Time-discretization of nonlinear control systems with state-delay via Taylor–Lie series

The state-delay is always existent in the practical systems. Analysis of the delay phenomenon in a continuous-time domain is sophisticated. It is appropriate to obtain its corresponding discrete-time model for implementation via digital computer. In this paper, we propose a new scheme for the discretization of nonlinear systems using Taylor series expansion and the zero-order hold assumption. This scheme is applied to the sample-data representation of a nonlinear system with constant state time-delay. The mathematical expressions of the discretization scheme are presented and the effect of the time-discretization method on equilibrium properties of nonlinear control system with state time-delay is examined. The proposed scheme provides a finite-dimensional representation for nonlinear systems with state time-delay enabling existing controller design techniques to be applied to them. The performance of the proposed discretization procedure is evaluated using a nonlinear system. For this nonlinear system, various sampling rates and time-delay values are considered.     

Composite nonlinear feedback based discrete integral sliding mode controller for uncertain systems

In this paper, a discrete integral sliding mode (ISM) controller based on composite nonlinear feedback (CNF) method is proposed. The aim of the controller is to improve the transient performance of uncertain systems. The CNF based discrete ISM controller consists of a linear and a nonlinear term. The linear control law is used to decrease the damping ratio of the closed-loop system for yielding a quick transient response. The nonlinear feedback control law is used to increase the damping ratio with an aim to reduce the overshoot of the closed-loop system as it approaches the desired reference position. It is observed that the discrete CNF-ISM controller produces superior transient performance as compared to the discrete ISM controller. The closed-loop control system remains stable during the sliding condition. Simulation results demonstrate the effectiveness of the proposed controller.     

Fuzzy guaranteed cost controller for trajectory tracking in nonlinear systems

In this paper, we propose a fuzzy logic based guaranteed cost controller for trajectory tracking in nonlinear systems. Takagi–Sugeno (T–S) fuzzy model is used to represent the dynamics of a nonlinear system and the controller design is carried out using this fuzzy model. State feedback law is used for building the fuzzy controller whose performance is evaluated using a quadratic cost function. For designing the fuzzy logic based controller which satisfies guaranteed performance, linear matrix inequality (LMI) approach is used. Sufficient conditions are derived in terms of matrix inequalities for minimizing the performance function of the controller. The performance function minimization problem with polynomial matrix inequalities is then transformed into a problem of minimizing a convex performance function involving standard LMIs. This minimization problem can be solved easily and efficiently using the LMI optimization techniques. Our controller design method also ensures that the closed-loop system is asymptotically stable. Simulation study is carried out on a two-link robotic manipulator tracking a reference trajectory. From the results of the simulation study, it is observed that our proposed controller tracks the reference trajectory closely while maintaining a guaranteed minimum cost.     

一类带有不确定性的时滞系统的控制器设计

针对一类带有不确定性的单输入单输出的时滞非线性系统,提出了一种鲁棒非线性控制算法.利用反步设计的迭代设计思想,在每一步构造李亚普诺夫-克拉索夫斯基函数,用放大不等式的方法获得控制器,保证闭环系统的稳定性.以连续搅拌化学反应器为例的仿真结果也验证了控制器具有良好的控制特性.     

Real-coded Genetic Algorithm for system identification and tuning of a modified Model Reference Adaptive Controller for a hybrid tank system

Modeling and controlling of level process is one of the most common problems in the process industry. As the level process is nonlinear, Model Reference Adaptive Control (MRAC) strategy is employed in this paper. To design an MRAC with equally good transient and steady state performance is a challenging task. The main objective of this paper is to design an MRAC with very good steady-state and transient performance for a nonlinear process such as the hybrid tank process. A modification to the MRAC scheme is proposed in this study. Real-coded Genetic Algorithm (RGA) is used to tune off-line the controller parameters. Three different versions of MRAC and also a Proportional Integral Derivative (PID) controller are employed, and their performances are compared by using MATLAB. Input–output data of a coupled tank setup of the hybrid tank process are obtained by using Lab VIEW and a system identification procedure is carried out. The accuracy of the resultant model is further improved by parameter tuning using RGA. The simulation results shows that the proposed controller gives better transient performance than the well-designed PID controller or the MRAC does; while giving equally good steady-state performance. It is concluded that the proposed controllers can be used to achieve very good transient and steady state performance during the control of any nonlinear process.     

Robust digital controllers for uncertain chaotic systems: A digital redesign approach

In this paper, a new and systematic method for designing robust digital controllers for uncertain nonlinear systems with structured uncertainties is presented. In the proposed method, a controller is designed in terms of the optimal linear model representation of the nominal system around each operating point of the trajectory, while the uncertainties are decomposed such that the uncertain nonlinear system can be rewritten as a set of local linear models with disturbed inputs. Applying conventional robust control techniques, continuous-time robust controllers are first designed to eliminate the effects of the uncertainties on the underlying system. Then, a robust digital controller is obtained as the result of a digital redesign of the designed continuous-time robust controller using the state-matching technique. The effectiveness of the proposed controller design method is illustrated through some numerical examples on complex nonlinear systems––chaotic systems.     

