Output tracking of constrained nonlinear processes with offset-free input-to-state stable fuzzy predictive control

This paper develops an efficient offset-free output feedback predictive control approach to nonlinear processes based on their approximate fuzzy models as well as an integrating disturbance model. The estimated disturbance signals account for all the plant-model mismatch and unmodeled plant disturbances. An augmented piecewise observer, constructed by solving some linear matrix inequalities, is used to estimate the system states and the lumped disturbances. Based on the reference from an online constrained target generator, the fuzzy model predictive control law can be easily obtained by solving a convex semi-definite programming optimization problem subject to several linear matrix inequalities. The resulting closed-loop system is guaranteed to be input-to-state stable even in the presence of observer estimation error. The zero offset output tracking property of the proposed control approach is proved, and subsequently demonstrated by the simulation results on a strongly nonlinear benchmark plant.     

An improved approach for constrained robust model predictive control

In this paper, we present a new technique to address constrained robust model predictive control. The main advantage of this new approach with respect to other well-known techniques is the reduced conservativeness. Specifically, the technique described in this paper can be applied to polytopic uncertain systems and is based on the use of several Lyapunov functions each one corresponding to a different vertex of the uncertainty's polytope.     

Dynamic observer-based controllers for linear uncertain systems

This paper addresses robust controller design for uncertain linear systems via a dynamic observer-based controller. A dynamic observer is an alternative structure for a classical observer which can be regarded as a general form of a usual observer and has additional degrees of freedom in the observer structure. Using this new observer structure, a new observer-based controller for linear systems is proposed. Some strict linear matrix inequalities (LMIs) have been given to find the dynamic observer parameters and controller gain. It is shown that dynamic observer can be used effectively for tackling the drawbacks of the classical observer-based robust controller design methods. As an advantage, LMIs are derived even in the presence of uncertainties in system, input and output matrices simultaneously, whereas by using the traditional observer, bilinear matrix inequalities (BMIs) are given in the presence of such uncertainties. Moreover, the proposed LMIs do not imply the equality constraint. Simulation results are used to illustrate the effectiveness of the proposed design technique.     

Output feedback model predictive control for LPV systems based on quasi-min–max algorithm

This paper proposes a robust output feedback model predictive control (MPC) scheme for linear parameter varying (LPV) systems based on a quasi-min–max algorithm. This approach involves an off-line design of a robust state observer for LPV systems using linear matrix inequality (LMI) and an on-line robust output feedback MPC algorithm using the estimated state. The proposed MPC method for LPV systems is applicable for a variety of systems with constraints and guarantees the robust stability of the output feedback systems. A numerical example for an LPV system subject to input constraints is given to demonstrate its effectiveness.     

Feasibility conditions for circle criterion designs

We derive necessary and sufficient conditions for the existence of a control law that renders the closed-loop system strictly positive real with respect to a disturbance input. The result is used to establish feasibility of recent nonlinear controller and observer designs based on the circle criterion.     

A complete algebraic solvability test for the nonstrict Lyapunov inequality

For arbitrary equally sized square complex matrices A and Q (Q Hermitian), the paper provides a complete algebraic test for verifying the existence of a Hermitian solution X of the nonstrict Lyapunov inequality A^*X + XA + Q 0. If existing, we exhibit how to construct a solution. Our approach involves the validation problem for the linear matrix inequality Σ_j=1^k (A_j^*X_jB_j + B_j^*X_j^*A_j) + Q> 0 in X_j, for which we provide an algebraic solvability test and a construct solutions if the kernels of A_j or, dually, those of B_j form an isotonic sequence.     

同时含有状态和输入时滞系统的滑模控制

研究同时舍状态和输入时滞的系统交结构控制问题，基于LMI，给出了存在滑动模态的时滞相关的充分条件，利用LMI的解，得到了两种不同的滑动模态和控制器的设计方法，所提出的方法简单量行，具有较小的保守性，可进一步推广到多时滞和不确定时滞系统。     

噪声方差不确定约束系统的滚动时域估计

针对噪声方差不确定的约束系统,讨论了一种鲁棒滚动时域估计(MHE)方法.首先,根据噪声方差不确定模型,找到满足所有不确定性的最小方差上界,在线性矩阵不等式(LMI)框架下求解优化问题,得到近似到达代价的表达形式;然后再融合预测控制的滚动优化原理,把系统的硬约束直接表述在优化问题中,在线优化性能指标,估计出当前时刻系统的状态.仿真时与鲁棒卡尔曼滤波方法进行比较,结果表明了该方法的有效性.     

Nonlinear dynamic matrix control based on multiple operating models

This paper presents a method of nonlinear dynamic matrix control based on multiple operating models. Its closed-loop stability and asymptotically unbiased tracking properties are proved. The application software (SMART-NLS) is developed using this method, and the simulation results of two nonlinear benchmark processes verify the feasibility and effectiveness of the proposed method.     

Using stable input-output inversion for minimum-time feedforward constrained regulation of scalar systems

The paper approaches the feedforward minimum-time smooth control of non-minimum-phase linear scalar systems for set-point regulation. The aim is to synthesize a bounded input subject to non-saturating constraints on the input and its derivatives till a prespecified arbitrary order. The provided solution relies on a stable input-output dynamic inversion technique and an ad hoc parameterized family of output transition functions. The synthesized minimum-time input that exhibits pre- and post-actuation is determined by means of easily-implementable closed-form expressions. Examples are given to illustrate the methodology.     

