Decompositional Method of Modal Synthesis at Controlling a MIMO-system with Feedback by State Derivatives

We propose an effective analytic method for solving the problem of modal control by output for a wide class of linear stationary systems in which the sum of inputs and outputs can be not only greater than or equal to, but also less than the dimension of state vector. The method is based on bringing modal control by output to modal observation with fewer inputs. At the same time, it is not necessary to additionally ensure the solvability of the connecting equation between the matrix of observer and the desired matrix of controller by output. The reduction is performed by constructing a generalized dual canonical form of control using the operations of block transposing and rank decomposition of matrices. The method significantly expands the class of systems for which an analytic solution exists, compared to the previously proposed approaches, since it is not rigidly tied to the control system dimension and also does not require mandatory zeroing of the column and obtaining a system with a single input. Based on the proposed method, a strict algorithm for analytic solution of problems from the considering class is formed. A simple and convenient necessary condition for the reducibility of modal control by output to modal observation with fewer inputs is also obtained, which allows evaluating the possibility of its analytic solution only by the form of original task. Examples of various order tasks of modal control by output in which the sum of inputs and outputs is less than or equal to the dimension of state vector are considered in symbolic form. A detailed analytic solution of the proposed examples demonstrates the effectiveness of the proposed approach practical application.

This paper deals with an inaccessible control problem for a discrete time linear fixed parameter system. It is well known that when the state vector is completely detectable, an optimal feedback control system can be constructed for the so-called linear quadratic problem, at least theoretically. When the state vector is not completely detectable, the problem is not so straightforward, and many different approaches or devices have been tried. In this paper, the state vector of the controlled system is restored by an observer in order to generate optimal control. Under some appropriate assumptions, the state vector is restored within at most v stages, where v is the quotient of n divided by m (n = dimension of state vector, m = dimension of output vector, with divisibility assumed in this paper). The design method for such an observer reduces to the design of a minimum stage regulator and is explained in detail in this paper. Finally, the characteristics of the feedback control system with an observer are examined numerically and compared with those of an optimal feedback control system with complete state detectability.

In this paper, we propose a vision-based simultaneous localization and map-building (SLAM) algorithm. SLAM problem asks the location of mobile robot in the unknown environments. Therefore, this problem is one of the most important processes of mobile robots in the outdoor operation. To solve this problem, Extended Kalman filter (EKF) is widely used. However, this filter requires computational power (<TEX>${\sim}O(N)$</TEX>, N is the dimension of state vector). To reduce the computational complexity, we applied compressed extended Kalman filter (CEKF) to stereo image sequence. Moreover, because the mobile robots operate in the outdoor environments, we should estimate full d.o.f.s of mobile robot. To evaluate proposed SLAM algorithm, we performed the outdoor experiments. The experiment was performed by using new wheeled type mobile robot, Robhaz-6W. The performance results of CEKF SLAM are presented.

A general data fusion framework for distributed sensor systems of arbitrary redundancies is presented. By a general framework, we mean that the proposed method, referred to here as Covariance Extension (CE) Method, is able to directly fuse different dimensions of state vectors as well as constraints without additional processing. For instance, well-known Bar-Shalom Campo and Millman's formulae for the fusion of 2 and N correlated sensors, respectively, cannot properly handle state vectors of unequal dimensions. The proposed CE Method aggregates all the state vectors into a single vector in an extended space and transforms data fusion as a problem of satisfying the constraints among state vectors in the extended space. Specifically, the method orthogonally projects the mean and covariance of the aggregated state vectors on the equality constraint manifold in the extended space. The proposed CE Method is proven to be optimal in the sense of Minimum Mean Square Error (MMSE), while providing computational efficiency over Millman's formula. Simulation results shows the robust nature and effectiveness of the proposed method.

