non- linear control model based on one-input fuzzy logic PI (FLPI) controller was developed and applied to control the non-linear SHP. Using MATLAB/Si- mulink SimScape, the SHP was simulated with linear and non-linear plant models. The performance of the FLPI controller was investigated and compared with that of the conventional PI/PID controller. Results show that the settling time for the FLPI controller is about 8 times shorter;while the overshoot is about 15 times smaller compared to the conventional PI/PID controller. Therefore, the FLPI controller performs better than the conventional PI/PID controller not only in meeting the LFC control objective but also in ensuring increased dynamic stability of SHPs.

Application of Linear Model Predictive Control and Input-Output Linearization to Constrained Control of 3D Cable Robots

Cable robots are structurally the same as parallel robots but with the basic difference that cables can only pull the platform and cannot push it. This feature makes control of cable robots a lot more challenging compared to parallel robots. This paper introduces a controller for cable robots under force constraint. The controller is based on input-output linearization and linear model predictive control. Performance of input-output linearizing (IOL) controllers suffers due to constraints on input and output variables. This problem is successfully tackled by augmenting IOL controllers with linear model predictive controller (LMPC). The effecttiveness of the proposed method is illustrated by numerical simulation.

Max-plus-linear model-based predictive control for constrained hybrid systems: linear programming solution

In this paper, a linear programming method is proposed to solve model predictive control for a class of hybrid systems. Firstly, using the （max, ＋） algebra, a typical subclass of hybrid systems called max-plus-linear （MPL） systems is obtained. And then, model predictive control （MPC） framework is extended to MPL systems. In general, the nonlinear optimization approach or extended linear complementarity problem （ELCP） were applied to solve the MPL-MPC optimization problem. A new optimization method based on canonical forms for max-min-plus-scaling （MMPS） functions （using the operations maximization, minimization, addition and scalar multiplication） with linear constraints on the inputs is presented. The proposed approach consists in solving several linear programming problems and is more efficient than nonlinear optimization. The validity of the algorithm is illustrated by an example.

Model Predictive Control of Nonlinear Systems: Stability Region and Feasible Initial Control

This paper proposes a new method for model predictive control （MPC） of nonlinear systems to calculate stability region and feasible initial control profile/sequence, which are important to the implementations of MPC. Different from many existing methods, this paper distinguishes stability region from conservative terminal region. With global linearization, linear differential inclusion （LDI） and linear matrix inequality （LMI） techniques, a nonlinear system is transformed into a convex set of linear systems, and then the vertices of the set are used off-line to design the controller, to estimate stability region, and also to determine a feasible initial control profile/sequence. The advantages of the proposed method are demonstrated by simulation study.

Distributed Model Predictive Control with Actuator Saturation for Markovian Jump Linear System

This paper is concerned with the distributed model predictive control (MPC) problem for a class of discrete-time Markovian jump linear systems (MJLSs) subject to actuator saturation and polytopic uncertainty in system matrices. The global system is decomposed into several subsystems which coordinate with each other. A set of distributed controllers is designed by solving a min-max optimization problem in terms of the solutions of linear matrix inequalities (LMIs). An iterative algorithm is developed to achieve the online computation. Finally, a simulation example is employed to show the effectiveness of the proposed algorithm. © 2014 Chinese Association of Automation.

Modeling and Stability Analysis for Non-linear Network Control System Based on T-S Fuzzy Model

Based on the T-S fuzzy model,this paper presents a new model of non-linear network control system with stochastic transfer delay.Sufficient criterion is proposed to guarantee globally asymptotically stability of this two-levels T-S fuzzy model.Also a T-S fuzzy observer of NCS is designed base on this two-levels T-S fuzzy model.All these results present a new approach for networked control system analysis and design.

Robust Non-Fragile Guaranteed Cost Control for Nonlinear Time Delay Discrete-Time Systems Based on T-S Model

This paper concerns the robust non-fragile guaranteed cost control for nonlinear time delay discrete-time systems based on Takagi-Sugeno （T-S） model. The problem is to design a guaranteed cost state feedback controller which can tolerate uncertainties from both models and gain variation. Sufficient conditions for the existence of such controller are given based on the linear matrix inequality （LMI） approach combined with Lyapunov method and inequality technique. A numerical example is given to illustrate the feasibility and effectiveness of our result.

