非线性大系统的跟踪具有不同幅值轨线的分散型迭代学习控制器

在大型工业过程递阶稳态优化中, 可行的方法是利用系统的实际信息以修正基于模型的最优解. 在这种情形下, 得出一幅值不等的阶跃型控制值序列, 而且该控制值序列依次激励实际系统. 本文将一组迭代学习控制器分散地嵌入到一类非线性工业过程的递阶稳态优化进程中, 每一子系统的迭代学习控制器将产生一强化的控制信号序列以替代相应的具有不同幅值的阶跃型控制值序列, 目的是不断改进系统的暂态品质. 通过卷积的 Hausdorff-Young 不等式, 本文分析了学习控制律在 Lebesgue-P 范数意义下的收敛性, 讨论了系统的非线性性和关联性对控制律收敛性的影响. 最后, 数字仿真验证了所研究的学习控制机理的正确性和有效性.     

Iterative learning controllers for discrete-time large-scale systems to track trajectories with distinct magnitudes

In the procedure of steady-state hierarchical optimization for large-scale industrial processes, it is often necessary that the control system responds to a sequence of step function-type control decisions with distinct magnitudes. In this paper a set of iterative learning controllers are de-centrally embedded into the procedure of the steady-state optimization. This generates upgraded sequential control signals and thus improves the transient performance of the discrete-time large-scale systems. The convergence of the updating law is derived while the intervention from the distinction of the scales is analysed. Further, an optimal iterative learning control scheme is also deduced by means of a functional derivation. The effectiveness of the proposed scheme and the optimal rule is verified by simulation.     

Robust distributed model predictive control of linear systems with structured time-varying uncertainties

In this work, synthesis of robust distributed model predictive control (MPC) is presented for a class of linear systems subject to structured time-varying uncertainties. By decomposing a global system into smaller dimensional subsystems, a set of distributed MPC controllers, instead of a centralised controller, are designed. To ensure the robust stability of the closed-loop system with respect to model uncertainties, distributed state feedback laws are obtained by solving a min–max optimisation problem. The design of robust distributed MPC is then transformed into solving a minimisation optimisation problem with linear matrix inequality constraints. An iterative online algorithm with adjustable maximum iteration is proposed to coordinate the distributed controllers to achieve a global performance. The simulation results show the effectiveness of the proposed robust distributed MPC algorithm.     

离散非线性系统开闭环P型迭代学习控制律及其收敛性

本文在讨论了一般开环与闭环迭代学习控制的不足后，针对一类离散非线性系统，提出了新的开闭环ＰＧ型迭代学习控制律，给出了它的收敛性证明，仿真结果表明：开闭环Ｐ型迭代律优于单纯的开环或产才环Ｐ型迭代 律。     

Parametric output feedback control with response insensitivity

A recent parameterization of the class of linear output-feedback controllers that assign a set of desired self-conjugate eigenvalues to the closed-loop system is used to formulate and solve a fundamental response insensitivity problem. It is established to what extent output-feedback control can be used to render the closed-loop system response insensitive to possibly many not necessarily small parameter variations in the open-loop state space model. A non-conservative sequential design procedure is developed for making as many of the closed-loop system eigenmodes as possible totally insensitive while retaining arbitrary assignment of the maximum number of closed-loop eigenvalues. The main result is a class of desensitizing fixed-gain output-feedback controllers explicitly specified by a set of free parameters which may be chosen to satisfy additional design requirements. Conditions are given for total modal decoupling insensitivity to possibly many not necessarily small parameter variations in the open-loop state model. The mechanism of modal decoupling insensitivity for a given mode is interpreted in terms of the insensitivity of the corresponding left eigenmode. A parametric approach to output feedback design for modal decoupling insensitivity is discussed.     

