The Making of Optimal and Consistent Policy: An Implementation Theory Framework for Monetary Policy

This paper shows that optimal policy and consistent policy outcomes require the use of control-theory and game-theory solution techniques. While optimal policy and consistent policy often produce different outcomes even in a one-period model, we analyze consistent policy and its outcome in a simple model, finding that the cause of the inconsistency with optimal policy traces to inconsistent targets in the social loss function. As a result, the social loss function cannot serve as a direct loss function for the central bank. Accordingly, we employ implementation theory to design a central bank loss function (mechanism design) with consistent targets, while the social loss function serves as a social welfare criterion. That is, with the correct mechanism design for the central bank loss function, optimal policy and consistent policy become identical. In other words, optimal policy proves implementable (consistent).

Fuzzy Optimal Control for Double Inverted Pendulum

In this paper a fuzzy optimal control for stabilizing an upright position a double inverted pendulum (DIP) is developed and compared. Modeling is based on Euler-Lagrange equations. This results in a complicated nonlinear fast reaction, unstable multivariable system. Firstly, the mathematical models of double pendulum system are presented. The weight variable fuzzy input is gained by combining the fuzzy control theory with the optimal control theory. Simulation results show that the controller, which the upper pendulum is considered as main control variable, has high accuracy, quick convergence speed and higher precision.

In vivo regulation of muscle glycogen synthase and the control of glycogen synthesis.

The activity of glycogen synthase (GSase; EC 2.4.1.11) is regulated by covalent phosphorylation. Because of this regulation, GSase has generally been considered to control the rate of glycogen synthesis. This hypothesis is examined in light of recent in vivo NMR experiments on rat and human muscle and is found to be quantitatively inconsistent with the data under conditions of glycogen synthesis. Our first experiments showed that muscle glycogen synthesis was slower in non-insulin-dependent diabetics compared to normals and that their defect was in the glucose transporter/hexokinase (GT/HK) part of the pathway. From these and other in vivo NMR results a quantitative model is proposed in which the GT/HK steps control the rate of glycogen synthesis in normal humans and rat muscle. The flux through GSase is regulated to match the proximal steps by "feed forward" to glucose 6-phosphate, which is a positive allosteric effector of all forms of GSase. Recent in vivo NMR experiments specifically designed to test the model are analyzed by metabolic control theory and it is shown quantitatively that the GT/HK step controls the rate of glycogen synthesis. Preliminary evidence favors the transporter step. Several conclusions are significant: (i) glucose transport/hexokinase controls the glycogen synthesis flux; (ii) the role of covalent phosphorylation of GSase is to adapt the activity of the enzyme to the flux and to control the metabolite levels not the flux; (iii) the quantitative data needed for inferring and testing the present model of flux control depended upon advances of in vivo NMR methods that accurately measured the concentration of glucose 6-phosphate and the rate of glycogen synthesis.

On the necessary condition for optimal control of nonlinear systems.

"Prepared under contract Nonr-225(11) (NR-041-086) for Office of Naval Research."

Theory of mind and relational complexity

Cognitive complexity and control theory and relational complexity theory attribute developmental changes in theory of mind (TOM) to complexity. In 3 studies, 3-, 4-, and 5-year-olds performed TOM tasks (false belief, appearance-reality), less complex connections (Level 1 perspective-taking) tasks, and transformations tasks (understanding the effects of location changes and colored filters) with content similar to TOM. There were also predictor tasks at binary-relational and ternary-relational complexity levels, with different content. Consistent with complexity theories: (a) connections and transformations were easier and mastered earlier than TOM; (b) predictor tasks accounted for more than 80% of age-related variance in TOM; and (c) ternary-relational items accounted for TOM variance, before and after controlling for age and binary-relational items. Prediction did not require hierarchically structured predictor tasks.

Optimal unravellings for feedback control in linear quantum systems

For quantum systems with linear dynamics in phase space much of classical feedback control theory applies. However, there are some questions that are sensible only for the quantum case: Given a fixed interaction between the system and the environment what is the optimal measurement on the environment for a particular control problem? We show that for a broad class of optimal (state- based) control problems ( the stationary linear-quadratic-Gaussian class), this question is a semidefinite program. Moreover, the answer also applies to Markovian (current-based) feedback.

