Nonlinear predictive controller based on S-PARAFAC Volterra models applied to a communicating two-tank system

This paper proposes a new predictive controller approach for nonlinear process based on a reduced complexity homogeneous, quadratic discrete-time Volterra model called quadratic S-PARAFAC Volterra model. The proposed model is yielded by using the symmetry property of the Volterra kernels and their tensor decomposition using the PARAFAC technique that provides a parametric reduction compared to the conventional Volterra model. This property allows synthesising a new nonlinear-model-based predictive control (NMBPC). We develop the general form of a new predictor, and therefore, we propose an optimisation algorithm formulated as a quadratic programming under linear and nonlinear constraints. The performances of the proposed quadratic S-PARAFAC Volterra model and the developed NMBPC algorithm are illustrated on a numerical simulation and validated on a benchmark as a continuous stirred-tank reactor system. Moreover, the efficiency of the proposed quadratic S-PARAFAC Volterra model and the NMBPC approach are validated on an experimental communicating two-tank system.     

Sufficient conditions for stabilization of sampled-data nonlinear systems via discrete-time approximations

Given a parameterized (by sampling period T) family of approximate discrete-time models of a sampled nonlinear plant and given a family of controllers stabilizing the family of plant models for all T sufficiently small, we present conditions which guarantee that the same family of controllers semi-globally practically stabilizes the exact discrete-time model of the plant for sufficiently small sampling periods. When the family of controllers is locally bounded, uniformly in the sampling period, the inter-sample behavior can also be uniformly bounded so that the (time-varying) sampled-data model of the plant is uniformly semi-globally practically stabilized. The result justifies controller design for sampled-data nonlinear systems based on the approximate discrete-time model of the system when sampling is sufficiently fast and the conditions we propose are satisfied. Our analysis is applicable to a wide range of time-discretization schemes and general plant models.     

Robust sampled-data fuzzy control of nonlinear systems with parametric uncertainties: Its application to depth control of autonomous underwater vehicles

This paper presents a new direct discrete-time design methodology of a robust sampled-data fuzzy controller for a class of nonlinear system with parametric uncertainties that is exactly represented by Takagi-Sugeno (T-S) fuzzy model. Based on an exact discrete-time fuzzy model in an integral form, sufficient conditions for a robust asymptotic stabilization of the nonlinear system are investigated in the discrete-time Lyapunov sense. It is shown that the resulting sampled-data controller indeed robustly asymptotically stabilizes the nonlinear plant. To illustrate the effectiveness of the proposed methodology, an example, a sampled-data depth control of autonomous underwater vehicles (AUVs) is provided.     

Stability connection between sampled-data fuzzy control systems with quantization and their approximate discrete-time model

This paper concerns the stability of a sampled-data Takagi-Sugeno (T-S) fuzzy control system with quantization, when a controller design is based on an approximate discrete-time model of the plant without quantization. The motivations come from the facts that digital devices for interfacing a plant with a controller quantize signals and an exact discrete-time model of the T-S fuzzy system is generally not amenable to synthesis process. We show that the concerned system is Lagrange stabilizable by the controller asymptotically stabilizing the approximate discrete-time model. A constructive design algorithm for the developed stability analysis is proposed in terms of linear matrix inequalities.     

Robust discrete-time set-based adaptive predictive control for nonlinear systems

The problem of robust adaptive predictive control for a class of discrete-time nonlinear systems is considered. First, a parameter estimation technique, based on an uncertainty set estimation, is formulated. This technique is able to provide robust performance for nonlinear systems subject to exogenous variables. Second, an adaptive MPC is developed to use the uncertainty estimation in a framework of min–max robust control. A Lipschitz-based approach, which provides a conservative approximation for the min–max problem, is used to solve the control problem, retaining the computational complexity of nominal MPC formulations and the robustness of the min–max approach. Finally, the set-based estimation algorithm and the robust predictive controller are successfully applied in two case studies. The first one is the control of anonisothermal CSTR governed by the van de Vusse reaction. Concentration and temperature regulation is considered with the simultaneous estimation of the frequency (or pre-exponential) factors of the Arrhenius equation. In the second example, a biomedical model for chemotherapy control is simulated using control actions provided by the proposed algorithm. The methods for estimation and control were tested using different disturbances scenarios.     

Adaptive-Predictive Control of a Class of SISO Nonlinear Systems

In this paper, an adaptive-predictive control algorithm is developed for a class of SISO nonlinear discrete-time systems based on a generalized predictive control (GPC) approach. The design is model-free, based directly on pseudo-partial-derivatives derived on-line from the input and output information of the system using a recursive least squares type of identification algorithm. The proposed control is especially useful for nonlinear systems with vaguely known dynamics. Robust stability of the closed-loop system is analyzed and proven in the paper. Simulation and real-time application examples are provided for real nonlinear systems which are known to be difficult to model and control.     