Robust design of feedback feed-forward iterative learning control based on 2D system theory for linear uncertain systems

For a class of linear discrete-time uncertain systems, a feedback feed-forward iterative learning control (ILC) scheme is proposed, which is comprised of an iterative learning controller and two current iteration feedback controllers. The iterative learning controller is used to improve the performance along the iteration direction and the feedback controllers are used to improve the performance along the time direction. First of all, the uncertain feedback feed-forward ILC system is presented by an uncertain two-dimensional Roesser model system. Then, two robust control schemes are proposed. One can ensure that the feedback feed-forward ILC system is bounded-input bounded-output stable along time direction, and the other can ensure that the feedback feed-forward ILC system is asymptotically stable along time direction. Both schemes can guarantee the system is robust monotonically convergent along the iteration direction. Third, the robust convergent sufficient conditions are given, which contains a linear matrix inequality (LMI). Moreover, the LMI can be used to determine the gain matrix of the feedback feed-forward iterative learning controller. Finally, the simulation results are presented to demonstrate the effectiveness of the proposed schemes.     

Barrier function based model predictive control

A new formulation of nonlinear model predictive control (MPC) is developed by including a weighted barrier function in the control objective. While the barrier ensures that inequality constraints are strictly satisfied it also provides a smooth transition between points in the interior and those on the boundary of the constraint set. In addition, the resulting optimisation problem, to be solved at each control step, is effectively unconstrained and thus amenable to elegant optimisation techniques. The barrier must satisfy certain conditions in order that the state converges to the origin and we show how to construct such a barrier. Conventional MPC may be seen as a limiting case of the new class as the barrier weighting itself approaches zero. We pay particular attention to the novel approach of fixing the weighting parameter to some positive value—possibly large—and observe that this provides a degree of controller caution near constraint boundaries. We construct an ellipsoidal invariant set by exploiting the geometry of self-concordant functions and show nominal closed-loop stability for this class of controllers under full state feedback.     

Robust control of linear uncertain systems with regional pole and variance constraints

This paper concerns the design problem of state feedback controllers which guarantee the closed-loop poles within a specified disc and steady-state variances to be less than a set of given upper bounds for linear systems with norm-bounded parameter uncertainties. Using the linear matrix inequality approach, the existence conditions of such controllers are derived. A parametrized representation of the desired controllers is presented in terms of the feasible solutions to a certain linear matrix inequality system. Based on this, a solution to the minimum-effect guaranteed-performance design problem is presented in the sense that the required control effort is minimized subject to performance constraints.     

一种推广的组合非线性输出反馈控制

针对多变量饱和线性系统的时变参考输入跟踪问题,研究了一种组合非线性输出反馈控制器的设计方法.基于原始的组合非线性反馈理论,构造了全阶和降阶输出反馈控制器.控制器由线性输出反馈项和非线性反馈项组成,使得闭环系统在包含于吸引域的不变集内渐近稳定.除了能够跟踪时变参考输入外,系统还具有良好的动态性能.仿真结果说明了所开发控制器的有效性.     

Observer-based adaptive iterative learning control for nonlinear systems with time-varying delays

An observer-based adaptive iterative learning control (AILC) scheme is developed for a class of nonlinear systems with unknown time-varying parameters and unknown time-varying delays. The linear matrix inequality (LMI) method is employed to design the nonlinear observer. The designed controller contains a proportional-integral-derivative (PID) feedback term in time domain. The learning law of unknown constant parameter is differential-difference-type, and the learning law of unknown time-varying parameter is difference-type. It is assumed that the unknown delay-dependent uncertainty is nonlinearly parameterized. By constructing a Lyapunov-Krasovskii-like composite energy function (CEF), we prove the boundedness of all closed-loop signals and the convergence of tracking error. A simulation example is provided to illustrate the effectiveness of the control algorithm proposed in this paper.     

