The Herglotz variational problem on spheres and its optimal control approach

The main goal of this paper is to extend the generalized variational problem of Herglotz type to the more general context of the Euclidean sphere S^n. Motivated by classical results on Euclidean spaces, we derive the generalized Euler-Lagrange equation for the corresponding variational problem defined on the Riemannian manifold S^n. Moreover, the problem is formulated from an optimal control point of view and it is proved that the Euler-Lagrange equation can be obtained from the Hamiltonian equations. It is also highlighted the geodesic problem on spheres as a particular case of the generalized Herglotz problem.

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.

H-infinity control design for time-delay linear systems: a rational transfer function based approach

The aim of this paper is to present new results on H-infinity control synthesis for time-delay linear systems. We extend the use of a finite order LTI system, called comparison system to H-infinity analysis and design. Differently from what can be viewed as a common feature of other control design methods available in the literature to date, the one presented here treats time-delay systems control design with classical numeric routines based on Riccati equations arisen from H-infinity theory. The proposed algorithm is simple, efficient and easy to implement. Some examples illustrating state and output feedback design are solved and discussed in order to put in evidence the most relevant characteristic of the theoretical results. Moreover, a practical application involving a 3-DOF networked control system is presented.

AN ENERGY BASED MINIMUM-TIME OPTIMAL CONTROL OF DC-DC CONVERTERS

Time-optimal response is an important and sometimes necessary characteristic of dynamic systems for specific applications. Power converters are widely used in different electrical systems and their dynamic response will affect the whole system. In many electrical systems like microgrids or voltage regulators which supplies sensitive loads fast dynamic response is a must. Minimum time is the fastest converter to compensate the step output reference or load change. Boost converters as one of the wildly used power converters in the electrical systems are aimed to be controlled in optimal time in this study. Linear controllers are not able to provide the optimal response for a boost converter however they are still useful and functional for other applications like reference tracking or stabilization. To obtain the fastest possible response from boost converters, a nonlinear control approach based on the total energy of the system is studied in this research. Total energy of the system considers as the basis for developing the presented method, since it is easy and accurate to measure besides that the total energy of the system represents the actual operating condition of the boost converter. The detailed model of a boost converter is simulated in MATLAB/Simulink to achieve the time optimal response of the boost converter by applying the developed method. The simulation results confirmed the ability of the presented method to secure the time optimal response of the boost converter under four different scenarios.

Optimal control of non-linear systems through hybrid cell-mapping/artificial-neural-networks techniques

In this paper, a real-time optimal control technique for non-linear plants is proposed. The control system makes use of the cell-mapping (CM) techniques, widely used for the global analysis of highly non-linear systems. The CM framework is employed for designing approximate optimal controllers via a control variable discretization. Furthermore, CM-based designs can be improved by the use of supervised feedforward artificial neural networks (ANNs), which have proved to be universal and efficient tools for function approximation, providing also very fast responses. The quantitative nature of the approximate CM solutions fits very well with ANNs characteristics. Here, we propose several control architectures which combine, in a different manner, supervised neural networks and CM control algorithms. On the one hand, different CM control laws computed for various target objectives can be employed for training a neural network, explicitly including the target information in the input vectors. This way, tracking problems, in addition to regulation ones, can be addressed in a fast and unified manner, obtaining smooth, averaged and global feedback control laws. On the other hand, adjoining CM and ANNs are also combined into a hybrid architecture to address problems where accuracy and real-time response are critical. Finally, some optimal control problems are solved with the proposed CM, neural and hybrid techniques, illustrating their good performance.

Switching-off in a minimal time a fitzhugh-nagumo system

This paper deals with a system that describes an electrical circuitcomposed by a linear system coupled to a nonlinear one involving a tunneldiode in a flush-and-fill circuit. One of the most comprehensive models for thiskind of circuits was introduced by R. Fitzhugh in 1961, when taking on carebiological tasks. The equation has in its phase plane only two periodic solutions,namely, the unstable singular point S0 and the stable cycle Γ. If the system isat rest on S0, the natural flow of orbits seeks to switch-on the process by going- as time goes by - toward its steady-state, Γ. By using suitable controls it ispossible to reverse such natural tendency going in a minimal time from Γ toS0, switching-off in this way the system. To achieve this goal it is mandatorya minimal enough strength on controls. These facts will be shown by means ofconsiderations on the null control sets in the process.

