Image-based visual servoing with depth estimation

For the depth estimation problem in the image-based visual servoing (IBVS) control, this paper proposes a new observer structure based on Kalman filter (KF) to recover the feature depth in real time. First, according to the number of states, two different mathematical models of the system are established. The first one is to extract the depth information from the Jacobian matrix as the state vector of the system. The other is to use the depth information and the coordinate point information of the two-dimensional image plane as the state vector of the system. The KF is used to estimate the unknown depth information of the system in real time. And an IBVS controller gain adjustment method for 6-degree-of-freedom (6-DOF) manipulator is obtained using fuzzy controller. This method can obtain the gain matrix by taking the depth and error information as the input of the fuzzy controller. Compared with the existing works, the proposed observer has less redundant motion while solving the Jacobian matrix depth estimation problem. At the same time, it will also be beneficial to reducing the time for the camera to reach the target. Conclusively, the experimental results of the 6-DOF robot with eye-in-hand configuration demonstrate the effectiveness and practicability of the proposed method.

DeepCME: A deep learning framework for computing solution statistics of the chemical master equation

Stochastic models of biomolecular reaction networks are commonly employed in systems and synthetic biology to study the effects of stochastic fluctuations emanating from reactions involving species with low copy-numbers. For such models, the Kolmogorov’s forward equation is called the chemical master equation (CME), and it is a fundamental system of linear ordinary differential equations (ODEs) that describes the evolution of the probability distribution of the random state-vector representing the copy-numbers of all the reacting species. The size of this system is given by the number of states that are accessible by the chemical system, and for most examples of interest this number is either very large or infinite. Moreover, approximations that reduce the size of the system by retaining only a finite number of important chemical states (e.g. those with non-negligible probability) result in high-dimensional ODE systems, even when the number of reacting species is small. Consequently, accurate numerical solution of the CME is very challenging, despite the linear nature of the underlying ODEs. One often resorts to estimating the solutions via computationally intensive stochastic simulations. The goal of the present paper is to develop a novel deep-learning approach for computing solution statistics of high-dimensional CMEs by reformulating the stochastic dynamics using Kolmogorov’s backward equation. The proposed method leverages superior approximation properties of Deep Neural Networks (DNNs) to reliably estimate expectations under the CME solution for several user-defined functions of the state-vector. This method is algorithmically based on reinforcement learning and it only requires a moderate number of stochastic simulations (in comparison to typical simulation-based approaches) to train the “policy function”. This allows not just the numerical approximation of various expectations for the CME solution but also of its sensitivities with respect to all the reaction network parameters (e.g. rate constants). We provide four examples to illustrate our methodology and provide several directions for future research.

Rare roll event modeling of unmanned catamaran

Статья посвящена вопросу моделирования редких событий, которые возникают при качке катамарана. Система управления автономного катамарана должна уметь распознавать нежелательные ситуации, которые могут привести к осуществлению редких событий. В данной статье приводится несколько методов, позволяющих проводить моделирование редких событий и делать оценку риска возникновения редкого события. Методы основываются на теории больших уклонений. Первый метод позволяет оценить возможные «ожидаемые потери» при достижении редкого события путём оценки скорости убывания вероятности компонентов вектора состояния в редком состоянии. Оценка осуществляется путём расчёта квазипотенциалов из аттрактора до порогового значения состояния. Второй метод позволяет оценить вероятность движения вдоль наиболее вероятной траектории к редкому событию. Оценка осуществляется путём сравнения вектора состояния с состояниями на наиболее вероятной траектории к редкому событию. Точность оценок зависит от вектора состояния. Приводится сравнение с результатами, полученными с помощью метода Монте-Карло. Указанные методы могут быть использованы для создания систем супервизорного управления и систем поддержки принятия решений при оценке рискованности совершения морских переходов. The article is devoted to the issue of modeling rare events that occur when a catamaran is pitching. The control system of an autonomous catamaran should be able to recognize undesirable situations that can lead to the rare events. This article provides several methods for modeling rare events and making estimation of risk of a rare event occurrence. The methods are based on the large deviations theory for dynamical systems. The first method allows to estimate possible losses via calculation of the probability decreasing rate of the state vector components in a rare state. The estimation is carried out by calculating the quasipotential from the state close to the attractor to the threshold state. The second method allows to estimate the probability of moving along the most likely trajectory to a rare event. The evaluation is carried out by comparing the studied state vector with the states on the most likely trajectory. The accuracy of the estimates depends on the studied state vector. A comparison with the results obtained using the Monte Carlo method. These methods can be used to create supervisory control systems and decision support systems when assessing the riskiness of sea navigation.

