A convex characterization of distributed control problems in spatially invariant systems with communication constraints

In this paper we consider the problem of distributed controller design in spatially invariant systems for which communication among sites is limited. In particular, the controller is constrained so that information is propagated with a delay that depends on the distance between subsystems—a structure we refer to as “funnel” causality. We show that the problem of optimal design can be cast as a convex problem provided that the plant has a similar funnel-causality structure, and the propagation speeds in the controller are at least as fast as those in the plant. As an example, we consider the case of the wave dynamics with limited propagation speed control.     

An Efficient Finite Difference Method for The Time‐Delay Optimal Control Problems With Time‐Varying Delay

In this paper, an efficient finite difference method is presented for the solution of time‐delay optimal control problems with time‐varying delay in the state. By using the Pontryagin's maximum principle, the original time‐delay optimal control problem is first transformed into a system of coupled two‐point boundary value problems involving both delay and advance terms. Then the derived system is converted into a system of linear algebraic equations by using a second‐order finite difference formula and a Hermite interpolation polynomial for the first‐order derivatives and delay terms, respectively. The convergence analysis of the proposed approach is provided. The new scheme is also successful for the optimal control of time‐delay systems affected by external persistent disturbances. Numerical examples are included to demonstrate the validity and applicability of the new technique. Some comparative results are included to illustrate the effectiveness of the proposed method.     

A decade of progress in iterative process control design: from theory to practice

One of the most active areas of research in the nineties has been the study of the interplay between system identification and robust control design. It has led to the development of “control-oriented identification design”, the paradigm being that, since the model is only a tool for the design of a controller, its accuracy (or its error distribution) must be tuned towards the control design objective. This observation has led to the concept of “iterative identification and control design” and, subsequently, to model-free iterative controller design, in which the controller parameters are iteratively tuned on the basis of successive experiments performed on the real plant, leading to better and better closed-loop behaviour. These iterative methods have found immediate applications in industry; they have also been applied to the optimal tuning of PID controllers. This paper presents the progress that has been accomplished in iterative process control design over the last decade. It is illustrated with some applications in the chemical industry.     

Collective knowledge systems: Where the Social Web meets the Semantic Web

What can happen if we combine the best ideas from the Social Web and Semantic Web? The Social Web is an ecosystem of participation, where value is created by the aggregation of many individual user contributions. The Semantic Web is an ecosystem of data, where value is created by the integration of structured data from many sources. What applications can best synthesize the strengths of these two approaches, to create a new level of value that is both rich with human participation and powered by well-structured information? This paper proposes a class of applications called collective knowledge systems, which unlock the “collective intelligence” of the Social Web with knowledge representation and reasoning techniques of the Semantic Web.     

Optimal LQ tracking control for continuous-time systems with pointwise time-varying input delay

This paper investigates the linear quadratic (LQ) tracking problem for linear continuous-time systems with pointwise time-varying input delays. It is assumed that the time-varying input delay takes only one value from a finite set at a given time instant. By defining an indicator, the investigated LQ tracking problem is firstly transformed into a special optimal control problem for continuous-time systems with multiple delays in a single input channel. Then the duality between the LQ tracking for the system with multiple input delay and the smoothing for an associated backward delay free system is established. Finally, an explicit analytical solution to the proposed LQ tracking problem is presented by solving the smoothing problem.

     

A Generic Finite State Compiler for Tagging Rules

We describe a novel method of compiling ranked tagging rules into a “bimachine”, i.e. a deterministic finite state device composed of two finite automata: a left-to-right one and a right-to-left one. The actual compilation is based on algorithms for finite state acceptors rather than transducers, which guarantees determinizability and the efficiency of compilation. The compiler has been used in a number of applications within a speech synthesis system.     

离散时滞系统的近似最优扰动抑制

研究了状态变量合有时滞的离散系统在外部扰动下的最优控制问题．通过引入一个灵敏度参数,将原系统的最优扰动抑制问题转化为一族不含超前项和时滞项的两点边值问题,并由此导出了最优扰动抑制控制器的这代近似设计方法．得到的最优扰动抑制控制律由解析的前馈一反馈项和伴随向量级数和形式的补偿项组成,截取伴随向量级数的有限和得到原系统的次优扰动抑制控制律．数值仿真表明该近似最优控制器对外部持续扰动具有良好的鲁棒性。     

有限时间二次型数值算法研究及其应用

为了实际需要和学术发展的要求,研究了以倒立摆为控制对象,通过闭环网络形成的反馈控制系统的随机传输时延的最优控制问题。在求解有限时间最优控制律过程中,通过矩阵Raccati方程的离散变换,利用Matlab中计算无限时间二次型最优控制器的LQR函数,从而求出有限时间LQR问题的数值解。通过仿真结果证明,研究的方法能够使倒立摆系统最终稳定,从而说明提出的算法对于求解有限时间LQR问题是有效的。     