When do firms conform? The effect of regulatory control processes on compliance and opportunism

The authors use social control theory to develop a conceptual model that addresses the effectiveness of regulatory agencies’ (e.g., Food and Drug Administration, Occupational Safety and Health Administration) field-level efforts to obtain conformance with product safety laws. Central to the model are the control processes agencies use when monitoring organizations and enforcing the safety rules. These approaches can be labeled formal control (e.g., rigid enforcement) and informal control (e.g., social instruction). The theoretical framework identifies an important antecedent of control and the relative effectiveness of control’s alternative forms in gaining compliance and reducing opportunism. Furthermore, the model predicts that the regulated firms’ level of agreement with the safety rules moderates the relationships between control and firm responses. A local health department’s administration of state food safety regulations provides the empirical context for testing the hypotheses. The results from a survey of 173 restaurants largely support the proposed model. The study findings inform a discussion of effective methods of administering product safety laws. The authors use social control theory to develop a conceptual model that addresses the effectiveness of regulatory agencies’ (e.g., Food and Drug Administration, Occupational Safety and Health Administration) field-level efforts to obtain conformance with product safety laws. Central to the model are the control processes agencies use when monitoring organizations and enforcing the safety rules. These approaches can be labeled formal control (e.g., rigid enforcement) and informal control (e.g., social instruction). The theoretical framework identifies an important antecedent of control and the relative effectiveness of control’s alternative forms in gaining compliance and reducing opportunism. Furthermore, the model predicts that the regulated firms’ level of agreement with the safety rules moderates the relationships between control and firm responses. A local health department’s administration of state food safety regulations provides the empirical context for testing the hypotheses. The results from a survey of 173 restaurants largely support the proposed model. The study findings inform a discussion of effective methods of administering product safety laws.

Mathematical modelling and optimal multivariable control of chemical processes

This work reports the developnent of a mathenatical model and distributed, multi variable computer-control for a pilot plant double-effect climbing-film evaporator. A distributed-parameter model of the plant has been developed and the time-domain model transformed into the Laplace domain. The model has been further transformed into an integral domain conforming to an algebraic ring of polynomials, to eliminate the transcendental terms which arise in the Laplace domain due to the distributed nature of the plant model. This has made possible the application of linear control theories to a set of linear-partial differential equations. The models obtained have well tracked the experimental results of the plant. A distributed-computer network has been interfaced with the plant to implement digital controllers in a hierarchical structure. A modern rnultivariable Wiener-Hopf controller has been applled to the plant model. The application has revealed a limitation condition that the plant matrix should be positive-definite along the infinite frequency axis. A new multi variable control theory has emerged fram this study, which avoids the above limitation. The controller has the structure of the modern Wiener-Hopf controller, but with a unique feature enabling a designer to specify the closed-loop poles in advance and to shape the sensitivity matrix as required. In this way, the method treats directly the interaction problems found in the chemical processes with good tracking and regulation performances. Though the ability of the analytical design methods to determine once and for all whether a given set of specifications can be met is one of its chief advantages over the conventional trial-and-error design procedures. However, one disadvantage that offsets to some degree the enormous advantages is the relatively complicated algebra that must be employed in working out all but the simplest problem. Mathematical algorithms and computer software have been developed to treat some of the mathematical operations defined over the integral domain, such as matrix fraction description, spectral factorization, the Bezout identity, and the general manipulation of polynomial matrices. Hence, the design problems of Wiener-Hopf type of controllers and other similar algebraic design methods can be easily solved.