Shock control bump design optimization on Natural Laminar Aerofoil

The chapter investigates Shock Control Bumps (SCB) on a Natural Laminar Flow (NLF) aerofoil; RAE 5243 for Active Flow Control (AFC). A SCB approach is used to decelerate supersonic flow on the suction/pressure sides of transonic aerofoil that leads delaying shock occurrence or weakening of shock strength. Such an AFC technique reduces significantly the total drag at transonic speeds. This chapter considers the SCB shape design optimisation at two boundary layer transition positions (0 and 45%) using an Euler software coupled with viscous boundary layer effects and robust Evolutionary Algorithms (EAs). The optimisation method is based on a canonical Evolution Strategy (ES) algorithm and incorporates the concepts of hierarchical topology and parallel asynchronous evaluation of candidate solution. Two test cases are considered with numerical experiments; the first test deals with a transition point occurring at the leading edge and the transition point is fixed at 45% of wing chord in the second test. Numerical results are presented and it is demonstrated that an optimal SCB design can be found to significantly reduce transonic wave drag and improves lift on drag (L/D) value when compared to the baseline aerofoil design.

Optimal-stopping control for airborne collision avoidance and return-to-course flight

This paper considers an aircraft collision avoidance design problem that also incorporates design of the aircraft’s return-to-course flight. This control design problem is formulated as a non-linear optimal-stopping control problem; a formulation that does not require a prior knowledge of time taken to perform the avoidance and return-to-course manoeuvre. A dynamic programming solution to the avoidance and return-to-course problem is presented, before a Markov chain numerical approximation technique is described. Simulation results are presented that illustrate the proposed collision avoidance and return-to-course flight approach.

Optimal dynamic inversion-based semi-active control of benchmark bridge using MR dampers

A new two-stage state feedback control design approach has been developed to monitor the voltage supplied to magnetorheological (MR) dampers for semi-active vibration control of the benchmark highway bridge. The first stage contains a primary controller, which provides the force required to obtain a desired closed-loop response of the system. In the second stage, an optimal dynamic inversion (ODI) approach has been developed to obtain the amount of voltage to be supplied to each of the MR dampers such that it provides the required force prescribed by the primary controller. ODI is formulated by optimization with dynamic inversion, such that an optimal voltage is supplied to each damper in a set. The proposed control design has been simulated for both phase-I and phase-II study of the recently developed benchmark highway bridge problem. The efficiency of the proposed controller is analyzed in terms of the performance indices defined in the benchmark problem definition. Simulation results demonstrate that the proposed approach generally reduces peak response quantities over those obtained from the sample semi-active controller, although some response quantities have been seen to be increasing. Overall, the proposed control approach is quite competitive as compared with the sample semi-active control approach.

Continuous-time Single Network Adaptive Critic for Regulator Design of Nonlinear Control Affine Systems

An optimal control law for a general nonlinear system can be obtained by solving Hamilton-Jacobi-Bellman equation. However, it is difficult to obtain an analytical solution of this equation even for a moderately complex system. In this paper, we propose a continuoustime single network adaptive critic scheme for nonlinear control affine systems where the optimal cost-to-go function is approximated using a parametric positive semi-definite function. Unlike earlier approaches, a continuous-time weight update law is derived from the HJB equation. The stability of the system is analysed during the evolution of weights using Lyapunov theory. The effectiveness of the scheme is demonstrated through simulation examples.

Optimal glycaemic control, pre-eclampsia and gestational hypertension in women with type 1 diabetes in the Diabetes and Pre-Eclampsia Intervention Trial

OBJECTIVE
To assess the relationship between glycemic control, pre-eclampsia, and gestational hypertension in women with type 1 diabetes.

RESEARCH DESIGN AND METHODS
Pregnancy outcome (pre-eclampsia or gestational hypertension) was assessed prospectively in 749 women from the randomized controlled Diabetes and Pre-eclampsia Intervention Trial (DAPIT). HbA1c (A1C) values were available up to 6 months before pregnancy (n = 542), at the first antenatal visit (median 9 weeks) (n = 721), at 26 weeks’ gestation (n = 592), and at 34 weeks’ gestation (n = 519) and were categorized as optimal (<6.1%: referent), good (6.1–6.9%), moderate (7.0–7.9%), and poor (=8.0%) glycemic control, respectively.