Two Simultaneous Leak Diagnosis in Pipelines Based on Input–Output Numerical Differentiation

This paper addresses the two simultaneous leak diagnosis problem in pipelines based on a state vector reconstruction as a strategy to improve water shortages in large cities by only considering the availability of the flow rate and pressure head measurements at both ends of the pipeline. The proposed algorithm considers the parameters of both leaks as new state variables with constant dynamics, which results in an extended state representation. By applying a suitable persistent input, an invertible mapping in x can be obtained as a function of the input and output, including their time derivatives of the third-order. The state vector can then be reconstructed by means of an algebraic-like observer through the computation of time derivatives using a Numerical Differentiation with Annihilatorsconsidering its inherent noise rejection properties. Experimental results showed that leak parameters were reconstructed with accuracy using a test bed plant built at Cinvestav Guadalajara.

Hydrological Concept Formation inside Long Short-Term Memory (LSTM) networks

Neural networks have been shown to be extremely effective rainfall-runoff models, where the river discharge is predicted from meteorological inputs. However, the question remains, what have these models learned? Is it possible to extract information about the learned relationships that map inputs to outputs? And do these mappings represent known hydrological concepts? Small-scale experiments have demonstrated that the internal states of Long Short-Term Memory Networks (LSTMs), a particular neural network architecture predisposed to hydrological modelling, can be interpreted. By extracting the tensors which represent the learned translation from inputs (precipitation, temperature) to outputs (discharge), this research seeks to understand what information the LSTM captures about the hydrological system. We assess the hypothesis that the LSTM replicates real-world processes and that we can extract information about these processes from the internal states of the LSTM. We examine the cell-state vector, which represents the memory of the LSTM, and explore the ways in which the LSTM learns to reproduce stores of water, such as soil moisture and snow cover. We use a simple regression approach to map the LSTM state-vector to our target stores (soil moisture and snow). Good correlations (R2 > 0.8) between the probe outputs and the target variables of interest provide evidence that the LSTM contains information that reflects known hydrological processes comparable with the concept of variable-capacity soil moisture stores. The implications of this study are threefold: 1) LSTMs reproduce known hydrological processes. 2) While conceptual models have theoretical assumptions embedded in the model a priori, the LSTM derives these from the data. These learned representations are interpretable by scientists. 3) LSTMs can be used to gain an estimate of intermediate stores of water such as soil moisture. While machine learning interpretability is still a nascent field, and our approach reflects a simple technique for exploring what the model has learned, the results are robust to different initial conditions and to a variety of benchmarking experiments. We therefore argue that deep learning approaches can be used to advance our scientific goals as well as our predictive goals.

Research of Divergence Trajectory with a Given Risk of Ships Collisions

There were considered the issues of the optimal collision avoidance in the target’s risk field. A method of optimal divergence by course maneuvering is proposed, which makes it possible to minimize the divergence trajectory for a given risk of collision and consists in organizing the movement of the vessel along the trajectory of a given risk. The risk field of the target is a normal distribution law characterized by the root-mean-square parameters of the uncertainties associated with measurement errors of the parameters of the vessel's state vector and target, errors of actuators, errors of the used mathematical models, errors of calculation, etc. The operability and efficiency of the proposed method, algorithmic and software were tested on the Imitation Modeling Stand, which is the Navi Trainer 5000 navigation simulator and a model of on-board controller included in its local network with the software of the risk divergence module. The Imitation Modeling Stand allows to work out the software of control systems, including the considered optimal divergence module, in a closed circuit with the Navi Trainer 5000 navigation simulator, using all its advantages.