Since the raw pseudorange and pseudorange rate are taken as the measurements, the measurement equation of the tightly coupled SINS/GPS integrated navigation system is nonlinear. As a typical non-linear filtering algorithm, the Extended Kalman Filtering (EKF) linearizes the measurements and has high estimation accuracy in the tightly coupled SINS/GPS integrated navigation system. The state vector of the tightly coupled SINS/GPS integrated navigation system includes the states of two subsystems, therefore the dimension of the state vector is high. The dimension of the measurement vector depends on the number of received satellite signals. If many satellite signals are received, the dimension of the measurement vector is high. The high dimensions of the state vector and measurement vector will result in large computation load for the EKF. To solve this problem, this paper proposes an optimized filtering scheme based on the two-stage Kalman filtering and sequential Kalman filtering. In that case, the estimation accuracy is not seriously affected while the computation load is significantly reduced. The semi-physical simulation results prove the estimation accuracy of the proposed optimized filtering scheme.

Enhancing network lifespan in wireless sensor networks using deep learning based Graph Neural Network

The commercial incentives to obtain improved control of the steelmaking process in the electric-arc furnace are presented, and the progress made in applying computer control is reviewed. The development of a mathematical model of the refining process is shown to be restricted by the complex metallurgical nature of the process and the deficiency of existing plant instrumentation. The ability of a mathematical model, evolved from theoretical considerations, to simulate, accurately, a limited class of operating practice is demonstrated. A compromise between complexity and implied certainty of the model is obtained by a reduction in the dimension of the model state vector, and by the introduction of a white-Gaussian-noise process to account for the effect of the ignored states and the hypotheses on which the model is developed. Techniques developed recently for obtaining noisecorrupted measurements of the carbon content and temperature of the process are investigated, and the statistics of the uncertainty of these measurements is determined. The implementation of the extended Kalman filter for online state estimation is considered, and the operation of the filter under varied conditions of uncertainty is discussed. A technique for controlling divergence of the filter algorithm is presented, and the results of simulations indicate that estimates of the states can be obtained to the accuracy required for the design of a refining control strategy.

Abstract. Numerical models solved on adaptive moving meshes have become increasingly prevalent in recent years. Motivating problems include the study of fluids in a Lagrangian frame and the presence of highly localized structures such as shock waves or interfaces. In the former case, Lagrangian solvers move the nodes of the mesh with the dynamical flow; in the latter, mesh resolution is increased in the proximity of the localized structure. Mesh adaptation can include remeshing, a procedure that adds or removes mesh nodes according to specific rules reflecting constraints in the numerical solver. In this case, the number of mesh nodes will change during the integration and, as a result, the dimension of the model's state vector will not be conserved. This work presents a novel approach to the formulation of ensemble data assimilation (DA) for models with this underlying computational structure. The challenge lies in the fact that remeshing entails a different state space dimension across members of the ensemble, thus impeding the usual computation of consistent ensemble-based statistics. Our methodology adds one forward and one backward mapping step before and after the ensemble Kalman filter (EnKF) analysis, respectively. This mapping takes all the ensemble members onto a fixed, uniform reference mesh where the EnKF analysis can be performed. We consider a high-resolution (HR) and a low-resolution (LR) fixed uniform reference mesh, whose resolutions are determined by the remeshing tolerances. This way the reference meshes embed the model numerical constraints and are also upper and lower uniform meshes bounding the resolutions of the individual ensemble meshes. Numerical experiments are carried out using 1-D prototypical models: Burgers and Kuramoto–Sivashinsky equations and both Eulerian and Lagrangian synthetic observations. While the HR strategy generally outperforms that of LR, their skill difference can be reduced substantially by an optimal tuning of the data assimilation parameters. The LR case is appealing in high dimensions because of its lower computational burden. Lagrangian observations are shown to be very effective in that fewer of them are able to keep the analysis error at a level comparable to the more numerous observers for the Eulerian case. This study is motivated by the development of suitable EnKF strategies for 2-D models of the sea ice that are numerically solved on a Lagrangian mesh with remeshing.