RESULTS
Pre-eclampsia and gestational hypertension developed in 17 and 11% of pregnancies, respectively. Women who developed pre-eclampsia had significantly higher A1C values before and during pregnancy compared with women who did not develop pre-eclampsia (P < 0.05, respectively). In early pregnancy, A1C =8.0% was associated with a significantly increased risk of pre-eclampsia (odds ratio 3.68 [95% CI 1.17–11.6]) compared with optimal control. At 26 weeks’ gestation, A1C values =6.1% (good: 2.09 [1.03–4.21]; moderate: 3.20 [1.47–7.00]; and poor: 3.81 [1.30–11.1]) and at 34 weeks’ gestation A1C values =7.0% (moderate: 3.27 [1.31–8.20] and poor: 8.01 [2.04–31.5]) significantly increased the risk of pre-eclampsia compared with optimal control. The adjusted odds ratios for pre-eclampsia for each 1% decrement in A1C before pregnancy, at the first antenatal visit, at 26 weeks’ gestation, and at 34 weeks’ gestation were 0.88 (0.75–1.03), 0.75 (0.64–0.88), 0.57 (0.42–0.78), and 0.47 (0.31–0.70), respectively. Glycemic control was not significantly associated with gestational hypertension.

CONCLUSIONS
Women who developed pre-eclampsia had significantly higher A1C values before and during pregnancy. These data suggest that optimal glycemic control both early and throughout pregnancy may reduce the risk of pre-eclampsia in women with type 1 diabetes.

On an Optimal Linear Control Applied to a Non-Ideal Load Transportation System, Modeled with Periodic Coefficients

In this paper, a load transportation system in platforms or suspended by cables is considered. It is a monorail device and is modelled as an inverted pendulum built on a car driven by a DC motor. The governing equations of motion were derived via Lagrange's equations. In the mathematical model we consider the interaction between the DC motor and the dynamical system, that is, we have a so-called non-ideal periodic problem. The problem is analysed and we also developed an optimal linear control design to stabilize the problem.

Architectures and design patterns for functional design of logic control and diagnostics in industrial automation

