Control Theoretic Concepts Research Articles

Ergodicity, Output-Controllability, and Antithetic Integral Control of Uncertain Stochastic Reaction Networks

The ergodicity and the output-controllability of stochastic reaction networks have been shown to be essential properties to fulfill to enable their control using, for instance, antithetic integral control (Briat, Gupta, Khammash, “Antithetic integral feedback ensures robust perfect adaptation in noisy biomolecular networks,” Cell Syst., vol. 2, pp. 17-28, 2016). We propose here to extend those properties to the case of uncertain networks. To this aim, the notions of interval, robust, sign, and structural ergodicity/output-controllability are introduced. The obtained results lie in the same spirit as those obtained in [1], where those properties are characterized in terms of control theoretic concepts, linear algebraic conditions, linear programs, and graph-theoretic/algebraic conditions. An important conclusion is that all those properties can be characterized by linear programs. Two examples are given for illustration.

Flatness and structural analysis as a constructive framework for private communication

This paper deals with the use of control theoretical concepts, essentially flatness, along with structural analysis, in the context of private communication. A new and systematic methodology to design a cryptographic architecture belonging to the special class of ciphers called Self Synchronizing Stream Ciphers (SSSC) is proposed. Till now, the constructions of SSSC were based on automata with finite input memory involving shifts or triangular functions (T-functions) as state transition functions. Besides, only ad-hoc approaches were available in the literature. The contribution of this paper is to propose a general framework to design SSSC involving dynamical systems taking the form of switched linear systems over finite fields with arbitrary state transition functions. An example of cipher with complete specifications is given. Its implementation on a small scale breeding of an ICS-SCADA equipment is described.

Design of Self-Synchronizing Stream Ciphers: a New Control-Theoretical Paradigm

This paper deals with the use of control theoretical concepts in the context of private communication. It is proposed a new and systematic methodology to design a cryptographic architecture belonging to the special class of ciphers called Self Synchronizing Stream Ciphers (SSSC). Till now, the constructions of SSSC were based on automata with finite input memory involving shifts or triangular functions (T-functions) as state transition functions. Besides, only ad-hoc approaches were available in the literature. The contribution of this paper is to propose not only a general framework to design SSSC, but with potentially more general state transition functions as well. Two control-theoretical issues are treated to this end: as a new paradigm, the construction of flat dynamical systems, and on the other hand, the notion of mortality of a set of matrices, a problem which is in general not decidable.

Control theory meets synthetic biology.

The past several years have witnessed an increased presence of control theoretic concepts in synthetic biology. This review presents an organized summary of how these control design concepts have been applied to tackle a variety of problems faced when building synthetic biomolecular circuits in living cells. In particular, we describe success stories that demonstrate how simple or more elaborate control design methods can be used to make the behaviour of synthetic genetic circuits within a single cell or across a cell population more reliable, predictable and robust to perturbations. The description especially highlights technical challenges that uniquely arise from the need to implement control designs within a new hardware setting, along with implemented or proposed solutions. Some engineering solutions employing complex feedback control schemes are also described, which, however, still require a deeper theoretical analysis of stability, performance and robustness properties. Overall, this paper should help synthetic biologists become familiar with feedback control concepts as they can be used in their application area. At the same time, it should provide some domain knowledge to control theorists who wish to enter the rising and exciting field of synthetic biology.

Goal-Oriented Inference: Approach, Linear Theory, and Application to Advection Diffusion

Inference of model parameters is one step in an engineering process often ending in predictions that support decision in the form of design or control. Incorporation of end goals into the inference process leads to more efficient goal-oriented algorithms that automatically target the most relevant parameters for prediction. In the linear setting the control-theoretic concepts underlying balanced truncation model reduction can be exploited in inference through a dimensionally optimal subspace regularizer. The inference-for-prediction method exactly replicates the prediction results of either truncated singular value decomposition, Tikhonov-regularized, or Gaussian statistical inverse problem formulations independent of data; it sacrifices accuracy in parameter estimate for online efficiency. The new method leads to low-dimensional parameterization of the inverse problem enabling solution on smartphones or laptops in the field.

Goal-Oriented Inference: Approach, Linear Theory, and Application to Advection Diffusion

Inference of model parameters is one step in an engineering process often ending in predictions that support decision in the form of design or control. Incorporation of end goals into the inference process leads to more efficient goal-oriented algorithms that automatically target the most relevant parameters for prediction. In the linear setting the control-theoretic concepts underlying balanced truncation model reduction can be exploited in inference through a dimensionally optimal subspace regularizer. The inference-for-prediction method exactly replicates the prediction results of either truncated singular value decomposition, Tikhonov-regularized, or Gaussian statistical inverse problem formulations independent of data; it sacrifices accuracy in parameter estimate for online efficiency. The new method leads to low-dimensional parameterization of the inverse problem enabling solution on smartphones or laptops in the field.