Investigation on full vehicle height control algorithm using feedback linearization method

Aiming to improve the control accuracy of the vehicle height for the air suspension system,deeply analyzing the processes of variable mass gas thermodynamics and vehicle dynamics,a nonlinear height control model of the air suspension vehicle was built. To deal with the nonlinear characteristic existing in the lifting and lowering processes,the nonlinear model of vehicle height control was linearized by using a feedback linearization method. Then,based on the linear full vehicle model,the sliding model controller was designed to achieve the control variables. Finally,the nonlinear control algorithm in the original coordinates can be achieved by the inverse transformation of coordinates. To validate the accuracy and effectiveness of the sliding mode controller,the height control processes were simulated in Matlab,i. e.,the lifting and lowering processes of the air suspension vehicle were taken when vehicle was in stationary and driving at a constant speed. The simulation results show that,compared to other controllers,the designed sliding model controller based on the feedback linearization can effectively solve the ＂overshoot＂problem,existing in the height control process,and force the vehicle height to reach the desired value,so as to greatly improve the speed and accuracy of the height control process. Besides,the sliding mode controller can well regulate the roll and pitch motions of the vehicle body,thereby improving the vehicle＇s ride comfort.

A Modified Model Predictive Control Scheme

In implementations of MPC (Model Predictive Control) schemes, two issues need to be addressed. One is how to enlarge the stability region as much as possible. The other is how to guarantee stability when a computational time limitation exists. In this paper, a modified MPC scheme for constrained linear systems is described. An offline LMI-based iteration process is introduced to expand the stability region. At the same time, a database of feasible control sequences is generated offline so that stability can still be guaranteed in the case of computational time limitations. Simulation results illustrate the effectiveness of this new approach. Keywords Model predictive control - linear matrix inequality - stability region - terminal region - feasibility Xiao-Bing Hu received the B.S. degree in Aviation Electronic Engineering at Civil Aviation Institute of China, Tianjin, China, in 1998, the M.S. degree in Automatic Control Engineering at Nanjing University of Aeronautics & Astronautics, Nanjing, China, in 2001, and the Ph.D. degree in Aeronautical and Automotive Engineering at Loughborough University, UK, in 2005.He is currently a Research Fellow in Department of Informatics at Sussex University, UK. His major field of research includes predictive control, artificial intelligence, air traffic management, and flight control. Wen-Hua Chen received his MSc and Ph.D. degrees from Department of Automatic Control at Northeast University, China, in 1989 and 1991, respectively.From 1991 to 1996, he was a Lecturer in Department of Automatic Control at Nanjing University of Aeronautics & Astronautics, China. He held a research position and then a Lectureship in Control Engineering in Center for Systems and Control at University of Glasgow, UK, from 1997 to 2000. He holds a Lectureship in Flight Control Systems in Department of Aeronautical and Automotive Engineering at Loughborough University, UK. He has published one book and more than 60 papers on journals and conferences. His research interests are the development of advanced control strategies and their applications in aerospace engineering.

Fuzzy modelling and impulsive control of the hyperchaotic L system

This paper presents a novel approach to hyperchaos control of hyperchaotic systems based on impulsive control and the Takagi-Sugeno （T-S） fuzzy model. In this study, the hyperchaotic Lu system is exactly represented by the T-S fuzzy model and an impulsive control framework is proposed for stabilizing the hyperchaotic Lu system, which is also suitable for classes of T-S fuzzy hyperchaotic systems, such as the hyperchaotic Rossler, Chen, Chua systems and so on. Sufficient conditions for achieving stability in impulsive T-S fuzzy hyperchaotic systems are derived by using Lyapunov stability theory in the form of the linear matrix inequality, and are less conservative in comparison with existing results. Numerical simulations are given to demonstrate the effectiveness of the proposed method.

MODELING OF NONLINEAR SYSTEMS BY MULTIPLE LINEARIZED MODELS

In order to design linear controller for nonlinear systems,a simple but efficient method of modeling a nonlinear system was proposed by means of multiple linearized models at different operating points in the entire range of the expected changes of the operating points.The original nonlinear system was described by linear combination of these multiple linearized models,with the linear combination parameters being identified on line based on least squares method.Model Predictive Control,an optimization based technique,was used to design the linear controller.A sufficient condition for ensuring the existence of a linear controller for the original nonlinear system was also given.Good performance indicated by two simulated examples confirms the usefulness of the proposed method.