Recently in most of the industrial automation process an ever increasing degree of automation has been observed. This increasing is motivated by the higher requirement of systems with great performance in terms of quality of products/services generated, productivity, efficiency and low costs in the design, realization and maintenance. This trend in the growth of complex automation systems is rapidly spreading over automated manufacturing systems (AMS), where the integration of the mechanical and electronic technology, typical of the Mechatronics, is merging with other technologies such as Informatics and the communication networks. An AMS is a very complex system that can be thought constituted by a set of flexible working stations, one or more transportation systems. To understand how this machine are important in our society let considerate that every day most of us use bottles of water or soda, buy product in box like food or cigarets and so on. Another important consideration from its complexity derive from the fact that the the consortium of machine producers has estimated around 350 types of manufacturing machine. A large number of manufacturing machine industry are presented in Italy and notably packaging machine industry,in particular a great concentration of this kind of industry is located in Bologna area; for this reason the Bologna area is called “packaging valley”. Usually, the various parts of the AMS interact among them in a concurrent and asynchronous way, and coordinate the parts of the machine to obtain a desiderated overall behaviour is an hard task. Often, this is the case in large scale systems, organized in a modular and distributed manner. Even if the success of a modern AMS from a functional and behavioural point of view is still to attribute to the design choices operated in the definition of the mechanical structure and electrical electronic architecture, the system that governs the control of the plant is becoming crucial, because of the large number of duties associated to it. Apart from the activity inherent to the automation of themachine cycles, the supervisory system is called to perform other main functions such as: emulating the behaviour of traditional mechanical members thus allowing a drastic constructive simplification of the machine and a crucial functional flexibility; dynamically adapting the control strategies according to the different productive needs and to the different operational scenarios; obtaining a high quality of the final product through the verification of the correctness of the processing; addressing the operator devoted to themachine to promptly and carefully take the actions devoted to establish or restore the optimal operating conditions; managing in real time information on diagnostics, as a support of the maintenance operations of the machine. The kind of facilities that designers can directly find on themarket, in terms of software component libraries provides in fact an adequate support as regard the implementation of either top-level or bottom-level functionalities, typically pertaining to the domains of user-friendly HMIs, closed-loop regulation and motion control, fieldbus-based interconnection of remote smart devices. What is still lacking is a reference framework comprising a comprehensive set of highly reusable logic control components that, focussing on the cross-cutting functionalities characterizing the automation domain, may help the designers in the process of modelling and structuring their applications according to the specific needs. Historically, the design and verification process for complex automated industrial systems is performed in empirical way, without a clear distinction between functional and technological-implementation concepts and without a systematic method to organically deal with the complete system. Traditionally, in the field of analog and digital control design and verification through formal and simulation tools have been adopted since a long time ago, at least for multivariable and/or nonlinear controllers for complex time-driven dynamics as in the fields of vehicles, aircrafts, robots, electric drives and complex power electronics equipments. Moving to the field of logic control, typical for industrial manufacturing automation, the design and verification process is approached in a completely different way, usually very “unstructured”. No clear distinction between functions and implementations, between functional architectures and technological architectures and platforms is considered. Probably this difference is due to the different “dynamical framework”of logic control with respect to analog/digital control. As a matter of facts, in logic control discrete-events dynamics replace time-driven dynamics; hence most of the formal and mathematical tools of analog/digital control cannot be directly migrated to logic control to enlighten the distinction between functions and implementations. In addition, in the common view of application technicians, logic control design is strictly connected to the adopted implementation technology (relays in the past, software nowadays), leading again to a deep confusion among functional view and technological view. In Industrial automation software engineering, concepts as modularity, encapsulation, composability and reusability are strongly emphasized and profitably realized in the so-calledobject-oriented methodologies. Industrial automation is receiving lately this approach, as testified by some IEC standards IEC 611313, IEC 61499 which have been considered in commercial products only recently. On the other hand, in the scientific and technical literature many contributions have been already proposed to establish a suitable modelling framework for industrial automation. During last years it was possible to note a considerable growth in the exploitation of innovative concepts and technologies from ICT world in industrial automation systems. For what concerns the logic control design, Model Based Design (MBD) is being imported in industrial automation from software engineering field. Another key-point in industrial automated systems is the growth of requirements in terms of availability, reliability and safety for technological systems. In other words, the control system should not only deal with the nominal behaviour, but should also deal with other important duties, such as diagnosis and faults isolations, recovery and safety management. Indeed, together with high performance, in complex systems fault occurrences increase. This is a consequence of the fact that, as it typically occurs in reliable mechatronic systems, in complex systems such as AMS, together with reliable mechanical elements, an increasing number of electronic devices are also present, that are more vulnerable by their own nature. The diagnosis problem and the faults isolation in a generic dynamical system consists in the design of an elaboration unit that, appropriately processing the inputs and outputs of the dynamical system, is also capable of detecting incipient faults on the plant devices, reconfiguring the control system so as to guarantee satisfactory performance. The designer should be able to formally verify the product, certifying that, in its final implementation, it will perform itsrequired function guarantying the desired level of reliability and safety; the next step is that of preventing faults and eventually reconfiguring the control system so that faults are tolerated. On this topic an important improvement to formal verification of logic control, fault diagnosis and fault tolerant control results derive from Discrete Event Systems theory. The aimof this work is to define a design pattern and a control architecture to help the designer of control logic in industrial automated systems. The work starts with a brief discussion on main characteristics and description of industrial automated systems on Chapter 1. In Chapter 2 a survey on the state of the software engineering paradigm applied to industrial automation is discussed. Chapter 3 presentes a architecture for industrial automated systems based on the new concept of Generalized Actuator showing its benefits, while in Chapter 4 this architecture is refined using a novel entity, the Generalized Device in order to have a better reusability and modularity of the control logic. In Chapter 5 a new approach will be present based on Discrete Event Systems for the problemof software formal verification and an active fault tolerant control architecture using online diagnostic. Finally conclusive remarks and some ideas on new directions to explore are given. In Appendix A are briefly reported some concepts and results about Discrete Event Systems which should help the reader in understanding some crucial points in chapter 5; while in Appendix B an overview on the experimental testbed of the Laboratory of Automation of University of Bologna, is reported to validated the approach presented in chapter 3, chapter 4 and chapter 5. In Appendix C some components model used in chapter 5 for formal verification are reported.

Efficient control of an autonomous underwater vehicle while accounting for thruster failure

This paper is concerned with the design and implementation of control strategies onto a test-bed vehicle with six degrees-of-freedom. We design our trajectories to be efficient in time and in power consumption. Moreover, we also consider cases when actuator failure can arise and discuss alternate control strategies in this situation. Our calculations are supplemented by experimental results.

Implementable efficient time and energy consumption trajectories design for an autonomous underwater vehicle

In this paper we consider the implementation of time and energy efficient trajectories onto a test-bed autonomous underwater vehicle. The trajectories are losely connected to the results of the application of the maximum principle to the controlled mechanical system. We use a numerical algorithm to compute efficient trajectories designed using geometric control theory to optimize a given cost function. Experimental results are shown for the time minimization problem.