具有区间时变时滞的离散Markov跳变系统鲁棒H∞控制

研究一类具有区间时变时滞的离散时间不确定Ｍａｒｋｏｖ跳变系统的时滞相关鲁棒H_∞ 控制问题．通过构造新的ＬｙａｐｕｎｏｖＫｒａｓｏｖｓｋｉｉ泛函,基于有限和不等式方法设计状态反馈控制器,使得闭环系统在容许不确定性下鲁棒稳定,且对能量有界的输入噪声满足一定输入输出H_∞ 增益．在新控制器存在条件中未引入任何自由变量矩阵,使之可更为有效地求解．基于锥补线性化的迭代算法可有效求解H_∞ 次优控制器．数值算例表明了所提出方法的有效性．     

Control of reactive distillation process for production of ethyl acetate

In this paper, plant-wide control for the production of ethyl acetate using reactive distillation is studied. Four important issues are considered in developing control schemes, including: (1) economics; (2) steady-state deviation of key product purities; (3) controllability in terms of degree of oscillation and settling time; and (4) feasible region of disturbances for effective control. Starting with two basic control schemes that have been studied before, new control schemes are developed to improve the operability of the process. These new control schemes have evolved from the basic schemes by making a trade-off between optimal design and control or by selecting sensor locations using closed-loop sensitivity analysis. It is found that, while being subjected to fluctuations in the composition of the acid feed or in the production flow-rate, sensor location based on traditional open-loop sensitivity causes a larger overshoot and steady-state deviation of key product purities. Sensor location on the basis of a closed-loop sensitivity analysis provides a better alternative for feedback control. The resulting scheme for control is found to be effective in reducing the steady-state deviation and in promoting good control performance.     

ROBUST Hinfinity CONTROL FOR SYSTEMS WITH TIME-VARYING PARAMETER UNCERTAINTY AND VARIANCE CONSTRAINTS

In this paper, the problem of designing robust Hinfinity controllers for linear continuous-time systems subjected to time-varying parameter uncertainty and steady-state variance constraints is considered. The goal of this problem is to design the state feedback controller, such that for all admissible time-varying parameter perturbations, the steady-state variance of each state is not more than the individual prespecified upper bound and the Hinfinity norm of the transfer function from disturbance inputs to system outputs meets the prespecified upper bound constraint, simultaneously. The parameter uncertainties are allowed to be time-varying and norm-bounded. A purely algebraic matrix equation approach is effectively utilized to solve the problem addressed. The existence conditions as well as the explicit expression of desired controllers are presented, and two illustrative examples are used to demonstrate the applicability of the proposed design procedure.     

Time-varying feedback laws for decentralized control

Decentralized control schemes are considered for time-invariant, finite dimensional, linear systems with know state equations. It is assumed that the systems are reachable and observable at a fictitious centralized control station, and that there is strong connectivity between the decentralized control stations via the system where necessary. It is shown that whether or not there are decentralized fixed modes in the open-loop system, periodically varying feedback gains at all but one of the control stations permit the remaining control station to observe and control the system given knowledge of the control laws implemented at the other control stations. Certain time-invariant systems which cannot be stabilized by decentralized time-invariant controllers, namely those with unstable decentralized fixed modes, can thus be stabilized by decentralized time-varying controllers.     

Stabilisation of time-varying linear systems via Lyapunov differential equations

This article studies stabilisation problem for time-varying linear systems via state feedback. Two types of controllers are designed by utilising solutions to Lyapunov differential equations. The first type of feedback controllers involves the unique positive-definite solution to a parametric Lyapunov differential equation, which can be solved when either the state transition matrix of the open-loop system is exactly known, or the future information of the system matrices are accessible in advance. Different from the first class of controllers which may be difficult to implement in practice, the second type of controllers can be easily implemented by solving a state-dependent Lyapunov differential equation with a given positive-definite initial condition. In both cases, explicit conditions are obtained to guarantee the exponentially asymptotic stability of the associated closed-loop systems. Numerical examples show the effectiveness of the proposed approaches.     