Design of a stock control methodology for use within an oil blending company

The thesis deals with the background, development and description of a mathematical stock control methodology for use within an oil and chemical blending company, where demand and replenishment lead-times are generally non-stationary. The stock control model proper relies on, as input, adaptive forecasts of demand determined for an economical forecast/replenishment period precalculated on an individual stock-item basis. The control procedure is principally that of the continuous review, reorder level type, where the reorder level and reorder quantity 'float', that is, each changes in accordance with changes in demand. Two versions of the Methodology are presented; a cost minimisation version and a service level version. Realising the importance of demand forecasts, four recognised variations of the Trigg and Leach adaptive forecasting routine are examined. A fifth variation, developed, is proposed as part of the stock control methodology. The results of testing the cost minimisation version of the Methodology with historical data, by means of a computerised simulation, are presented together with a description of the simulation used. The performance of the Methodology is in addition compared favourably to a rule-of-thumb approach considered by the Company as an interim solution for reducing stack levels. The contribution of the work to the field of scientific stock control is felt to be significant for the following reasons:- (I) The Methodology is designed specifically for use with non-stationary demand and for this reason alone appears to be unique. (2) The Methodology is unique in its approach and the cost-minimisation version is shown to work successfully with the demand data presented. (3) The Methodology and the thesis as a whole fill an important gap between complex mathematical stock control theory and practical application. A brief description of a computerised order processing/stock monitoring system, designed and implemented as a pre-requisite for the Methodology's practical operation, is presented as an appendix.

Fully probabilistic control design in an adaptive critic framework

Optimal stochastic controller pushes the closed-loop behavior as close as possible to the desired one. The fully probabilistic design (FPD) uses probabilistic description of the desired closed loop and minimizes Kullback-Leibler divergence of the closed-loop description to the desired one. Practical exploitation of the fully probabilistic design control theory continues to be hindered by the computational complexities involved in numerically solving the associated stochastic dynamic programming problem. In particular very hard multivariate integration and an approximate interpolation of the involved multivariate functions. This paper proposes a new fully probabilistic contro algorithm that uses the adaptive critic methods to circumvent the need for explicitly evaluating the optimal value function, thereby dramatically reducing computational requirements. This is a main contribution of this short paper.

Fuzzy Modeling and Control Based Virtual Machine Resource Management

Virtual machines (VMs) are powerful platforms for building agile datacenters and emerging cloud systems. However, resource management for a VM-based system is still a challenging task. First, the complexity of application workloads as well as the interference among competing workloads makes it difficult to understand their VMs’ resource demands for meeting their Quality of Service (QoS) targets; Second, the dynamics in the applications and system makes it also difficult to maintain the desired QoS target while the environment changes; Third, the transparency of virtualization presents a hurdle for guest-layer application and host-layer VM scheduler to cooperate and improve application QoS and system efficiency. This dissertation proposes to address the above challenges through fuzzy modeling and control theory based VM resource management. First, a fuzzy-logic-based nonlinear modeling approach is proposed to accurately capture a VM’s complex demands of multiple types of resources automatically online based on the observed workload and resource usages. Second, to enable fast adaption for resource management, the fuzzy modeling approach is integrated with a predictive-control-based controller to form a new Fuzzy Modeling Predictive Control (FMPC) approach which can quickly track the applications’ QoS targets and optimize the resource allocations under dynamic changes in the system. Finally, to address the limitations of black-box-based resource management solutions, a cross-layer optimization approach is proposed to enable cooperation between a VM’s host and guest layers and further improve the application QoS and resource usage efficiency. The above proposed approaches are prototyped and evaluated on a Xen-based virtualized system and evaluated with representative benchmarks including TPC-H, RUBiS, and TerraFly. The results demonstrate that the fuzzy-modeling-based approach improves the accuracy in resource prediction by up to 31.4% compared to conventional regression approaches. The FMPC approach substantially outperforms the traditional linear-model-based predictive control approach in meeting application QoS targets for an oversubscribed system. It is able to manage dynamic VM resource allocations and migrations for over 100 concurrent VMs across multiple hosts with good efficiency. Finally, the cross-layer optimization approach further improves the performance of a virtualized application by up to 40% when the resources are contended by dynamic workloads.

