Dynamical decoupling in quantum control: A system theoretic approach

Suppressing decoherence is one of the most challenging problems in the control of quantum dynamical systems. Dynamical decoupling is an open-loop decoherence control technique based on high-frequency and high-amplitude periodic controls. Here, we reformulate the effects of the basic strategy in terms of linear, symmetric matrix equations. Such a reformulation proves to be useful both in the analysis and in the synthesis of the needed unitary control actions. A general framework is provided, and simple, but significant, particular cases are studied in detail.     

Information theoretic approach to man-machine interface complexityevaluation

We analyze the interactions between human operators and control room equipment and find that several factors affect the information-gathering and decision-making processes of operators: contents of the provided information, the way information is provided, and knowledge of the operators. These factors contribute to the perceived cognitive complexity by human operators in plant operation. Based on the information theory concept, we propose an integrated framework for evaluating this complexity. The proposed framework is designed to be applied to various types of control room equipment which have different types of man-machine interface and contain different types of information. An experimental verification for the proposed framework is performed and its result shows that the framework successfully integrates various aspects of man-machine interface systems and estimates the mental workload of human operators     

Information theoretic clustering using a k-nearest neighbors approach

We develop a new non-parametric information theoretic clustering algorithm based on implicit estimation of cluster densities using the k-nearest neighbors (k-nn) approach. Compared to a kernel-based procedure, our hierarchical k-nn approach is very robust with respect to the parameter choices, with a key ability to detect clusters of vastly different scales. Of particular importance is the use of two different values of k, depending on the evaluation of within-cluster entropy or across-cluster cross-entropy, and the use of an ensemble clustering approach wherein different clustering solutions vote in order to obtain the final clustering. We conduct clustering experiments, and report promising results.     

Long swings in exchange rates: a stochastic control approach

A regime‐switching model to describe the exchange rate dynamics is derived as solution to a stochastic control problem. We assume exchange rates evolve according to some macroeconomic variables (fundamental) whose dynamics could be described by a Brownian motion with a state‐dependent drift. The local Monetary Authority is assumed to intervene influencing the evolution of the fundamental, causing the exchange rate to switch from a depreciating to an appreciating regime (and vice versa). We assume the behaviour of the Monetary Authority can be modeled using an optimal control framework where the state variable is represented by the fundamental. The solution of the model allows the determination of an endogenous tolerance band within which the exchange rate freely fluctuates.     

Characterization of a complementary sensitivity property in feedback control: An information theoretic approach

This paper addresses a characterization of a complementary sensitivity property in feedback control using an information theoretic approach. We derive an integral-type constraint of the complementary sensitivity function with respect to the unstable zeros of the open-loop transfer function. It is an analogue of Bode’s integral formula for the sensitivity gain. To show the constraint, we first show a conservation law of the entropy and mutual information of signals in the feedback system. Then, we clarify the relationship between the mutual information of control signals and the unstable zeros of the open-loop transfer function.     

Optimal allocation of testing effort during testing and debugging phases: a control theoretic approach

Allocation of efforts to a software development project during the testing phase is a multifaceted task for software managers. The challenges become stiffer when the nature of the development process is considered in the dynamic environment. Many software reliability growth models have been proposed in last decade to minimise the total testing-effort expenditures, but mostly under static assumption. The main purpose of this article is to investigate an optimal resource allocation plan to minimise the cost of software during the testing and operational phase under dynamic condition. An elaborate optimisation policy based on the optimal control theory is proposed and numerical examples are illustrated. This article also studies the optimal resource allocation problems for various conditions by examining the behaviour of the model parameters and also suggests policy for the optimal release time of the software. The experimental results greatly help us to identify the contribution of each selected parameter and its weight.     

Realization of Petrinets: a system theoretic approach

Petrinets have become a useful tool for modelling various classes of systems, especially those involving parallel computations and concurrent processes. The present paper deals with a method for identification of the Petrinet model from a given set of input-output observations. The method actually involves a modification of the system identification techniques of linear system theory. It has been shown that, by assuming the net to be a discrete-time linear dynamical system, it is possible to arrive at a reduced-order Petrinet model for a dynamical process. This procedure will enable one to obtain a Petrinet model for subsequent analysis systematically, thus bypassing normally used trial-and-error techniques.     

On improving bandwidth assurance in AF-based DiffServ networks using a control theoretic approach

The assured forwarding (AF) based service in a differentiated services (DiffServ) network fails to provide bandwidth assurance among competing aggregates under certain conditions, for example, where there exists a large disparity in the round-trip times, packet sizes, or target rates of the aggregates, or there exist non-adaptive aggregates. Several mechanisms have been proposed in order to address the problem of providing bandwidth assurance for aggregates, using only the knowledge gathered at ingress routers. In this paper, we present a control theoretic approach to analyze these mechanisms and explore the reasons when they fail to achieve bandwidth assurance under some circumstances. Then we propose a simple but robust controller for this problem, namely, the variable-structure adaptive CIR threshold (VS-ACT) mechanism. We validate the analysis and demonstrate that VS-ACT outperforms several other mechanisms proposed in the literature over a wide range of network dynamics through extensive simulations.     