Analysis of the bullwhip effect with order batching in multi‐echelon supply chains

Purpose – The purpose of this paper is to understand the effect of batching on bullwhip effect in a model of multi‐echelon supply chain with information sharing.Design/methodology/approach – The model uses the system dynamics and control theoretic concepts of variables, flows and feedback processes and is implemented using iThink® software.Findings – It has been seen that the relationship between batch size and demand amplification is non‐monotonic. Large batch sizes, that when combined in integer multiples can produce order rates that are close to the actual demand, produce little demand amplification, i.e. it is the size of the remainder of the quotient that is the determinant. It is further noted that the value of information sharing is greatest for smaller batch sizes, for which there is a much greater improvement in the amplification ratio.Research limitations/implications – Batching is associated with the inventory holding and backlog cost. Therefore, future work should investigate the cost implicat...

Analysis of the bullwhip effect with order batching in multi‐echelon supply chains

PurposeThe purpose of this paper is to analyze the effect of batching on bullwhip effect in a model of multi‐echelon supply chain with information sharing.Design/methodology/approachThe model uses the system dynamics and control theoretic concepts of variables, flows, and feedback processes and is implemented using iThink® software.FindingsIt has been seen that the relationship between batch size and demand amplification is non‐monotonic. Large batch sizes, when combined in integer multiples, can produce order rates that are close to the actual demand and produce little demand amplification, i.e. it is the size of the remainder of the quotient that is the determinant. It is further noted that the value of information sharing is greatest for smaller batch sizes, for which there is a much greater improvement in the amplification ratio.Research limitations/implicationsBatching is associated with the inventory holding and backlog cost. Therefore, future work should investigate the cost implications of order batching in multi‐echelon supply chains.Practical implicationsThis is a contribution to the continuing research into the bullwhip effect, giving supply chain operations managers and designers a practical way into controlling the bullwhip produced by batching across multi‐echelon supply chains. Economies of scale processes usually favor large batch sizes. Reducing batch size in order to reduce the demand amplification is not a good solution.Originality/valuePrevious similar studies have used control theoretic techniques and it has been pointed out that control theorists are unable to solve the lot sizing problem. Therefore, system dynamic simulation is then applied to investigate the impact of various batch sizes on bullwhip effect.

Discrete-Event Coordination Design for Distributed Agents

This paper presents new results on the formal design of distributed coordinating agents in a discrete-event framework. In this framework, agents are modeled to be individually equipped with a coordination module, through which they interact and communicate. In terms of existing control-theoretic concepts, we first define the concept of a coordinable language and show that it is the necessary and sufficient existence condition of coordination modules for distributed agents to achieve conformance to a prespecified interagent constraint language. Following, we present a synthesis algorithm to compute near-optimal coordination modules. An example is provided to illustrate the design synthesis using the proposed algorithm. Finally, a discussion with related work distinguishes our coordination design problem from related problems in the literature.

Using dynamic perturbations to identify fragilities in biochemical networks

AbstractBiological functions at the cellular level result from interactions between genes, proteins and metabolites within complex biochemical reaction networks. Identifying specific and localized fragilities in such networks is important to understand the source of biological malfunctions, and to devise strategies for fighting disease states that have developed robustness. Herein we consider a method based on robust control theoretic concepts for identifying network fragilities. In particular, we consider adding static or dynamic perturbations to the network edges, i.e. the direct binary interactions within the network, and compute the smallest perturbation that induces a bifurcation, and hence a qualitative change, in the network function. The proposed method can also serve as a powerful modeling tool in that it can be used to identify parts of a model that require more detailed descriptions of the underlying processes. The method is demonstrated by application to models of sustained oscillations in the glycolytic pathway and bistability in the mitogen‐activated protein kinase (MAPK) signal transduction. Copyright © 2010 John Wiley & Sons, Ltd.