On constrained infinite-time linear quadratic optimal control with stochastic disturbances

In this work, we study the infinite-time linear quadratic optimal control problem for systems with stochastic disturbances and constrained inputs. A number of stochastic problem formulations under the full state information (FSI) structure are considered with a particular focus on the subject of feedback structure and its impact on certainty equivalence. In particular, we clarify results concerning the open-loop hard constrained, closed-loop statistically constrained, and closed-loop hard constrained cases. Extension to the infinite-time framework provides a vehicle for interpreting these controllers and indicates that the last of the three is of most interest to regulation type applications. Additionally, the partial state information problem is considered, and conditions are given for which a separated configuration consisting of the optimal estimator cascaded with the FSI optimal controller remains optimal.     

具有闭环极点和方差约束的不确定离散系统鲁棒控制

对一类具有范数有界不确定性的离散时间系统,研究了使得闭环系统的所有极点位于一给定圆盘,且稳定状态方差不超过给定上界的状态反馈鲁棒方差控制律设计问题,基于线性矩阵不等式的处理方法,导出了鲁棒方差控制律的存在条件,并用一组线性矩阵不等式的珂行解给出了鲁棒方差控制律的一个参数化表示,进而,通过建立和求解一个凸优化问题,给出了具有最泸控制能量的鲁棒方差控制律设计方法。     

Achievable closed-loop properties of systems under decentralizedcontrol: conditions involving the steady-state gain

The question of the existence of decentralized controllers for open-loop stable multivariable systems which provide particular closed-loop properties is investigated. In particular, we study the existence of decentralized controllers which provide integral action (Type I closed-loop performance) and also demonstrate one or more of: unconditional stability, integrity with respect to actuator and sensor failure, and decentralized unconditional stability. Necessary, sufficient, and, in some cases, necessary and sufficient conditions on the open-loop steady-state gain are derived such that there exists a controller which provides these desired closed-loop characteristics. These results provide the basis for a systematic approach to control structure selection for decentralized controller design     

A Hybrid Brain-Computer Interface for Closed-Loop Position Control of a Robot Arm

Brain-Computer interfacing (BCI) has currently added a new dimension in assistive robotics. Existing brain-computer interfaces designed for position control applications suffer from two fundamental limitations. First, most of the existing schemes employ open-loop control, and thus are unable to track positional errors, resulting in failures in taking necessary online corrective actions. There are examples of a few works dealing with closed-loop electroencephalography (EEG)-based position control. These existing closed-loop brain-induced position control schemes employ a fixed order link selection rule, which often creates a bottleneck preventing time-efficient control. Second, the existing brain-induced position controllers are designed to generate a position response like a traditional first-order system, resulting in a large steady-state error. This paper overcomes the above two limitations by keeping provisions for steady-state visual evoked potential (SSVEP) induced link-selection in an arbitrary order as required for efficient control and generating a second-order response of the position-control system with gradually diminishing overshoots/undershoots to reduce steady-state errors. Other than the above, the third innovation is to utilize motor imagery and P300 signals to design the hybrid brain-computer interfacing system for the said application with gradually diminishing error-margin using speed reversal at the zero-crossings of positional errors. Experiments undertaken reveal that the steady-state error is reduced to 0.2%. The paper also provides a thorough analysis of the stability of the closed-loop system performance using the Root Locus technique.      

Non-fragile robust optimal guaranteed cost control of uncertain 2-D discrete state-delayed systems

This paper is concerned with the problem of non-fragile robust optimal guaranteed cost control for a class of uncertain two-dimensional (2-D) discrete state-delayed systems described by the general model with norm-bounded uncertainties. Our attention is focused on the design of non-fragile state feedback controllers such that the resulting closed-loop system is asymptotically stable and the closed-loop cost function value is not more than a specified upper bound for all admissible parameter uncertainties and controller gain variations. A sufficient condition for the existence of such controllers is established under the linear matrix inequality framework. Moreover, a convex optimisation problem is proposed to select a non-fragile robust optimal guaranteed cost controller stabilising the 2-D discrete state-delayed system as well as achieving the least guaranteed cost for the resulting closed-loop system. The proposed method is compared with the previously reported criterion. Finally, illustrative examples are given to show the potential of the proposed technique.