Model predictive control for perturbed max-plus-linear systems: a stochastic approach

Model predictive control (MPC) is a popular controller design technique in the process industry. Conventional MPC uses linear or non-linear discrete-time models. Recently, we have extended MPC to a class of discrete event systems that can be described by a model that is ‘linear’ in the (max,?+) algebra. In our previous work we have only considered MPC for the perturbations-free case and for the case with bounded noise and/or modelling errors. In this paper we extend these results on MPC for max-plus-linear systems to a stochastic setting. We show that under quite general conditions the resulting optimization problems turn out to be convex and can thus be solved very efficiently.     

A theoretic and practical framework for scheduling in a stochastic environment

There are many systems and techniques that address stochastic planning and scheduling problems, based on distinct and sometimes opposite approaches, especially in terms of how generation and execution of the plan, or the schedule, are combined, and if and when knowledge about the uncertainties is taken into account. In many real-life problems, it appears that many of these approaches are needed and should be combined, which to our knowledge has never been done. In this paper, we propose a typology that distinguishes between proactive, progressive, and revision approaches. Then, focusing on scheduling and schedule execution, a theoretic model integrating those three approaches is defined. This model serves as a general template to implement a system that will fit specific application needs: we introduce and discuss our experimental prototypes which validate our model in part, and suggest how this framework could be extended to more general planning systems.     

A control theoretic model for piloted approach to landing

A previously developed, optimal control model for manned-vehicle systems analysis is extended to analyze a piloted approach to landing task. The system model that is developed is used to investigate pictorial display requirements for a light aircraft. The effects, on system performance, of different display symbology are predicted by the model and are compared with data obtained in an independent experimental study. The comparison demonstrates the validity of our pilot model and its utility in manned vehicle analysis and synthesis.     

Sensor fault detection and isolation: a game theoretic approach

This paper studies sensor fault detection using a game theoretic approach. Sensor fault detection is considered as change point analysis in the coefficients of a regression model. A new method for detecting faults, referred to as two-way fault detection, is introduced which defines a game between two players, i.e. the fault detectors. In this new strategic environment, assuming that the independent states of the regression model are known, the test statistics are derived and their finite sample distributions under the null hypothesis of no change are derived. These test statistics are useful for testing the fault existence, as well as, the pure and mixed Nash equilibriums are derived for at-most-one-change and epidemic change models. A differential game is also proposed and solved using the Pontryagin maximum principle. This solution is useful for studying the fault detection problem in unknown state cases. Kalman filter and linear matrix inequality methods are used in finding the Nash equilibrium for the case of unknown states. Illustrative examples are presented to show the existence of the Nash equilibriums. Also, the proposed fault detection scheme is numerically evaluated via its application on a practical system and its performance is compared with the cumulative sum method.     

A graph theoretic approach to multivariable control system design

A graph theoretic approach is described for the design of multivariable control for large systems as an alternative to geometric methods. An example is given f⊙r a distillation column to demonstrate the technique, with a particular reference to aspects of disturbance rejection and the possibilities for pole assignment.     

Fault diagnosis in dynamical systems: a graph theoretic approach

Fault diagnosis is a vital aspect in the design of operational control systems for large-scale systems with stringent requirements on safety and reliability. In this paper, we develop graph representations for the failure propagation in large-scale systems. Using this model, we present efficient algorithms for failure source identification for single and multiple faults, for diagnosis of faulty alarms, and for forewarning and fault simulation. All these algorithms are analysed for their worst-case complexities. The treatment is algorithmic and graph theoretic and no reference is made to the underlying physical systems.     

Designing free software samples: a game theoretic approach

We develop a vertical differentiation game-theoretic model that addresses the issue of designing free software samples (shareware) for attaining follow-on sales. When shareware can be reinstalled, cannibalization of sales of the commercial product may ensue. We analyze the optimal design of free software according to two characteristics: the evaluation period allotted for sampling (potentially renewable) and the proportion of features included in the sample. We introduce a new software classification scheme based on the characteristics of the sample that aid consumer learning. We find that the optimal combination of features and trial time greatly depends on the category of software within the classification scheme. Under alternative learning scenarios, we show that the monopolist may be better off not suppressing potential shareware reinstallation.

Nonlinear state estimation for suspension control applications: a Takagi-Sugeno Kalman filtering approach

A new nonlinear state estimation approach, which combines classical Kalman filter theory and Takagi-Sugeno (TS) modeling, is proposed in this paper. To ensure convergence of the TS observer, conditions are derived that explicitly account for the TS model's confined region of validity. Thereby, the secured domain of attraction (DA) of the TS error dynamics is maximized within given bounds. The TS Kalman filtering concept is then applied to a hybrid vehicle suspension configuration, whose nonlinear dynamics are exactly represented by a continuous-time TS system. The benefit of the novel estimation technique is analyzed in comparison with the well-known EKF and UKF variants in simulations and experiments of a passive and an actively controlled suspension configuration in a quarter-car set-up. Employing a real road profile as disturbance input, the TS Kalman filter shows the highest estimation quality of the concepts studied. Moreover, as its computational complexity adds up to only one third of the one involved with the classical methods, the new approach operates remarkably efficient.     

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.