An adaptive drug delivery design using neural networks for effective treatment of infectious diseases: A simulation study

An adaptive drug delivery design is presented in this paper using neural networks for effective treatment of infectious diseases. The generic mathematical model used describes the coupled evolution of concentration of pathogens, plasma cells, antibodies and a numerical value that indicates the relative characteristic of a damaged organ due to the disease under the influence of external drugs. From a system theoretic point of view, the external drugs can be interpreted as control inputs, which can be designed based on control theoretic concepts. In this study, assuming a set of nominal parameters in the mathematical model, first a nonlinear controller (drug administration) is designed based on the principle of dynamic inversion. This nominal drug administration plan was found to be effective in curing “nominal model patients” (patients whose immunological dynamics conform to the mathematical model used for the control design exactly. However, it was found to be ineffective in curing “realistic model patients” (patients whose immunological dynamics may have off-nominal parameter values and possibly unwanted inputs) in general. Hence, to make the drug delivery dosage design more effective for realistic model patients, a model-following adaptive control design is carried out next by taking the help of neural networks, that are trained online. Simulation studies indicate that the adaptive controller proposed in this paper holds promise in killing the invading pathogens and healing the damaged organ even in the presence of parameter uncertainties and continued pathogen attack. Note that the computational requirements for computing the control are very minimal and all associated computations (including the training of neural networks) can be carried out online. However it assumes that the required diagnosis process can be carried out at a sufficient faster rate so that all the states are available for control computation.

Linear Controllers for the Stabilization of Unknown Steady States of Chaotic Systems

The problem of stabilization of unknown steady states of chaotic systems by means of linear controllers is studied. A complete solution of the problem is given for the case of state feedback stabilization. For the case of output feedback stabilization, some partial results are given. The paper shows that the control theoretic concepts of controllability, stabilizability and root-locus are instrumental in the solution of the problem. All results are illustrated by means of the stabilization of unknown steady states of a controlled Lorenz system

SUPPLY SYSTEM DYNAMICS: DISTRIBUTED CONTROL IN SUPPLY CHAINS AND NETWORKS

The purpose of this article is to make a contribution to a more effective management for supply chains and networks, which we are subsuming under the title supply systems. We conceive of supply systems management as the design, control, and development of logistics along the value chain or in value networks. In this article, we concentrate on control, i.e., the regulation and steering of supply systems from production to customer and vice versa, with the help of system dynamics modeling and simulation. Traditionally, supply chain management has been heavily supported by discrete event simulation and optimization models on very detailed levels. Established tools, e.g., Manufacturing Resources Planning, Enterprise Resources Planning, and Production Planning Systems, have emphasized highly specialized functions, such as the planning for optimal capacity use and achievement of delivery goals, via the sequencing, scheduling, and dispatching of individual orders, or the global allocation of resources but without the possibility to evaluate different outcomes of the allocation process. In the quest for efficiency and effectiveness, new approaches to control, which lead beyond these functions of disposition, are needed. We present a model that combines two systemic methodologies that operate on higher levels of aggregation and complement each other: system dynamics to model and simulate the supply chain and cybernetic control to apply control-theoretical concepts, namely proportional, derivative, and integral control, in a combined mode as well as according to a recursive logic of distributed control. This way, substantial improvements in both efficiency and effectiveness can be achieved, and ultimately organizational viability can be enhanced.

Eye movement instabilities and nystagmus can be predicted by a nonlinear dynamics model of the saccadic system

The study of eye movements and oculomotor disorders has, for four decades, greatly benefitted from the application of control theoretic concepts. This paper is an example of a complementary approach based on the theory of nonlinear dynamical systems. Recently, a nonlinear dynamics model of the saccadic system was developed, comprising a symmetric piecewise-smooth system of six first-order autonomous ordinary differential equations. A preliminary numerical investigation of the model revealed that in addition to generating normal saccades, it could also simulate inaccurate saccades, and the oscillatory instability known as congenital nystagmus (CN). By varying the parameters of the model, several types of CN oscillations were produced, including jerk, bidirectional jerk and pendular nystagmus. The aim of this study was to investigate the bifurcations and attractors of the model, in order to obtain a classification of the simulated oculomotor behaviours. The application of standard stability analysis techniques, together with numerical work, revealed that the equations have a rich bifurcation structure. In addition to Hopf, homoclinic and saddlenode bifurcations organised by a Takens-Bogdanov point, the equations can undergo nonsmooth pitchfork bifurcations and nonsmooth gluing bifurcations. Evidence was also found for the existence of Hopf-initiated canards. The simulated jerk CN waveforms were found to correspond to a pair of post-canard symmetry-related limit cycles, which exist in regions of parameter space where the equations are a slow-fast system. The slow and fast phases of the simulated oscillations were attributed to the geometry of the corresponding slow manifold. The simulated bidirectional jerk and pendular waveforms were attributed to a symmetry invariant limit cycle produced by the gluing of the asymmetric cycles. In contrast to control models of the oculomotor system, the bifurcation analysis places clear restrictions on which kinds of behaviour are likely to be associated with each other in parameter space, enabling predictions to be made regarding the possible changes in the oscillation type that may be observed upon changing the model parameters. The analysis suggests that CN is one of a range of oculomotor disorders associated with a pathological saccadic braking signal, and that jerk and pendular nystagmus are the most probable oscillatory instabilities. Additionally, the transition from jerk CN to bidirectional jerk and pendular nystagmus observed experimentally when the gaze angle or attention level is changed is attributed to a gluing bifurcation. This suggests the possibility of manipulating the waveforms of subjects with jerk CN experimentally to produce waveforms with an extended foveation period, thereby improving visual resolution.