Complete model-free siding mode control (CMFSMC)

This study presents a complete model-free sliding mode control (CMFSMC) framework for the control of continuous-time non-affine nonlinear dynamic systems with unknown models. The novelty lies in the introduction of two equalities to assign the derivative of the sliding functions, which generally bridges the designs of those model-based SMC and model-free SMC. The study includes a double SMC (DSMC) design, state observer design, and desired reference state vector design (whole system performance), which all do not require plant nominal models. The preconditions required in the CMFSMC are the plant dynamic order and the boundedness of plant and disturbances. U-model based control (U-control) is incorporated to configure the whole control system, that is (1) taking model-free double SMC as a robust dynamic inverter to cancel simultaneously both nonlinearity and dynamics of the underlying plants, (2) taking a model-free state observer to estimate the state vector, (3) taking invariant controller to specify the whole control system performance in a linear output feedback control and to provide desired reference state vector. The related properties are studied to support the concept/configuration development and the analytical formulations. Simulated case studies demonstrate the developed framework and show off the transparent design procedure for applications and expansions.

Application of Mini-Batch Metaheuristic Algorithms in Problems of Optimization of Deterministic Systems with Incomplete Information about the State Vector

In this paper, we consider the application of the zero-order mini-batch optimization method in the problem of finding optimal control of a pencil of trajectories of nonlinear deterministic systems in the case of incomplete information about the state vector. The pencil of trajectories originates from a given set of initial states. To solve the problem, the structure of a feedback system is proposed, which contains models of the plant, measuring system, nonlinear state observer and control law of the fixed structure with unknown coefficients. The objective function proposed considers the quality of pencil of trajectories control, which is estimated by the average value of the Bolz functional over the given set of initial states. Unknown control laws of a plant and an observer are found in the form of expansions in terms of orthonormal systems of basis functions, which are specified on the set of possible states of a dynamical system. The original pencil of trajectories control problem is reduced to a global optimization problem, which is solved using the well-proven zero-order method, which uses a modified mini-batch approach in a random search procedure with adaptation. An algorithm for solving the problem is proposed. The satellite stabilization problem with incomplete information is solved.

Kalman Filter Adaptation to Disturbances of the Observer’s Parameters

Currently, one of the most effective algorithms for state estimation of stochastic systems is a Kalman filter. This filter provides an optimal root-mean-square error in state vector estimation only when the parameters of the dynamic system and its observer are precisely known. In real conditions, the observer’s parameters are often inaccurately known; moreover, they change randomly over time. This in turn leads to the divergence of the Kalman estimation process. The problem is currently being solved in a variety of ways. They include the use of interval observers, the use of an extended Kalman filter, the introduction of an additional evaluating observer by nonlinear programming methods, robust scaling of the observer’s transmission coefficient, etc. At the same time, it should be borne in mind that, firstly, all of the above ways are focused on application in specific technical systems and complexes, and secondly, they fundamentally do not allow estimating errors in determining the parameters of the observer themselves in order to compensate them for further improving the accuracy and stability of the filtration process of the state vector. To solve this problem, this paper proposes the use of accurate observations that are irregularly received in a complex measuring system (for example, navigation) for adaptive evaluation of the observer’s true parameters of the stochastic system state vector. The development of the proposed algorithm is based on the analytical dependence of the Kalman estimate variation on the observer’s parameters disturbances obtained using the mathematical apparatus for the study of perturbed multidimensional dynamical systems. The developed algorithm for observer’s parameters adaptive estimation makes it possible to significantly increase the accuracy and stability of the stochastic estimation process as a whole in the time intervals between accurate observations, which is illustrated by the corresponding numerical example.