A NEW REDUCED-ORDER ADAPTIVE FILTER FOR STATE ESTIMATION IN HIGH DIMENSIONAL SYSTEMS

A Hierarchical Principle of the Control System Decomposition Based on Motion Separation

This paper introduces a new L-D measurement update algorithm. The new algorithm is superior to the conventional one when the ratio between the dimension of the state vector and the number of states directly related to the measurements is greater than one. The computational efficiency of the new algorithm is directly proportional to this ratio. The new algorithm is developed and discussed and its computation load is analyzed in comparison with the conventional L-D algorithm. An example demonstrates its efficiency. This measurement update algorithm together with recently introduced modified L-D propagation algorithm render an overall efficient L-D filtering scheme.

A New Reduced-Order Adaptive Filter for State Estimation in High Dimensional Systems

Computer implemented parameter search techniques for optimization problems have become useful engineering design tools over the past few years. Many, if not most of the techniques, are based on deterministic schemes which have inherent limitations when the system is nonlinear. Random search techniques have been suggested which propose to overcome some of the difficulties. References 1--3 give good general discussions of the merits of random techniques. Reference 4 develops an algorithm, based on random methods, to solve the difficult mixed two-point boundary value problem that results from an application of the Maximum Principle. The method was shown to be remarkably effective in solving a fairly complex fifth-order, nonlinear orbital-transfer problem. The purpose of this paper is to discuss the application of the random search algorithm to a still more complex problem to demonstrate its feasibility. The example chosen was the three-dimensional, large-angle, single-axis attitude acquisition control problem in which it is desired to minimize fuel expenditure to accomplish the acquisition. The equations are highly nonlinear since small angle assumptions cannot be made; the control torques are assumed to be limited. This problem is more complex than the orbit-transfer problem in that the dimension of the state vector is greater by 1 and the number of degrees of freedom allowed the control action is greater. The same acquisition problem was discussed in Reference 5 but a proportional control law was assumed. A random parameter search was used in that paper to find the optimal set of feedback constants for the given control system structure so as to minimize system performance (fuel). Systems performances will be compared to indicate the striking improvement in performance with optimal nonlinear control.

Developing efficient and accurate algorithms for chemistry integration is a challenging task due to its strong stiffness and high dimensionality. The current work presents a deep learning-based numerical method called DeepCombustion0.0 to solve stiff ordinary differential equation systems. The homogeneous autoignition of DME/air mixture, including 54 species, is adopted as an example to illustrate the validity and accuracy of the algorithm. The training and testing datasets cover a wide range of temperature, pressure, and mixture conditions between 750-1200 K, 30-50 atm, and equivalence ratio = 0.7-1.5. Both the first-stage low-temperature ignition (LTI) and the second-stage high-temperature ignition (HTI) are considered. The methodology highlights the importance of the adaptive data sampling techniques, power transform preprocessing, and binary deep neural network (DNN) design. By using the adaptive random samplings and appropriate power transforms, smooth submanifolds in the state vector phase space are observed, on which two three-layer DNNs can be appropriately trained. The neural networks are end-to-end, which predict temporal gradients of the state vectors directly. The results show that temporal evolutions predicted by DNN agree well with traditional numerical methods in all state vector dimensions, including temperature, pressure, and species concentrations. Besides, the ignition delay time differences are within 1%. At the same time, the CPU time is reduced by more than 20 times and 200 times compared with the HMTS and VODE method, respectively. The current work demonstrates the enormous potential of applying the deep learning algorithm in chemical kinetics and combustion modeling.

The impact of unknown or poorly modeled correlations in an integrated navigation system that uses a bank of filters (local filters) is analyzed. Such architectures are expected to be more prevalent in future multi-senor navigation systems, in order to successfully apply these systems to safety-critical applications. To this end, the continuity and integrity performance of such filters is analyzed. Analysis and Monte Carlo simulations are used to asses and characterize the impact of the number of local filters, state vector dimensions and magnitude of correlation between the local filters on the false alarm rate and protection levels observed in the fused solution. It is shown that poorly modeled inter-filter correlations can lead to higher false alarm rates than expected and errors in protection level calculations, hence increasing the integrity and continuity risk in the system. To mitigate this impact, a protection level overbounding method is proposed and demonstrated to meet integrity requirements.