Solving obstacle problems with guaranteed accuracy

In this paper, we consider a numerical technique which enables us to verify the existence of solutions for some simple obstacle problems. Using the finite element approximation and constructive error estimates, we construct, on a computer, a set of solutions which satisfies the hypothesis of the Schauder fixed-point theorem for a compact map on a certain Sobolev space. We describe the numerical verification algorithm for solving a two-dimensional obstacle problems and report some numerical results.     

Method of non-uniform coverages to solve the multicriteria optimization problems with guaranteed accuracy

Application of the non-uniform coverage method to the multicriteria optimization problems was considered, and the concept of the ?-Pareto set was formulated and studied. An algorithm to construct a ?-Pareto set with a guaranteed accuracy ? was described. Efficient implementation of this approach was described, and the results of experiments were presented.     

A guaranteed prediction model for complex linear systems

The method of approximation in the norm is used to design a linear predictor for the output of a complex linear system at a given future time. It is shown that the computed output is an optimal linear transformation of some variables denoted the "most important" states of the system. The proposed method allows to obtain the system output prediction as a signal belonging to a guaranteed uncertainty tube.     

网络化非线性系统的非脆弱保性能控制

对具有对数量化和马尔可夫链数据包丢失的网络化Lipschitz非线性系统的非脆弱保性能控制问题进行研究。将网络化控制系统描述为马尔可夫跳变系统,根据Lyapunov稳定性理论,以线性矩阵不等式形式给出网络化Lipschitz非线性系统具有加性和乘性摄动的非脆弱保性能控制器存在的充分条件,控制器增益矩阵可通过解一组线性矩阵不等式求出。数值算例验证了该方法的有效性。     

随机分布系统可靠保性能控制算法的研究

针对随机分布系统采用数值优化算法设计的控制器不稳定的问题, 研究了可靠保性能控制算法。该控制算法可实现将随机分布系统的值优化算法转换为线性矩阵不等式的可行解问题, 并通过线性矩阵不等式的方法给出可靠保性能控制算法的充分条件, 采用凸优化技术进行优化。通过实例仿真, 证明该算法能够实现输出概率密度函数渐进追踪目标概率密度函数, 并使随机分布系统的鲁棒性和稳定性有较好的改善。     

基于T-S模型的非线性网络控制系统的量化保成本控制

研究一类非线性网络控制系统的量化保成本控制问题．首先在考虑量化因素的影响下,基于Ｔ-Ｓ模糊模型方法建立包含时延、丢包和量化信息的新的非线性网络控制系统模型;其次运用Ｌｙａｐｕｎｏｖ稳定性理论和并行分布式补偿（ＰＤＣ）方法给出系统稳定性条件,运用锥补方法和线性矩阵不等式（ＬＭＩ）技术求解量化保成本控制器．仿真结果和横向比较结果验证了该方法的有效性．     

Two guaranteed equilibrated error estimators for Harmonic formulations in eddy current problems

In this paper a guaranteed equilibrated error estimator is developed for the 3D harmonic magnetodynamic problem of Maxwell’s system. This system is recasted in the classical $\mathbf{A}?\phi$ potential formulation and solved by the Finite Element method. The error estimator is built starting from the $\mathbf{A}?\phi$ numerical solution by a local flux reconstruction technique. Its equivalence with the error in the energy norm is established. A comparison of this estimator with an equilibrated error estimator already developed through a complementary problem points out the advantages and drawbacks of these two estimators. In particular, an analytical benchmark test illustrates the obtained theoretical results and a physical benchmark test shows the efficiency of these two estimators.     

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.     

Non-fragile guaranteed cost control for discrete-time uncertain linear systems

This paper studies the problem of non-fragile guaranteed cost control (GCC) state-feedback design for discrete-time uncertain linear systems. The systems are assumed to have norm-bounded system uncertainties in both the state and the input matrices. The state-feedback gains are assumed to have norm-bounded controller uncertainties which can be either additive or multiplicative. The non-fragile GCC state-feedback designs, which are related to solutions of some matrix inequalities, guarantee the cost of the system to be within a certain bound for all these admissible uncertainties. Our proposed design approach of separating the controller uncertainty from the system uncertainty gives a less conservative solution. A numerical example is given to illustrate the design methods and the design benefits.     

On Pareto set in control and filtering problems under stochastic and deterministic disturbances

We consider two-criteria control or filtering problems for linear systems, where one criterion is the level of suppression for Gaussian white noise with unknown covariance, and another is the level of suppression for a deterministic signal of bounded power. We define a new criterion, the level of suppression for stochastic and deterministic disturbances that act jointly in the general case on different inputs. This criterion is characterized in terms of solutions of Riccati equations or linear matrix inequalities. We establish that for the choice of optimal controller or filter with respect to this criterion relative losses with respect to each of the original criteria compared to Pareto optimal solutions do not exceed the value \(1 - {{\sqrt 2 } \mathord{\left/ {\vphantom {{\sqrt 2 } 2}} \right. \kern-\nulldelimiterspace} 2}\). We extend these results to dual control and filtering problems for systems with one input and two outputs, generalize them to the case of N criteria with loss estimate \(1 - {{\sqrt N } \mathord{\left/{\vphantom {{\sqrt N } N}} \right.\kern-\nulldelimiterspace} N}\), and also apply them for systems with external and initial disturbances. We show a numerical example.     

