An LMI Method to Robust Iterative Learning Fault-tolerant Guaranteed Cost Control for Batch Processes

Based on an equivalent two-dimensional Fornasini-Marchsini model for a batch process in industry, a closed-loop robust iterative learning fault-tolerant guaranteed cost control scheme is proposed for batch processes with actuator failures. This paper introduces relevant concepts of the fault-tolerant guaranteed cost control and formulates the robust iterative learning reliable guaranteed cost controller (ILRGCC). A significant advantage is that the proposed ILRGCC design method can be used for on-line optimization against batch-to-batch process uncertainties to realize robust tracking of set-point trajectory in time and batch-to-batch sequences. For the convenience of implementation, only measured output errors of current and previous cycles are used to design a synthetic controller for iterative learning control, consisting of dynamic output feedback plus feed-forward control. The proposed controller can not only guarantee the closed-loop convergency along time and cycle sequences but also satisfy the H∞performance level and a cost function with upper bounds for all admissible uncertainties and any actuator failures. Sufficient conditions for the controller solution are derived in terms of linear matrix inequalities (LMIs), and design procedures, which formulate a convex optimization problem with LMI constraints, are presented. An example of injection molding is given to illustrate the effectiveness and advantages of the ILRGCC design approach.

Exponential passive filtering for a class of nonlinear jump systems

The exponential passive filtering problem for a class of nonlinear Markov jump systems with uncertainties and time-delays is studied. The uncertain parameters are assumed unknown but norm bounded, and the nonlinearities satisfy the quadratic condition. Based on the passive filtering theory, the sufficient condition for the existence of the mode-dependent passive filter is given by analyzing the reconstructed observer system. By using the appropriate Lyapnnov-Krasovskii function and applying linear matrix inequalities, the design scheme of the passive filter is derived and described as an optimization one. The presented exponential passive filter makes the error dynamic systems exponentially stochastically stable for all the admissible uncertainties, time-delays and nonlinearities, has the better abilities of state tracking and satisfies the given passive norm index. Simulation results demonstrate the validity of the proposed approach.

Fault-tolerant control of linear uncertain systems using H∞ robust predictive control

The robust fault-tolerant control problem of linear uncertain systems is studied. It is shown that a solution for this problem can be obtained from a H∞ robust predictive controller （RMPC） by the method of linear matrix inequality （LMI）. This approach has the advantages of both H∞ control and MPC： the robustness and ability to handle constraints explicitly. The robust closed-loop stability of the linear uncertain system with input and output constraints is proven under an actuator and sensor faults condition. Finally, satisfactory results of simulation experiments verify the validity of this algorithm.

Observer-based passive control for uncertain linear systems with delay in state and control input

This paper deals with the robust passivity synthesis problem for a class of uncertain linear systems with timevarying delay in state and control input. The parameter uncertainties are norm-bounded and allowed to appear in all matrices of the model. The problem aims at designing an observer-based dynamic output-feedback controller that robustly stabilizes the uncertain systems and achieves the strict passivity of closed-loop systems for all admissible uncertainties. By converting the problem at hand into a class of strictly passive control problem for a parameterized system, the explicit solution is established and expressed in terms of a linear matrix inequality. A numerical example is provided to demonstrate the validity of the proposed approach.

Research on fault-tolerant control of networked control systems based on information scheduling

A kind of networked control system is studied; the networked control system with noise disturbance is modeled based on information scheduling and control co-design. Augmented state matrix analysis method is introduced, and robust fault-tolerant control problem of networked control systems with noise disturbance under actuator failures is studied. The parametric expression of the controller under actuator failures is given. Furthermore, the result is analyzed by simulation tests, which not only satisfies the networked control systems stability, but also decreases the data information number in network channel and makes full use of the network resources.

Stability Criterion with Less LMI Variables for Linear Discrete-time Systems with Additive Time-delays

In this correspondence paper, an equivalent stability criterion with minimal number of linear matrix inequality （LMI） variables is presented for a delay-dependent stability criterion reported recently in the International Journal of Automation and Computing for a class of linear discrete-time systems with additive time delays. The reported stability criterion for the additive timedelay systems has more number of matrix variables in the LMI and, hence, demand additional computational burden. The proposed equivalent stability criterion, unlike the reported one, does not involve free-weighing matrices and encompass only the matrix variables that are associated in the Lyapunov-Krasovskii functional, making the criterion mathematically less complex and computationally more effective.

A delay-dependent passivity criterion of linear neutral delay systems

The problem of delay-dependent stability and passivity for linear neutral systems is discussed. By constructing a novel type Lyapunov-krasovskii functional, a new delay-dependent passivity criterion is presented in terms of linear matrix inequalities （LMIs）. Model transformation, bounding for cross terms and selecting free weighting matrices [12-14] are not required in the arguments. Numerical examples show that the proposed criteria are available and less conservative than existing results .

基于LMI的分段线性系统共存吸引子转迁控制研究

以一类两自由度含间隙分段线性系统为研究对象,利用线性矩阵不等式(linear matrix inequality,LMI)和线性反馈方法对系统共存的吸引子进行在预期目标轨道引导下的转迁控制。在状态平面上利用胞映射方法对系统随参数变化时的共存吸引子进行识别,并基于Poincaré映射和Lyapunov指数研究了系统共存吸引子的稳定性及转迁机理。基于LMI和Lyapunov理论,并利用系统的向量场信息和S-procedure,将系统施加线性反馈控制器后的稳定性和反馈增益矩阵的求解问题转化为LMI描述。利用数值方法验证了所应用的线性反馈控制器及其增益矩阵选取方法的可行性及正确性。

Observer-based passive control for descriptor systems with time-delay

This article is concerned with the problem of observer-based passive control for descriptor systems with time delay. Sufficient conditions are first presented for the closed loop systems to be admissible and passive with dissipation η in the case of that the time delay is known, and two kinds of methods are given to design the expected observer. Then, the case of that the time delay is unknown or uncertain is discussed. The observer-based control gains could be obtained from the solutions of linear matrix inequalities （LMIs）. Simulation examples are given to show the effectiveness of the designed methods.

