Neural Network Based Optimal Control with Constraints

In the present paper the problems of the optimal control of systems when constraints are imposed on the control is considered. The optimality conditions are given in the form of Pontryagin’s maximum principle. The obtained piecewise linear function is approximated by using feedforward neural network. A numerical example is given.

Optimal Control of a Second Order Parabolic Heat Equation

In this paper, we are concerned with the optimal control boundary control of a second order parabolic heat equation. Using the results in [Evtushenko, 1997] and spatial central finite difference with diagonally implicit Runge-Kutta method (DIRK) is applied to solve the parabolic heat equation. The conjugate gradient method (CGM) is applied to solve the distributed control problem. Numerical results are reported.

A Gradient-Type Optimization Technique for the Optimal Control for Schrodinger Equations

In this paper, we are considered with the optimal control of a schrodinger equation. Based on the formulation for the variation of the cost functional, a gradient-type optimization technique utilizing the finite difference method is then developed to solve the constrained optimization problem. Finally, a numerical example is given and the results show that the method of solution is robust.

Notes on the Solution of Dynamic Optimization Problems with Explicit Controls in Discrete-Time Economic Models

Йордан Йорданов, Андрей Василев - В работата се изследват методи за решаването на задачи на оптималното управление в дискретно време с безкраен хоризонт и явни управления. Дадена е обосновка на една процедура за решаване на такива задачи, базирана на множители на Лагранж, коята често се употребява в икономическата литература. Извеждени са необходимите условия за оптималност на базата на уравнения на Белман и са приведени достатъчни условия за оптималност при допускания, които често се използват в икономиката.

Optimal Control of Heterogeneous Systems

Цветомир Цачев - В настоящия доклад се прави преглед на някои резултати от областта на оптималното управление на непрекъснатите хетерогенни системи, публикувани в периодичната научна литература в последните години. Една динамична система се нарича хетерогенна, ако всеки от нейните елементи има собствена динамиката. Тук разглеждаме оптимално управление на системи, чиято хетерогенност се описва с едномерен или двумерен параметър – на всяка стойност на параметъра отговаря съответен елемент на системата. Хетерогенните динамични системи се използват за моделиране на процеси в икономиката, епидемиологията, биологията, опазване на обществената сигурност (ограничаване на използването на наркотици) и др. Тук разглеждаме модел на оптимално инвестиране в образование на макроикономическо ниво [11], на ограничаване на последствията от разпространението на СПИН [9], на пазар на права за въглеродни емисии [3, 4] и на оптимален макроикономически растеж при повишаване на нивото на върховите технологии [1]. Ключови думи: оптимално управление, непрекъснати хетерогенни динамични системи, приложения в икономиката и епидемиолегията

A novel near real-time quality-control procedure for radiometric profiles measured by Bio-Argo floats: protocols and performances

An array of Bio-Argo floats equipped with radiometric sensors has been recently deployed in various open ocean areas representative of the diversity of trophic and bio-optical conditions prevailing in the so-called Case 1 waters. Around solar noon and almost everyday, each float acquires 0-250 m vertical profiles of Photosynthetically Available Radiation and downward irradiance at three wavelengths (380, 412 and 490 nm). Up until now, more than 6500 profiles for each radiometric channel have been acquired. As these radiometric data are collected out of operator’s control and regardless of meteorological conditions, specific and automatic data processing protocols have to be developed. Here, we present a data quality-control procedure aimed at verifying profile shapes and providing near real-time data distribution. This procedure is specifically developed to: 1) identify main issues of measurements (i.e. dark signal, atmospheric clouds, spikes and wave-focusing occurrences); 2) validate the final data with a hierarchy of tests to ensure a scientific utilization. The procedure, adapted to each of the four radiometric channels, is designed to flag each profile in a way compliant with the data management procedure used by the Argo program. Main perturbations in the light field are identified by the new protocols with good performances over the whole dataset. This highlights its potential applicability at the global scale. Finally, the comparison with modeled surface irradiances allows assessing the accuracy of quality-controlled measured irradiance values and identifying any possible evolution over the float lifetime due to biofouling and instrumental drift.