Control and synchronize a novel hyperchaotic system

The control and hybrid projective synchronization (HPS) strategies for a novel hyperchaotic system are investigated. Firstly, the novel hyperchaotic system is controlled to the unsteady equilibrium point or limit cycle via only one scalar controller which includes two state variables. Secondly, based on Lyapunov’s direct method HPS between two novel hyperchaotic systems is studied. A new nonlinear feedback vector controller is designed to guarantee HPS, which can be simplified ulteriorly into a single scalar controller to achieve complete synchronization between two novel hyperchaotic systems. Finally, numerical simulations are given to verify the effectiveness of these strategies. The proposed methods have certain significances for reducing the cost and complexity for controller implementation.     

一类非线性系统的自适应反步控制

研究一类带有未知常数参量的非线性系统的镇定及自适应控制器设计问题,提出了一类非线性系统参数估计器设计及自适应反步控制器设计的新方法.构造出Lyapunov函数, 并给出闭环系统全局渐近稳定的新的充分条件.例子表明了所获方法的有效性.     

On large scale nonlinear Network optimization

Partial separability and partitioned quasi-Newton updating have been recently introduced and experimented with success in large scale nonlinear optimization, large nonlinear least squares calculations and in large systems of nonlinear equations. It is the purpose of this paper to apply this idea to large dimensional nonlinear network optimization problems. The method proposed thus uses these techniques for handling the cost function, while more classical tools as variable partitioning and specialized data structures are used in handling the network constraints. The performance of a code implementing this method, as well as more classical techniques, is analyzed on several numerical examples.     

A new time-discretization for delay multiple-input nonlinear systems using the Taylor method and first order hold

A new discretization method is proposed for multi-input-driven nonlinear continuous systems with time-delays, based on a combination of the Taylor series expansion and the first-order hold (FOH) assumption. The mathematical structure of the new discretization scheme is explored. On the basis of this structure, the sampled-data representation of the time-delayed multi-input nonlinear system is derived. First the new approach is applied to nonlinear systems with two inputs, and then the delayed multi-input general equation is derived. The resulting time discretization method provides a finite-dimensional representation for multi-input nonlinear systems with time-delays, thereby enabling the application of existing controller design techniques to such systems. The performance of the proposed method is evaluated using a nonlinear system with time-delays (maneuvering an automobile). Various sampling rates, time-delay values and control inputs are considered to evaluate the proposed method. The results demonstrate that the proposed discretization scheme can meet the system requirements even when using a large sampling period with precision limitations. The discretization results of the FOH method are also compared with those of the zero order hold (ZOH) method. The precision of the FOH method in the discretization procedure combined with the Taylor series expansion is much higher than that of the ZOH method except in the case of constant inputs.     

Input-to-state stability and sliding mode control of the nonlinear singularly perturbed systems via trajectory-based small-gain theorem

This paper presents the trajectory-based input-to-state stability (ISS) and input-to-output stability (IOS) small-gain theorem, and the finite-time ISS (FTISS) and finite-time IOS (FTIOS) of nonlinear singularly perturbed systems. The contribution of this paper is threefold. Firstly, a novel idea is proposed to analyze the stability of the nonlinear singularly perturbed system, which is regarded as an interconnected system by using two-time-scale decomposition. Secondly, the trajectory-based approach is applied to establish ISS and IOS small-gain theorem for singularly perturbed systems and the FTISS and FTIOS properties are proposed. Thirdly, a novel sliding mode controller is developed for a class of nonlinear singularly perturbed systems. Finally, the effectiveness of proposed method is illustrated by using a numerical example, a DC motor simulation and a multi-agent singularly perturbed system.     

Nonlinear sliding surface based second order sliding mode controller for uncertain linear systems

A second order sliding mode (SOSM) controller using nonlinear sliding surface is proposed in this paper. The aim of the proposed controller is to guarantee stability as well as enhance the transient performance of uncertain linear systems with parametric uncertainty. The nonlinear sliding surface consists of a linear term and a nonlinear term. The linear term comprises a gain matrix which has a very low value of damping ratio and thereby facilitates fast response. The nonlinear term is introduced to accommodate a variable damping ratio to reduce overshoot and settling time of the closed loop system as the output reaches nearer the desired reference position. A major gain of the proposed SOSM controller is the elimination of chattering in the control input. The proposed nonlinear sliding surface based SOSM controller achieves fast rise, low overshoot and low settling time. Simulation results demonstrate the effectiveness of the proposed SOSM controller.     

一类非线性上三角系统的实用输出跟踪控制

利用齐次系统控制理论,研究了一类非线性上三角系统的实用输出跟踪控制问题,提出了一种解决上三角系统跟踪问题的齐次控制方法.所研究的系统是高阶的,允许不可测状态具有高阶增长形式.设计的控制器具有不依赖参考信号,可使跟踪误差任意小和对干扰的鲁棒性的优点.最后的仿真例子说明了结论的正确性.     