Approximate reduction of dynamic systems

The reduction of dynamic systems has a rich history, with many important applications related to stability, control and verification. Reduction of nonlinear systems is typically performed in an “exact” manner–as is the case with mechanical systems with symmetry–which, unfortunately, limits the type of systems to which it can be applied. The goal of this paper is to consider a more general form of reduction, termed approximate reduction, in order to extend the class of systems that can be reduced. Using notions related to incremental stability, we give conditions on when a dynamic system can be projected to a lower dimensional space while providing hard bounds on the induced errors, i.e. when it is behaviourally similar to a dynamic system on a lower dimensional space. These concepts are illustrated on a series of examples.     

Anti-windup via constrained regulation with observers

A method is presented for the output-feedback control of discrete-time linear systems with hard constraints on state and control variables. Prior work has shown that optimal controllers for constrained systems take the form of a nonlinear feedback law acting on a set-valued state estimate. In this paper, conventional state estimation schemes are used. A nonlinear control law is derived which views the state estimation error as a disturbance. The resulting control law is then used in conjunction with the conventional observer, rather than set-valued observer, to achieve the desired constrained regulation. The significantly reduced real-time computations come at the cost of restricting the controller structure and thereby introducing possible conservatism in the achievable performance. The results are specialized to the problem of anti-windup for systems with control saturations. A “measurement governor” scheme is introduced that alters plant measurements in such a way to improve performance in the presence of controller saturations.     

Designing robust optimal dynamic experiments

The quality of experiments designed using standard optimisation-based techniques can be adversely affected by poor starting values of the parameters. Thus, there is a necessity for design methods that are insensitive (“robust”) to these starting values. Here, two novel, robust criteria are presented for computing optimal dynamic inputs for experiments aiming at improving parameter precision, based on previously proposed methods for providing design robustness — the expected value criterion and the max–min criterion. In this paper, both criteria are extended by use of the information matrix derived for dynamic systems. The experiment design problem is cast as an optimal control problem, with experiment decision variables such as sampling times of response variables, time-varying and time-invariant external controls, experiment duration, and initial conditions. Comparisons are made of experiment designs obtained using the conventional approach and the newly proposed criteria. A typical semi-continuous bioreactor application is presented.     

The Framework for Linear Periodic Time‐Delay Systems Based on Semi‐Discretization: Stability Analysis and Control

Stability analysis and control for linear periodic time‐delay systems are investigated in this paper. In this framework, a semi‐discretization method is used to develop a mapping of the system response in a finite‐dimensional state space. With the mapping, the stability region and stability boundary can be identified by comparing the maximum absolute value of its eigenvalues to 1. More importantly, an efficient stability criterion is presented for periodic neutral systems. In addition, minimization of the maximum absolute value of the mapping's eigenvalues leads to optimal control gains. The tracking control problem is also discussed. Two numerical examples are given to illustrate the effectiveness of the proposed method.     

Price-driven coordination method for solving plant-wide MPC problems

In large-scale model predictive control (MPC) applications, such as plant-wide control, two possible approaches to MPC implementation are centralized and decentralized MPC schemes. These represent the two extremes in the “trade-off” among the desired characteristics of an industrial MPC system, namely accuracy, reliability and maintainability. To achieve optimal plant operations, coordination of decentralized MPC controllers has been identified as both an opportunity and a challenge. Typically, plant-wide MPC problem can be formulated as a large-scale quadratic program (QP) with linking equality constraints. Such problems can be decomposed and solved with the price-driven coordination method and on-line solutions of these structured large-scale optimization problems require an efficient price-adjustment strategy to find an “equilibrium price”. This work develops an efficient price-adjustment algorithm based on Newton’s method, in which sensitivity analysis and active set change identification techniques are employed. With the off-diagonal element abstraction technique and the enhanced priced driven coordination algorithm, a coordinated, decentralized MPC framework is proposed. Several case studies show that the proposed coordination-based decentralized MPC scheme is an effective approach to plant-wide MPC applications, which provides a high degree of reliability and accuracy at a reasonable computational load.     