Matrosov theorem for parameterized families of discrete-time systems

A version of Matrosov's theorem for parameterized discrete-time time-varying systems is presented. The theorem is a discrete-time version of the continuous-time result in Loria et al., 2002 (δ-persistency of excitation: a necessary and sufficient condition for uniform attractivity, 2002, submitted for publication). Our result facilitates controller design for sampled-data nonlinear systems via their approximate discrete-time models. An application of the theorem to establishing uniform asymptotic stability of systems controlled by model reference adaptive controllers designed via approximate discrete-time plant models is presented.     

Neural network control of multivariable processes with a fast optimisation algorithm

A radial basis function (RBF) neural network model based predictive control scheme is developed for multivariable nonlinear systems in this paper. A fast convergence algorithm is proposed and employed in multidimensional optimisation in the control scheme to reduce the computing time and save required computer memory. The scheme is applied to a simulated two-input two-output nonlinear process for set-point tracking control. Simulation results demonstrate the effectiveness of the control strategy and the fast learning algorithm for multivariable non-linear processes. Comparison of the performance with PID control is included.     

广义预测控制器系数直接算法

为了简化广义预测控制算法的分析与设计，提出了广义预测控制器系数直接计算方法．该方法利用过程模型直接递推，把广义预测控制律表达成控制器系数与参考轨迹及过程历史信息乘积的形式．其控制器系数计算只与模型参数及设计参数有关，避免了在线求解Diophantine方程、输出预测表达式及自由响应项，简化了设计思路，减少了在线运算量．在一个DCS控制的非线性液位装置上得到的对比实验结果表明该方法是可行和有效的．     

Sampled-data H ∞ control for networked control systems with digital control inputs

In this article, the problem of sampled-data H _∞ control for networked control systems (NCSs) with digital control inputs is considered, where the physical plant is modelled as a continuous-time one, and the control inputs are discrete-time signals. By exploiting a novel Lyapunov–Krasovskii functional, using the Leibniz–Newton formula and a free-weighting matrix method, sufficient conditions for sampled-data H _∞ performance analysis and H _∞ controller design for such systems are given. Since the obtained conditions of H _∞ controller design are not expressed strictly in term of linear matrix inequalities, the sampled-data H _∞ controller is solved using modified cone complementary linearisation algorithm. In addition, the new sampled-data stability criteria for the NCSs is proved to be less conservative than some existing results. Numerical examples demonstrate the effectiveness of the proposed methods.     

H infinity Control of nonlinear discrete-time systems based on dynamical fuzzy models

This paper presents a solution to H infinity control problem for a class of discrete-time nonlinear systems. This class of nonlinear systems can be represented by a discretetime dynamical fuzzy model. A suitable quadratic L yapunov function is used to establish asymptotic stability with an l₂-norm bound gamma of the closed-loop system. Furthermore, a constructive algorithm is developed to obtain the stabilizing feedback control law. The controller design algorithm involves solving a set of suitable algebraic Riccati equations. An example is given to illustrate the application of the method.     

An efficient artificial bee colony algorithm with application to nonlinear predictive control

In this paper a constrained nonlinear predictive control algorithm, that uses the artificial bee colony (ABC) algorithm to solve the optimization problem, is proposed. The main objective is to derive a simple and efficient control algorithm that can solve the nonlinear constrained optimization problem with minimal computational time. Indeed, a modified version, enhancing the exploring and the exploitation capabilities, of the ABC algorithm is proposed and used to design a nonlinear constrained predictive controller. This version allows addressing the premature and the slow convergence drawbacks of the standard ABC algorithm, using a modified search equation, a well-known organized distribution mechanism for the initial population and a new equation for the limit parameter. A convergence statistical analysis of the proposed algorithm, using some well-known benchmark functions is presented and compared with several other variants of the ABC algorithm. To demonstrate the efficiency of the proposed algorithm in solving engineering problems, the constrained nonlinear predictive control of the model of a Multi-Input Multi-Output industrial boiler is considered. The control performances of the proposed ABC algorithm-based controller are also compared to those obtained using some variants of the ABC algorithms.     

非线性HAMMERSTEIN系统的预测控制及其pH过程应用

本文基于非线性离散Hammerstein模型,开发了一种非线性Hammerstein系统预测控制(Non-Linear Hammerstein Predic- tive Control,NLHPC)算法。遵循预测控制策略,该算法利用Hammerstein模型进行输出预测。理论分析结果表明,该算法不仅具有好的稳定性和鲁棒性,而且其自身具有积分作用。在一台工业PC机上实现了该NLHPC算法,并用于具有强非线性的酸碱中和过程实验装置pH值的控制。实验结果表明NLHPC有着比工业界常用的非线性PID控制(nonlinear PID,NL-PID)更好的控制性能。     

Exponential sampled-data control for T–S fuzzy systems: application to Chua's circuit

ABSTRACT

This study deals with the chaotic phenomenon of nonlinear Chua's circuit for power generator systems. Takagi–Sugeno (T–S) fuzzy model of a nonlinear system is established. By constructing a suitable Lyapunov functional, exponential stability conditions are obtained for fuzzy systems. Based on the sampled-data control theory, extreme sensitivity is visualised in the state trajectory depending on the initial conditions and sampled-data fuzzy controllers are designed in the form of linear matrix inequality (LMI). Finally, some numerical simulation results are shown that the sampled-data fuzzy control system adopts a well-designed methodology.     