Robust D-stability LMI conditions of matrix polytopes via affine parameter-dependent Lyapunov functions

The problem of the robust D-stability analysis for linear systems with parametric uncertainties is addressed. For matrix polytopes, new conditions via the affine parameter-dependent Lyapunov function of uncertain systems are developed with the benefit of the scalar multi-convex function. To be convenient for applications, such conditions are simplified into new linear matrix inequality （LMI） conditions, which can be solved by the powerful LMI toolbox. Numerical examples are provided to indicate that this new approach is less conservative than previous results for Hurwitz stability, Schur stability and D-stability of uncertain systems under certain circumstances.

Robust passive control for discrete-time T-S fuzzy systems with delays

This article deals with the robust stability analysis and passivity of uncertain discrete-time Takagi- Sugeno （T-S） fuzzy systems with time delays. The T-S fuzzy model with parametric uncertainties can approximate nonlinear uncertain systems at any precision. A sufficient condition on the existence of robust passive controller is established based on the Lyapunov stability theory. With the help of linear matrix inequality （LMI） method, robust passive controllers are designed so that the closed-loop system is robust stable and strictly passive. Furthermore, a convex optimization problem with LMI constraints is formulated to design robust passive controllers with the maximum dissipation rate. A numerical example illustrates the validity 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.

PASSIVE CONTROL FOR A CLASS OF UNCERTAIN TIME-DELAY SYSTEMS

This paper focuses on the passive control for a class of linear time delay system with norm bounded time varying parameter uncertainties by using a linear matrix inequality (LMI) approach. A sufficient condition under which the uncertain time delay system is quadratically stable and strictly passive for all admissible uncertainties was derived. It is shown that the solvability of problem of the robust passive controller design is implied by the feasibility of a linear matrix inequality.

基于LMI的不确定随机时滞系统输出反馈保性能控制

针对一类范数有界的随机时滞系统,研究在一定性能指标下的保性能控制问题。本文为获得能够实现系统保性能控制的最优输出反馈控制器,采用Lyapunov稳定性理论与LMI技术相结合的方法,将保性能控制问题转化为LMIs约束下的可行解问题。提出的控制器设计方案能够实现系统是依概率全局渐近稳定的,同时满足对系统性能指标的要求。此外,通过数值算例说明所提出控制方案的可行性。

Event-Triggered Finite-Time H∞ Filtering for Discrete-Time Nonlinear Stochastic Systems

This paper addresses the problem of event-triggered finite-time H∞ filter design for a class of discrete-time nonlinear stochastic systems with exogenous disturbances. The stochastic Lyapunov-Krasoviskii functional method is adopted to design a filter such that the filtering error system is stochastic finite-time stable (SFTS) and preserves a prescribed performance level according to the pre-defined event-triggered criteria. Based on stochastic differential equations theory, some sufficient conditions for the existence of H∞ filter are obtained for the suggested system by employing linear matrix inequality technique. Finally, the desired H∞ filter gain matrices can be expressed in an explicit form.

具有H_(∞)性能的输入受限三级倒立摆控制器设计

【目的】针对直线三级倒立摆控制输入受限下的稳摆控制问题,设计了具有H_(∞)性能的输入受限三级倒立摆控制器。【方法】利用线性矩阵不等式(LMI)方法,将控制输入约束问题转化为利用线性矩阵不等式求解优化值的优化问题,经Lyapunov稳定性推导出符合条件的LMI,利用MATLAB中的LMI工具箱求解得到有效的K。进一步在控制输入受限下引入H_(∞)性能指标,使所设计的控制输入受限下的算法具有H_(∞)性能。【结果】仿真结果表明,该控制器对于控制输入受限下的复杂高阶次不稳定系统具有很好的控制效果。【结论】控制输入信号在给定的受限范围内实现了三级倒立摆的稳摆要求,且引入H_(∞)性能指标后控制输入和摆杆波动更小。

基于LMI双故障动态输出反馈完整性控制

针对线性系统,基于线性矩阵不等式(LMI)给出了具有完整性的动态输出反馈控制器的设计方案,所得到的结论,不仅给出分别考虑执行器和传感器两类部件发生故障的完整性设计方案,而且给出了考虑执行器或传感器任何一类部件发生故障的完整性设计方案．本文使用了比离散故障模型更具有实际意义的连续故障模型．一个数值例子说明了所提方法的有效性．

低轨多星编队的相对运动差分气动控制

针对低轨纳卫星轨道机动能力不足的问题,本文研究了主动利用星间差分气动力的控制方法,创新性地提出了基于迎风姿态调整的多星编队拓展方案,并通过局部区域线性化方法实现系统的线性控制.本文研究了卫星姿态角与气动力的映射关系,建立了差分阻力和升力耦合控制的星间相对运动线性欠驱动模型,分析了此系统可控性和干扰形式,采用线性矩阵不等式(LMI)方法设计了考虑输入受限的反馈控制律.最后,针对包含两种队形的四星编队进行仿真,结果表明,卫星相对运动的稳定控制精度达到±0.4m,验证了所提出多星编队气动控制方案的可行性以及控制算法的有效性.