Further Study on Networked Control Systems with Unreliable Communication Channels

This paper focuses on the fundamental problems of linear quadratic gaussian (LQG) control and stabilization problems for networked control systems (NCSs) with unreliable communication channels (UCCs) where packet dropout, input delay and observation delay occur. These basic issues have attracted extensive attentions due to broad applications. Our contributions are as follows. For the finite horizon case, without time-stamping technique, the optimal estimator is derived by using the novelty method of innovation sequences based on the delayed intermittent observations; A necessary and sufficient condition for the optimal control problem is presented on the basis of the solution to the forward and backward difference equations (FBDEs) and two coupled Riccati equations. For the infinite horizon case, it is shown that under certain assumption, the system can stay bounded in the mean square sense if and only if the algebraic Riccati equation admits the unique positive solution.

     

Switched nonlinear systems with state-dependent dwell-time

The asymptotic convergence of a switched nonlinear system in the presence of disturbances is studied. The system switches among a family of integral input-to-state stable systems. The time between two consecutive switchings is not less than a value τ_D. This dwell-time τ_D is allowed to take different values according to a function whose argument is the state of the system at the switching times. We propose a dwell-time function which depends on the comparison functions which characterize the integral input-to-state stability property and guarantees the state of the switched system to converge to zero under the action of disturbances with “bounded energy”. The main feature of the analysis is that it does not rely on the property for the switching to stop in finite time. The two important cases of locally exponentially stable and feedforward systems are analyzed in detail.     

Optimal operation of Petlyuk distillation: steady-state behavior

The “Petlyuk” or “dividing-wall” or “fully thermally coupled” distillation column is an interesting alternative to the conventional cascaded binary columns for separation of multi-component mixtures. However, the industrial use has been limited, and difficulties in operation have been reported as one reason. With three product compositions controlled, the system has two degrees of freedom left for on-line optimization. We show that the steady-state optimal solution surface is quite narrow, and depends strongly on disturbances and design parameters. Thus it seems difficult to achieve the potential energy savings compared to conventional approaches without a good control strategy. We discuss candidate variables which may be used as feedback variables in order to keep the column operation close to optimal in a “self-optimizing” control scheme.     

Optimal design of two interconnected enzymatic bioreactors

This paper deals with the optimal design of two interconnected continuous stirred bioreactors in which a single enzymatic reaction occurs. The term “optimal” should be understood here as the minimum of the total volume of the reactors required to perform a given conversion rate, given a quantity of matter to be converted per time unit. In determining the optimal volume, it is considered that the input flow may be distributed among the tanks and also that a recirculation loop may be used. The optimal design problem is solved for a wide class of kinetics functions including, in particular, the well-known Michaelis–Menten kinetics function. The analysis of the optimal configurations is investigated, and it is shown that the concept of “Steady State Equivalent Biological System” (SSEBS) first introduced by Harmand et al. [AIChE J., in press] for microbial reactions only applies to enzymatic systems which have non-monotonic kinetics. In addition, a stability as well as a sensitivity analysis of the optimal configurations are performed.     

Finite‐Time Optimal Tracking Control for Dynamic Systems on Lie Groups

This paper investigates the problem of finite‐time optimal tracking control for dynamic systems on Lie groups for the situation when the tracking time and/or the cost functions need to be considered. The specific results are illustrated on SE(3) (the specific Euclidean groups of rigid body motions). The tracking time is given according to task requirements in advance. By using Pontryagin's maximum principle (PMP) on Lie groups and the backstepping method, a finite‐time optimal tracking control law is designed to track a desired reference trajectory at the given time. Simultaneously, the corresponding cost functions are guaranteed to be optimal. Compared with existing results of optimal control on Lie groups, it is noteworthy that we consider the finite‐time tracking control for dynamic systems rather than kinematic systems. Furthermore, the obtained optimal control law is described by explicit formulations, which is significant for practical applications.     

Source code verification of a secure payment applet

This paper discusses a case study in formal verification and development of secure smart card applications. An elementary Java Card electronic purse applet is presented whose specification can be simply formulated as “in normal operation, the applet’s balance field can only be decreased, never increased”. The applet features a challenge-response mechanism which allows legitimate terminals to increase the balance by putting the applet into a special operation mode. A systematic approach is used to guarantee a secure flow of control within the applet: appropriate transition properties are first formalized as a finite state machine, then incorporated in the specification, and finally formally verified using the Loop translation tool and the PVS theorem prover.     

CAD — State of the art and a tentative forecast

The most important contemporary phenomenon in the mechanical engineering applications of CAD is the very rapid proliferation of systems, even in small and medium companies, driven by market imperatives and attracted by vastly improved cost/performance indices. The systems have expanded “upwards” from drafting to the modelling and analysis areas and “downstream” to process planning and documentation.Outstanding trends for the future are the use of knowledge-engineering techniques for problem solving, of novel database structures for intergrating data-growth over the product cycle, and of distributed architectures for building cooperative systems.