Sampled-data control of networked linear control systems

In this paper, the problem of synthesis and analysis for the networked control systems (NCSs) with time-driven digital controllers and event-driven holders is considered. The NCS is modelled as a sampled-data system with time-delay in its discrete-time subsystem. This model is able to capture many network-induced features, for example, time-delay and packet dropout. Moreover, the model allows different combinations of the time-driven or event-driven mode of the devices, including the samplers, the controllers and the holders. By transforming time-delay in the discrete-time subsystem into its continuous-time subsystem of the sampled-data system, we have also obtained a less conservative time-delay dependent stability result for the NCSs, using a new Lyapunov function and a relaxed condition. Some limitations of the existing literatures on network-induced time-delay and sampling period are removed in the proposed framework. Furthermore, a sampled-data control design procedure is developed for the NCSs. Linear matrix inequality approach has been employed to solve the stability and control design problems. Finally, numerical examples are included to demonstrate the effectiveness of the proposed stability result and the potential of the proposed techniques.     

Design of an RMPC with a time‐varying terminal constraint set for tracking problem

This paper presents a robust model predictive control algorithm with a time‐varying terminal constraint set for systems with model uncertainty and input constraints. In this algorithm, the nonlinear system is approximated by a linear model where the approximation error is considered as an unstructured uncertainty that can be represented by a Lipschitz nonlinear function. A continuum of terminal constraint sets is constructed off‐line, and robust stability is achieved on‐line by using a variable control horizon. This approach significantly reduces the computational complexity. The proposed robust model predictive controller with a terminal constraint set is used in tracking set‐points for nonlinear systems. The effectiveness of the proposed method is illustrated with a numerical example. Copyright © 2015 John Wiley & Sons, Ltd.     

Design of reduced-order observers for nonlinear sampled-data strict-feedback systems with actuator dynamics and disturbances

We design reduced-order observers for nonlinear sampled-data strict-feedback systems with actuator dynamics and disturbances. First, we use the property of the Euler model of sampled-data systems and the structure of discrete-time observers to design reduced-order observers of the Euler model. Then, we show that the designed observers are semiglobal and practical in T for the exact model. We also give both numerical and practical examples to illustrate the proposed design of reduced-order observers.     

Constrained anti-disturbance control for a quadrotor based on differential flatness

The classical control design based on linearised model is widely used in practice even to those inherently nonlinear systems. Although linear design techniques are relatively mature and enjoy the simple structure in implementations, they can be prone to misbehaviour and failure when the system state is far away from the operating point. To avoid the drawbacks and exploit the advantages of linear design methods while tackling the system nonlinearity, a hybrid control structure is developed in this paper. First, the model predictive control is used to impose states and inputs constraints on the linearised model, which makes the linearisation satisfy the small-perturbation requirement and reduces the bound of linearisation error. On the other hand, a combination of disturbance observer-based control and H_∞ control, called composite hierarchical anti-disturbance control, is constructed for the linear model to provide robustness against multiple disturbances. The constrained reference states and inputs generated by the outer-loop model predictive controller are asymptotically tracked by the inner-loop composite anti-disturbance controller. To demonstrate the performance of the proposed framework, a case study on quadrotor is conducted.     

Tube-based robust sampled-data MPC for linear continuous-time systems

This note extends to the continuous-time case the “tube-based” approach for the design of discrete-time robust model predictive control (MPC) algorithms developed in Mayne, Seron, and Rakovi? (2005). This extension is of interest in view of the simplicity and popularity of the method as well as of the industrial relevance of continuous-time implementations of MPC. The proposed robust control law is composed of two terms: (1) a sampled-data MPC control law and (2) a continuous-time state feedback term.     

基于RVM的非线性预测控制及在聚丙烯牌号切换中的应用

针对由被控对象非线性和优化目标函数非凸性带来的建模与实时优化问题求解的困难,提出一种基于相关向量机(RVM)的非线性多步模型预测控制算法.采用RVM建立非线性预测模型,并将差分进化算法引入非线性预测控制中发挥其伞局最优、鲁棒、快速收敛等优点,在线求解多变量、多约束的非线性规划问题.利用实际生产数据进行聚丙烯牌号切换仿真,结果表明,该算法可大幅度减少切换时间,降低过渡料产量,提高经济效益.