Robust Stabilization of Nonlinear Time Delay Discrete-time Systems Based on T-S Model

A robust stabilization problem is considered for time delay nonlinear discrete-time systems based on T-S fuzzy model. A necessary and sufficient condition for the existence of such controllers is given through Lyapunov stability theorem. And it is further shown that this condition is equivalent to the solvability of a certain linear matrix inequality, which can be solved easily by using the LMI toolbox of Matlab. At last, an illustrative example of truck-trailer is presented to show the feasibility and effectiveness of the proposed method.

Robust model predictive control for continuous uncertain systems with state delay

This paper is concerned with robust model predictive control for linear continuous uncertain systems with state delay and control constraints, A piecewise constant control sequence is calculated by minimizing the upper-bound of the infinite horizon quadratic cost function, At each sampling time, the sufficient conditions for the existence of the model predictive control are derived, and expressed as a set of linear matrix inequalities. The robust stability of the closed-loop svstems is guaranteed bv the proposed design method. A numerical example is given to illustrate the main results.

Model Helicopter Control Using Body-Mounted Vibro-Tactile Transducers

The sense of touch as a man-machine communication channel can be as acute as the sense of sight and sound. In some scenarios such as those seen in aerobatics, stunt flying, and combat flights, tactile sensors can even outperform the conventional non-contact sensors in terms of situation awareness. Fusion of tactile sensory information with those obtained via sight and sound can avoid diverting the user’s attention away from the operational task at hand as well. In this study, the performance of an operator, to servo control the motion of a 2-dof model helicopter with pitch/yaw maneuverability, subjected to an intuitive body-referenced arrangement of a cluster of vibro-tactile sensors is investigated. A blindfolded operator will then control the helicopter to a safe attraction zone via a joystick based on this tactile sensory information. A fine-tuned local controller would take over for the end-of-motion precise homing. This study can pave the way towards a systematic integration and characterization of tactile sensors in high performance weapon platforms with improved situation awareness in visually awkward maneuvers such as those seen in aerial combat scenarios.

Non-Fragile Controller Design for 2-D Discrete Uncertain Systems Described by the Roesser Model

This paper is concerned with the design problem of non-fragile controller for a class of two-dimensional (2-D) discrete uncertain systems described by the Roesser model. The parametric uncertainties are assumed to be norm-bounded. The aim of this paper is to design a memoryless non-fragile state feedback control law such that the closed-loop system is asymptotically stable for all admissible parameter uncertainties and controller gain variations. A new linear matrix inequality (LMI) based sufficient condition for the existence of such controllers is established. Finally, a numerical example is provided to illustrate the applicability of the proposed method.

Robust Fuzzy Tracking Control for Nonlinear Networked Control Systems with Integral Quadratic Constraints

This paper investigates the robust tracking control problcm for a class of nonlinear networked control systems （NCSs） using the Takagi-Sugeno （T-S） fuzzy model approach. Based on a time-varying delay system transformed from the NCSs, an augmented Lyapunov function containing more useful information is constructed. A less conservative sufficient condition is established such that the closed-loop systems stability and time-domain integral quadratic constraints （IQCs） are satisfied while both time-varying network- induced delays and packet losses are taken into account. The fuzzy tracking controllers design scheme is derived in terms of linear matrix inequalities （LMIs） and parallel distributed compensation （PDC）. Furthermore, robust stabilization criterion for nonlinear NCSs is given as an extension of the tracking control result. Finally, numerical simulations are provided to illustrate the effectiveness and merits of the proposed method.

Fault tolerant synchronization of chaotic systems based on T-S fuzzy model with fuzzy sampled-data controller

In this paper the fault tolerant synchronization of two chaotic systems based on fuzzy model and sample data is investigated. The problem of fault tolerant synchronization is formulated to study the global asymptotical stability of the error system with the fuzzy sampled-data controller which contains a state feedback controller and a fault compensator. The synchronization can be achieved no matter whether the fault occurs or not. To investigate the stability of the error system and facilitate the design of the fuzzy sampled-data controller, a Takagi Sugeno （T-S） fuzzy model is employed to represent the chaotic system dynamics. To acquire good performance and produce a less conservative analysis result, a new parameter-dependent Lyapunov-Krasovksii functional and a relaxed stabilization technique are considered. The stability conditions based on linear matrix inequality are obtained to achieve the fault tolerant synchronization of the chaotic systems. Finally, a numerical simulation is shown to verify the results.