Constrained MPC design of nonlinear Markov jump system with nonhomogeneous process

In this paper, a differential-inclusion-based MPC scheme is developed for the controller design for a discrete time nonlinear Markov jump system with nonhomogeneous transition probability. By adopting a differential-inclusion-based convex model predictive control mechanism, the nonlinear Markov jump system with nonhomogeneous transition probability is enclosed by a set of linear Markov jump systems. In this way, the controller design for the nonlinear Markov jump system can be solved via solving a set of linear Markov jump systems. Two numerical examples with different weighting parameters R are presented to illustrate the applicability of the results obtained.     

Adaptive feedback control for a class of chaotic systems

In this paper, the problem of control for a class of chaotic systems is considered. The nonlinear functions of chaotic systems are not necessarily to satisfy the Lipsichtz conditions, but bounded by a polynomial with the gains unknown. Employing adaptive method, the corresponding controller which renders the closed-loop system asymptotically stable is constructed. The designed controller is robust with respect to certain class of disturbances in the chaotic systems. Simulations on unified chaotic systems and Arneodo chaotic system are performed and the results verify the validity of the proposed techniques.     

一类死区非线性输入系统的自适应模糊控制

针对一类具有死区非线性输入的非线性系统,基于滑模控制的基本原理,利用II型模糊逻辑系统对未知函数进行在线逼近,提出了一种具有监督器的自适应模糊滑模控制方法。该方法通过监督控制器保证闭环系统所有信号有界,并通过引入最优逼近误差的自适应补偿项来消除建模误差的影响。通过理论分析,证明了跟踪误差收敛到零。     

Modeling and nonlinear control of a flexible-link manipulator

The problem of modeling and controlling the tip position of a one-link flexible manipulator is considered. The proposed model has been used to investigate the effect of the open-loop control torque profile, and the payload. The control strategy is based on the nonlinear State Dependent Riccati Equation (SDRE) design method in the context of application to robotics and manufacturing systems. In this paper, an experimental test-bed was developed to demonstrate the concept of end-point position feedback on a single-link elastic manipulator, and the control strategy for a single-link flexible manipulator. The controller is designed based on the nonlinear SDRE developed by the authors and applied to a flexible manipulator. The experimental results are compared with conventional PD controller strategy. The results reveal that the nonlinear SDRE controller is near optimal and robustly; and its performance is improved comparing to the PD control scheme.     

Finite time control of a class of nonlinear switched systems in spite of unknown parameters and input saturation

This article is devoted to the problem of robust stabilization of uncertain nonlinear switched systems with canonical structure. It is assumed that the constant parameters of the subsystems are unknown and cannot be adopted in the controller design. In addition, the dynamics of the subsystems are perturbed via modeling errors and external disturbances. The effects of unknown actuator saturation are compensated via proper adaptive control signals. The derived controller is based on the terminal sliding mode theory and does not need any prior knowledge about the bounds of the lumped uncertain terms. It is proved that once the system states reach the prescribed sliding manifold in a finite time interval, the whole system becomes insensitive to both the lumped uncertainties and the switching dynamics of the system. The common assumption of having known quadratic Lyapunov functions for the subsystems is relaxed and the derived adaptive approach does not force any limitation on the switching signal of the system. Subsequently, non-conservative conditions are provided to guarantee the global finite time bounded stability of the equilibrium state for the overall uncertain nonlinear switched system under arbitrary switching signals. A numerical computer simulation demonstrates the robust performance of the proposed controller.     

Stabilization of nonlinear networked systems with sensor random packet dropout and time-varying delay

In this paper, a nonlinear stochastic system model is proposed to describe the networked control systems (NCSs) with both random packet dropout and network-induced time-varying delay. Based on this more general nonlinear NCSs model, by choosing appropriate Lyapunov functional and employing new discrete Jensen type inequality, a sufficient condition is derived to establish the quantitative relation of maximum allowable delay upper bound, packet dropout rate and the nonlinear level to the exponential stability of the nonlinear NCSs. Design procedures for output feedback controller are also presented in terms of utilizing cone complementarities linearization algorithm or solving corresponding linear matrix inequalities (LMIs). Illustrative examples are provided to demonstrate the effectiveness of the proposed method.     

A robust neurocontroller incorporating a priori knowledge of plant dynamics

This paper presents a nonlinear controller design method that integrates linear optimal control techniques and nonlinear neural networks. The multilayered neural networks (MNN's) are incorporated into a model-based linear optimal controller (LOR) to add nonlinear effects on the LOR. The proposed controller can tolerate a wider range of uncertainties than the LOR alone, because the MNN can compensate nonlinear system uncertainties that are not considered in the LOR design. The control performance is improved by using a priori knowledge of the plant dynamics as the system equation and the corresponding LOR. Using the similar technique, a nonlinear servo controller is designed by combining the MNN-based controller and the linear optimal servo controller. Computer simulations are performed to show the applicability and the limitation of the new nonlinear controllers.