A novel near real-time quality-control procedure for radiometric profiles measured by Bio-Argo floats: protocols and performances

An array of Bio-Argo floats equipped with radiometric sensors has been recently deployed in various open ocean areas representative of the diversity of trophic and bio-optical conditions prevailing in the so-called Case 1 waters. Around solar noon and almost everyday, each float acquires 0-250 m vertical profiles of Photosynthetically Available Radiation and downward irradiance at three wavelengths (380, 412 and 490 nm). Up until now, more than 6500 profiles for each radiometric channel have been acquired. As these radiometric data are collected out of operator’s control and regardless of meteorological conditions, specific and automatic data processing protocols have to be developed. Here, we present a data quality-control procedure aimed at verifying profile shapes and providing near real-time data distribution. This procedure is specifically developed to: 1) identify main issues of measurements (i.e. dark signal, atmospheric clouds, spikes and wave-focusing occurrences); 2) validate the final data with a hierarchy of tests to ensure a scientific utilization. The procedure, adapted to each of the four radiometric channels, is designed to flag each profile in a way compliant with the data management procedure used by the Argo program. Main perturbations in the light field are identified by the new protocols with good performances over the whole dataset. This highlights its potential applicability at the global scale. Finally, the comparison with modeled surface irradiances allows assessing the accuracy of quality-controlled measured irradiance values and identifying any possible evolution over the float lifetime due to biofouling and instrumental drift.

Optimal control of affine connection control systems from the point of view of Lie algebroids

The purpose of this paper is to use the framework of Lie algebroids to study optimal control problems for affine connection control systems (ACCSs) on Lie groups. In this context, the equations for critical trajectories of the problem are geometrically characterized as a Hamiltonian vector field.

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.

Recommendations for in-situ data Near Real Time Quality Control

With the construction of operational oceanography systems, the need for real-time has become more and more important. A lot of work had been done in the past, within National Data Centres (NODC) and International Oceanographic Data and Information Exchange (IODE) to standardise delayed mode quality control procedures. Concerning such quality control procedures applicable in real-time (within hours to a maximum of a week from acquisition), which means automatically, some recommendations were set up for physical parameters but mainly within projects without consolidation with other initiatives. During the past ten years the EuroGOOS community has been working on such procedures within international programs such as Argo, OceanSites or GOSUD, or within EC projects such as Mersea, MFSTEP, FerryBox, ECOOP, and MyOcean. In collaboration with the FP7 SeaDataNet project that is standardizing the delayed mode quality control procedures in NODCs, and MyOcean GMES FP7 project that is standardizing near real time quality control procedures for operational oceanography purposes, the DATA-MEQ working group decided to put together this document to summarize the recommendations for near real-time QC procedures that they judged mature enough to be advertised and recommended to EuroGOOS.

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.

Copernicus In Situ TAC, Real Time Quality Control for WAVES

In April 2017, CMEMS plans to launch the WAVES NRT products. This document is focused in the automatic RTQC of the collected wave data. The validation procedure includes the delayed mode quality control of the data and will be specified in another guideline. To perform any kind of quality control to wave data, first it’s necessary to know the nature of the measurements and the analysis performed to those measurements to obtain the wave parameters. For that reason next chapter is dedicated to show the usual wave analysis and the different parameters and estimators obtained.

Single network adaptive critic design for power system stabilisers

The recently developed single network adaptive critic (SNAC) design has been used in this study to design a power system stabiliser (PSS) for enhancing the small-signal stability of power systems over a wide range of operating conditions. PSS design is formulated as a discrete non-linear quadratic regulator problem. SNAC is then used to solve the resulting discrete-time optimal control problem. SNAC uses only a single critic neural network instead of the action-critic dual network architecture of typical adaptive critic designs. SNAC eliminates the iterative training loops between the action and critic networks and greatly simplifies the training procedure. The performance of the proposed PSS has been tested on a single machine infinite bus test system for various system and loading conditions. The proposed stabiliser, which is relatively easier to synthesise, consistently outperformed stabilisers based on conventional lead-lag and linear quadratic regulator designs.

New developments in batch process input profile optimisation

A novel algorithm for solving nonlinear discrete time optimal control problems with model-reality differences is presented. The technique uses dynamic integrated system optimisation and parameter estimation (DISOPE) which achieves the correct optimal solution in spite of deficiencies in the mathematical model employed in the optimisation procedure. A new method for approximating some Jacobian trajectories required by the algorithm is introduced. It is shown that the iterative procedure associated with the algorithm naturally suits applications to batch chemical processes.