Quantum Gate and Quantum State Preparation through Neighboring Optimal Control

Successful implementation of fault-tolerant quantum computation on a system of qubits places severe demands on the hardware used to control the many-qubit state. It is known that an accuracy threshold Pa exists for any quantum gate that is to be used for such a computation to be able to continue for an unlimited number of steps. Specifically, the error probability Pe for such a gate must fall below the accuracy threshold: Pe < Pa. Estimates of Pa vary widely, though Pa ∼ 10−4 has emerged as a challenging target for hardware designers. I present a theoretical framework based on neighboring optimal control that takes as input a good quantum gate and returns a new gate with better performance. I illustrate this approach by applying it to a universal set of quantum gates produced using non-adiabatic rapid passage. Performance improvements are substantial comparing to the original (unimproved) gates, both for ideal and non-ideal controls. Under suitable conditions detailed below, all gate error probabilities fall by 1 to 4 orders of magnitude below the target threshold of 10−4. After applying the neighboring optimal control theory to improve the performance of quantum gates in a universal set, I further apply the general control theory in a two-step procedure for fault-tolerant logical state preparation, and I illustrate this procedure by preparing a logical Bell state fault-tolerantly. The two-step preparation procedure is as follow: Step 1 provides a one-shot procedure using neighboring optimal control theory to prepare a physical qubit state which is a high-fidelity approximation to the Bell state |β01⟩ = 1/√2(|01⟩ + |10⟩). I show that for ideal (non-ideal) control, an approximate |β01⟩ state could be prepared with error probability ϵ ∼ 10−6 (10−5) with one-shot local operations. Step 2 then takes a block of p pairs of physical qubits, each prepared in |β01⟩ state using Step 1, and fault-tolerantly prepares the logical Bell state for the C4 quantum error detection code.

Modeling, control and field tests on an experimental irrigation canal

Irrigation canals are complex hydraulic systems difficult to control. Many models and control strategies have already been developed using linear control theory. In the present study, a PI controller is developed and implemented in a brand new prototype canal and its features evaluated experimentally. The base model relies on the linearized Saint-Venant equations which is compared with a reservoir model to check its accuracy. This technique will prove its capability and versatility in tuning properly a controller for this kind of systems.

Feedback control of underactuated cable-driven parallel robots

In this work an Underactuated Cable-Driven Parallel Robot (UACDPR) that operates in the three dimensional Euclidean space is considered. The End-Effector has 6 degrees of freedom and is actuated by 4 cables, therefore from a mechanical point of view the robot is defined underconstrained. However, considering only three controlled pose variables, the degree of redundancy for the control theory can be considered one. The aim of this thesis is to design a feedback controller for a point-to-point motion that satisfies the transient requirements, and is capable of reducing oscillations that derive from the reduced number of constraints. A force control is chosen for the positioning of the End-Effector, and error with respect to the reference is computed through data measure of several sensors (load cells, encoders and inclinometers) such as cable lengths, tension and orientation of the platform. In order to express the relation between pose and cable tension, the inverse model is derived from the kinematic and dynamic model of the parallel robot. The intrinsic non-linear nature of UACDPRs systems introduces an additional level of complexity in the development of the controller, as a result the control law is composed by a partial feedback linearization, and damping injection to reduce orientation instability. The fourth cable allows to satisfy a further tension distribution constraint, ensuring positive tension during all the instants of motion. Then simulations with different initial conditions are presented in order to optimize control parameters, and lastly an experimental validation of the model is carried out, the results are analysed and limits of the presented approach are defined.

Robust model predictive controller with output feedback and target tracking

A model predictive controller (MPC) is proposed, which is robustly stable for some classes of model uncertainty and to unknown disturbances. It is considered as the case of open-loop stable systems, where only the inputs and controlled outputs are measured. It is assumed that the controller will work in a scenario where target tracking is also required. Here, it is extended to the nominal infinite horizon MPC with output feedback. The method considers an extended cost function that can be made globally convergent for any finite input horizon considered for the uncertain system. The method is based on the explicit inclusion of cost contracting constraints in the control problem. The controller considers the output feedback case through a non-minimal state-space model that is built using past output measurements and past input increments. The application of the robust output feedback MPC is illustrated through the simulation of a low-order multivariable system.