Delay-range-dependent robust 2D iterative learning control for batch processes with state delay and uncertainties

This paper proposes the design of the integrated output feedback and iterative learning control (ILC) for batch processes with uncertain perturbations and interval time-varying delays, where the main idea is to transform the design into a robust delay-range-dependent H_∞ control of a 2D system described by a state-space model with varying delays. A sufficient criterion for delay-dependent H_∞ noise attenuation is derived through linear matrix inequality (LMI) by introducing a comprehensive 2D difference Lyapunov–Krasovskii functional candidate and adding a differential inequality to the difference in the Lyapunov function for the 2D system. Based on the criterion obtained, the delay-range-dependent output feedback controller combined with ILC is then developed. The developed system ensures that the closed-loop system for all admissible uncertainties is asymptotically stable and has a prescribed H_∞ performance level in terms of the LMI constraint. The controller is obtained by solving an LMI optimization problem with simple calculations and less constraint conditions. Moreover, the conditions can also be directly extended from delay-range-dependent to general delay-dependent stability. Applications in injection velocity control demonstrate the effectiveness and feasibility of the proposed method.     

LMI-based robust iterative learning controller design for discrete linear uncertain systems

This paper addresses the design problem of robust iterative learning controllers for a class of linear discrete-time systems with norm-bounded parameter uncertainties. An iterative learning algorithm with current cycle feedback is proposed to achieve both robust convergence and robust stability. The synthesis problem of the proposed iterative learmng control （ILC） system is reformulated as a γ-suboptimal H-infinity control problem via the linear fractional transformation （LFT）. A sufficient condition for the convergence of the ILC algorithm is presented in terms of linear matrix inequalities （LMIs）. Furthermore, the linear wansfer operators of the ILC algorithm with high convergence speed are obtained by using existing convex optimization techniques. The simulation results demonstrate the effectiveness of the proposed method.     

Robust MPC for the constrained system with polytopic uncertainty

An improved method for synthesising the constrained robust model predictive controller is proposed in this study. It constructs a continuum of terminal constraint sets off-line, and achieves robust stability with a variable control horizon on-line from the very beginning and a time-varying terminal constraint set, by solving the min–max optimisation problem, which can be formulated as a linear matrix inequality problem. This algorithm not only dramatically reduces the on-line computation burden, but also guarantees the control performance by reserving at least one free control move in the whole process. Simulation results for the three-tank system with uncertain dynamic behaviour on flux coefficients are given.     

A new approach to static output feedback stabilization of linear dynamic systems

The topic of this study is output feedback control of linear control system with output. Use of condensed forms of the linear system under static output feedback (SOF) control is made to derive sufficient conditions for stabilization. A minimal-order control-free observer is presented.     

挠性系统的鲁棒控制设计

提出一种新的鲁棒设计思想：将挠性模态部分的Nyquist图线安排到右半平面。由于综合运用了频域分析、极点配置、正实性引理、线性矩阵不等式等概念和算法，使得这种鲁棒控制设计得以实现，且简单直观。通过两个算例说明了该设计方法的有效性。     

An observer-based approach to controlling time-delay chaotic systems via Takagi-Sugeno fuzzy model

This study presents a fuzzy model-based control criterion for time-delay chaotic systems with uncertainty. The Takagi-Sugeno (T-S) fuzzy model is adopted for representing a chaotic system possessing a time delay. A unified approach for designing a fuzzy observer, which integrates parallel distributed compensation with an adaptive updating method, is first discussed. An observer-based fuzzy control scheme is then developed to deal with stabilization and tracking problems. Based on Lyapunov stability analysis, sufficient conditions that ensure robust control performance of time-delay chaotic systems are derived. These conditions are represented in terms of linear matrix inequalities and adaptive updating laws. Finally, the proposed approach is validated through numerical synchronization, stabilization, and model tracking control simulations.     

多面体不确定系统时滞依赖鲁棒预测控制

将线性状态变换引入连续时间多面体不确定时滞系统中,利用线性矩阵不等式(LMI)方法,设计时滞相关型鲁棒预测控制器;通过适当选择Lyapunov函数,推导出闭环系统渐近稳定的充分条件,并且该条件是时滞相关的.仿真算例验证了该方法的有效性.     

Reliable guaranteed cost sampling control for nonlinear time-delay systems

The problem of reliable guaranteed cost sampling control is investigated for nonlinear time-delay systems in this paper. Sufficient conditions for the existence of state feedback controller are derived in terms of linear matrix inequities (LMIs), which guarantee asymptotic stability with the provided performance index for the normal and possible actuator faults cases. The related optimization problem is also offered to minimize the guaranteed cost performance bound. Illustrative examples are given to show the validity of the present control scheme.     

A virtual actuator and sensor approach for fault tolerant control of LPV systems

In this paper, a fault tolerant control (FTC) strategy using virtual actuators and sensors for linear parameter varying (LPV) systems is proposed. The main idea of this FTC method, initially developed for LTI systems, is to reconfigure the control loop such that the nominal controller could still be used without need of retuning it. The plant with the faulty actuator/sensor is modified adding the virtual actuator/sensor block that masks the actuator/sensor fault. The suggested technique is an active FTC strategy that reconfigures the virtual actuator/sensor on-line taking into account faults and operating point changes. The stability of the reconfigured control loop is guaranteed if the faulty plant is stabilizable/detectable. The LPV virtual actuator/sensor is designed using polytopic LPV techniques and linear matrix inequalities (LMIs). A two-tank system simulator is used to assess the performance of the proposed method. In particular, it is shown that the application of the proposed technique results in an improvement, in terms of performance, with respect to the LTI counterpart.