Total annualized cost optimality properties of state space models for mass and heat exchanger networks

In this work, we employ a state space representation of a heat/mass exchanger network to derive a mathematical formulation of the minimum total annualized cost (TAC) problem. Mathematical properties of the resulting nonlinear program's global optimum are then derived, using a variation induced minimization (VIM) technique and control theoretic concepts. This technique successfully identifies variables which are zero at the global optimum, thus reducing the size of the optimization problem. It is established that, under certain conditions, all self-recycle and total network bypass flow rates can be chosen to be zero at the TAC minimum. Two heat exchange network (HEN) TAC synthesis problems are employed to illustrate the validity of these properties, as well as the importance of the conditions under which the properties are derived. A hybrid algorithm, which consists of branch and bound underestimation with imbedded interval analysis, is employed in identifying numerically the optimum of these HEN TAC problems.

The role of "control" in an embodied cognition

Borrett, Kelly, and Kwan follow the lead of Merleau-Ponty and develop a theory of neural-network modeling that emerges out of what they find wrong with current approaches to thought and action. Specifically, they take issue with "cognitivism" and its tendency to model cognitive agents as controlling, representational systems. While attempting to make the point that pre-predicative experience/action/place (i.e. grasping) involves neither representation nor control, the authors imply that control-theoretic concepts and representationalism necessarily go hand-in-hand. The purpose of the present paper is to demonstrate that this is not the case. Rather, it will be argued that such necessity is only assumed because the authors attempt to apply the control theory of servo-mechanisms to the behavior of organisms. By adopting this engineering control-theoretic perspective, the authors are led, as are most of the cognitivists with whom they disagree, to overlook critical aspects of how it is that biological systems do what they do. It is the ignoring of these critical aspects of biological control, due to the acceptance of an engineering approach to control, that makes it appear as though control theory and representationalism necessarily go hand-in-hand.

Using Control and Systems Theoretic Concepts to Set Prices of Goods and Services in Competitive Markets

In this paper, we describe how control theoretic methods of modelling, optimisation and learning/adaptation have been used to develop a generic approach to price setting in competitive markets. This generic approach has been incorporated into a set of decision support tools which are now routinely used to set prices of petrol at each petrol station for networks of petrol stations, for the pricing of mobile telephony tariffs as well as for the pricing of goods in mass retailing. Real life examples of the use of these tools are also provided in the paper.

Algorithmic Statistical Process Control: Some Practical Observations

Algorithmic Statistical Process Control (ASPC) is an approach to quality improvement that reduces predictable quality variations using feedback and feedforward techniques, and then monitors the entire system to detect changes. As such, it is a marriage of control theory and statistical process control (SPC). Control theoretical concepts are used to minimize deviations from target by process adjustments; sec is used to gain fundamental improvements. Where applicable, ASPC is a logical next step in the drive for continuous quality improvement. This paper presents the ASPC concept and its applications to practitioners. Technical and non-technical requirements and factors conducive to the use of ASPC are emphasized, and pre-planning for the use of ASPC in new processes is discussed.

Power system excitation and governor control design via time-scale decomposition

Power system excitation and governor control design using time-scale decomposition and optimal control theoretic concepts are presented. A synchronous machine with an excitation system and a prime-mover is decomposed into slow and fast subsystems using the iterative separation of time scales. The slow subsystem model is employed as the design model. The effectiveness of the proposed controller is studied through digital simulation. The simulation results are compared with those obtained via the classical quasi-steady-state (qss) technique. The approach presented does not require an explicit knowledge of the perturbation parameter.

Modern Hot-Strip Mill Thickness Control

The design and implementation of a hot-strip steel mill thickness control system is discussed. The use of structured design techniques and well-tuned control loops produced a thickness control system of world-class performance. A high-level software design approach provided the ability to make quick and accurate modifications to both control loops and tuning constants. Diligent work in the areas of mill calibration, tuning, and simulation resulted in a very effective commissioning stage. Integration of the automatic gauge control with the predictive and adaptive mill setup models resulted in a fully coordinated thickness control system. Control loop strategies and theoretical concepts of hot steel strip rolling are discussed. Performance results achieved during the startup of the Dofasco Incorporated No. 2 Hot Strip Mill are inclulded.