不确定离散时间系统积分滑模保性能控制

针对不确定离散时间系统,研究其积分滑模（ＩＳＭ）保性能控制的设计问题．将最优保性能积分滑模面设计问题,转化为一个具有线性矩阵不等式（ＬＭＩ）约束的目标函数凸优化问题,给出了最优保性能积分滑模面存在的充分条件,并结合干扰估计器设计相应的保性能控制器．与传统滑模控制相比较,积分滑模保性能控制系统具有全阶滑动模态,系统的鲁棒性得到加强,消除了控制抖振和稳态抖振．仿真结果验证了该方法的有效性．     

Worst‐case control policies for (terminal) linear–quadratic control problems under disturbances

We consider linear control systems under uncertainties. For such systems we solve the problem of constructing worst‐case feedback control policies that are allowed to be corrected at m fixed intermediate time moments. We propose two types of the approximative control policies. All of them guarantee that for all admissible uncertainties the terminal system state lies in a prescribed neighborhood of a given state x_* at a given final moment, and the value of the cost function does not exceed a given estimate. It is shown that computation of the estimate for each policy is equivalent to solving a corresponding convex mathematical programming (MP) problem with m decision variables. Based on the solution of the MP problem, we derive simple explicit rules (which can be easily implemented on‐line) for constructing the corresponding control policy in the original control problem. Copyright © 2009 John Wiley & Sons, Ltd.     

Time-optimal feedback control for small disturbances

This paper introduces a new technique for the analysis of time-optimal systems having multidimensional inputs. The method provides a cellular decomposition of the controllable set for small response times for a new generic class of systems called "minimally controllable systems." The decomposition permits a complete study of the time-optimal flow near the origin and forms the basis for the synthesis of closed-loop optimal control. The method, while generally applicable, is restricted here to the simplest, nontrivial case of third-order systems with two-dimensional controls.     

Fuzzy guaranteed cost control for nonlinear systems with time-varying delay

This paper focuses on the problem of guaranteed cost control for Takagi-Sugeno (T-S) fuzzy systems with time-varying delayed state. A linear quadratic cost function is considered as a performance index of the closed-loop fuzzy system. Then, the guaranteed cost control of the closed-loop fuzzy system is discussed, and the sufficient conditions are provided for the construction of a guaranteed cost controller via state feedback and observer-based output feedback. When these conditions, which are given in terms of the feasibility of linear matrix inequalities (LMIs), are satisfied, the designed state feedback controller and observer-based controller gain matrices can be obtained via a convex optimization problem. Two illustrative examples are provided to demonstrate the effectiveness of the approaches proposed in this paper.     

Resilient guaranteed cost control for uncertain discrete linear jump systems

Robust stochastic stabilization and guaranteed cost control for a class of uncertain discrete-time linear system with Markovian jumping parameters are discussed. Two classes of controller gain perturbations, additive and multiplicative, are considered. The necessary and sufficient conditions for the above problems are derived, which are in terms of positive-definite solutions of a set of coupled linear matrix inequalities (LMIs). Furthermore, resilient guaranteed cost controllers are designed. Finally, numerical examples are presented to illustrate the solvability and effectiveness of the results.     

Nonfragile guaranteed cost control for Delta operator-formulated uncertain time-delay systems

With consideration that the controller parameters may vary from the designed value when the controller is realized, based on Lyapunov stability theory, a design method of nonfragile guaranteed cost control for a class of Delta operator-formulated uncertain time-delay systems is studied. A sufficient condition for the existence of the nonfragile guaranteed cost controller is given. A numeric example is then given to illustrate the effectiveness and the feasibility of the designed method. The results show that even if the parameters of the designed controller are of variations, the closed-loop system is still asymptotically stable and the super value of the cost function can also be obtained, while the closed-loop system will be unstable if the variations of the controller parameters are not considered when the controller is designed. The nonfragile guaranteed cost controller derived from the traditional shift operator method may cause the closed-loop system to be unstable, while the nonfragile guaranteed cost controller based on Delta operator method can avoid the unstable problem of the closed-loop system.     

More relaxed conditions for model predictive control with guaranteed stability

1Introduction In recent years the receding horizon control(RHC)ormodel predictive control(MPC)has received muchattention[1].At each sampling time,model predictivecontrol(MPC)yields an optimal control sequence byonline solving a finite horizon open_loop optimizationproblem.Onlythefirst control actionis appliedtothe plantandthe process is repeated at the next samplingtime.The closed_loop stability of model predictive control hasbeenthe focus of research for a long time.In the90’s,through in…     

More relaxed conditions for model predictive control with guaranteed stability

For the model predictive c ontroller,terminal state satisfying a certain inequality can guarantee the stability but it is somewhat conservative.In this paper,we give a more r elaxed stability condition by considering the effect of the initial state.Based on that we propose an algorithm to guarantee that the closed loop s ystem is asymptotically stable.Finally,the conclusions are verifie d by a simulation.     

不确定非线性时滞系统的非脆弱保成本控制

研究了一类具有状态时滞的不确定非线性系统的非脆弱保成本控制问题。通过利用Lyapunov稳定性理论和线性矩阵不等式方法,设计非脆弱保成本控制律,使得闭环系统渐近稳定,并且系统的性能指标不超过某个确定的上界。通过求解一个具有线性矩阵不等式约束的凸优化问题来设计最优非脆弱保成本控制器,以使得闭环不确定系统的性能指标最小化。仿真结果验证了该控制算法的有效性。