Admissible Region Research Articles

A New Reference Governor Strategy For Union of Linear Constraints

Classical scalar Reference Governor (RG) schemes require a convex admissible region. Recently, a novel scalar RG approach has been proposed for the case of nonconvex constraints that can be approximated as union of polyhedral sets. This new method, specifically developed for the charge control of lithium-ion batteries, shows good performance and the capability of handling these kind of constraints while keeping a very low computational footprint. However, this method can guarantee that the system will reach the desired set point only under very specific properties of the constraints. In this paper, we analyze these limitations and propose a solution that ensures convergence of the RG scheme under much milder conditions on the topology of the constraints.

Comparison of the Methods of Classical and Synergetic Theories of Control of the Movement Autonomous Underwater Machine

The article deals with the problem of nonlinear synthesis of the laws of motion control of an autonomous underwater vehicle (APA) in the vertical plane. The tasks of the synthesis are the output of the underwater vehicle to a predetermined depth at a given speed. Based on the non-linear mathematical model of the APA, the control laws are synthesized by two different approaches: using the classical automatic control theory method, the proportional-integral-differential controller (PID controller), and using the synergetic control theory, the analytical design method for aggregated regulators (ADAR). Classical methods of the theory of automatic control assume a linear or linearized mathematical description of controlled processes and scalar control, which cannot but affect the adequacy of the mathematical description of processes and the efficiency of the developed algorithms. Such structures are ineffective because they do not allow to obtain the necessary stability margin of the system and are approximate. In addition, the scalar control principle often limits the ability to effectively influence the system, ignoring potential control channels. The vector control principle used in the work allows to more effectively influence the system through various control channels. The assumed laws of synergetic control endow the object in question with properties of asymptotic stability in the entire admissible region of change of state variables.The results of computer simulation of the APA motion, which confirm the achievement of control goals, are considered.

Exact Channel Synthesis

We consider the exact channel synthesis problem. This problem concerns the determination of the minimum amount of information required to create exact correlation remotely when there is a certain rate of randomness shared by two terminals. This problem generalizes an existing approximate version, in which the generated joint distribution is required to be close to a target distribution under the total variation (TV) distance measure (instead being exactly equal to the target distribution). We provide single-letter inner and outer bounds on the admissible region of the shared randomness rate and the communication rate for the exact channel synthesis problem. These two bounds coincide for doubly symmetric binary sources. We observe that for such sources, the admissible rate region for exact channel synthesis is strictly included in that for the TV-approximate version. We also extend the exact and TV-approximate channel synthesis problems to sources with countably infinite alphabets and continuous sources; the latter includes Gaussian sources. As by-products, lemmas concerning soft-covering under Rényi divergence measures are derived.

Common Reconstructions in the Successive Refinement Problem With Receiver Side Information

We study a variant of the successive refinement problem with receiver side information in which the receivers require identical, matching reconstructions. We present general inner and outer bounds for the rate region for this variant of the problem and present a single-letter characterization of the admissible rate region for several classes of the joint distribution of the source and the side information. Unlike in the general successive refinement problem, the characterization of the admissible rate region in the cases when the derived inner and outer bounds match requires only one auxiliary random variable. The characterization reveals that the side information can be fully used to reduce the communication rates via binning; however, the receiver reconstruction functions can depend only on a certain Gacs–Korner common randomness between shared by the two receivers. Since the entropy of the Gacs–Korner common randomness between two random variables is a discontinuous function of joint distribution of the variables, we establish the fact that the admissible rate region for this variant of the successive refinement problem is discontinuous in the underlying distribution of the source and side information even though the problem formulation does not involve the zero-error or functional reconstruction constraints.

Lossy-Forward Relaying for Lossy Communications: Rate-Distortion and Outage Probability Analyses

This paper presents an in-depth performance analysis of lossy communications in a single-relay system, where the recovered information is not necessarily lossless in both the relay and the destination. In this system, the relay continues transmitting the sequence with source-relay (S-R) link errors to the destination even if errors are detected after decoding, i.e., so-called lossy-forward (LF) strategy. The problem can be decomposed into two parts as follows: a point-to-point coding problem in the S-R link and a lossy source coding problem with an LF relay in the source–destination (S–D) and a relay-destination (R-D) links. To begin with, we derive the admissible rate region of the lossy source coding problem with the LF relay for a specified distortion requirement. Then, we focus on the analysis of outage probability over block Rayleigh fading channels. Finally, a practical encoding/decoding scheme is proposed for the evaluation of system performance by computer simulations. Due to the suboptimal channel coding and incomplete utilization of joint typicality, the theoretical performance cannot be achieved in the simulation; however, the tendency of curves in simulations matches that in theoretical calculation.

Determination of the admissible region of asteroids with data from one night of observation

During the night of the discovery of an asteroid, a large number of images spaced in time, that represent an arc too short to propagate an orbit, are obtained. Initially, it is necessary to recover the body in the celestial vault to have more observations to determine its orbit. The first step in this process is to establish the admissible region, defined as the region in space where the object can be found. In this paper we present the calculation of the Admissible Regions from data from a single night observation, considering the geocentric and topocentric versions and restrictions such as belonging to the Solar System, the object does not belong to the Earth-Moon gravitational system, and the body is at a minimum distance from Earth. This procedure was applied in the calculation of the admissible regions of 2003 BH84, 3122 Florence, 3200 Phaethon, 555 Norma, 1738 Oosterhoff and 2006 SO375. The respective admissible regions were generated in their geocentric and topocentric variant, and the respective metric changes were made to visualize their geometric characteristics. It was found that the topocentric version generates a simpler geometry than the geocentric version, decreasing the re-observation area. It was identified that the logarithmic metric is appropriate for the study of regions near the Earth (NEO’s).

Invariant Adaptive Dynamic Programming for Discrete-Time Optimal Control

For systems that can only be locally stabilized, control laws and their effective regions are both important. In this paper, invariant policy iteration is proposed to solve the optimal control of discrete-time systems. At each iteration, a given policy is evaluated in its invariantly admissible region, and a new policy and a new region are updated for the next iteration. Theoretical analysis shows the method is regionally convergent to the optimal value and the optimal policy. Combined with sum-of-squares polynomials, the method is able to achieve the near-optimal control of a class of discrete-time systems. An invariant adaptive dynamic programming algorithm is developed to extend the method to scenarios where system dynamics is not available. Online data are utilized to learn the near-optimal policy and the invariantly admissible region. Simulated experiments verify the effectiveness of our method.

Nonlinear Estimation and Decision-Making Methods in Short Track Identification and Orbit Determination Problem

Typically, near-Earth space objects are observable for a small fraction of the orbit revolution. In this paper, we consider the problem of identification and fusion of two short optical tracks of near-Earth space objects, as well as the problem of estimation of the parameters of the corresponding orbits directly from these tracks in the absence of a priori information. The popular approach to solving these problems is based on admissible regions of orbital parameters, which is typically computationally demanding. It is shown that the solution of these problems does not require admissible regions and computationally and algorithmically difficult operations with admissible regions. A new, purely statistical method for solving these problems is proposed.

Mean-square stabilizability via output feedback for a non-minimum phase networked feedback system

This work studies mean-square stabilizability via output feedback for a networked linear time invariant (LTI) feedback system with a non-minimum phase plant. In the feedback system, the control signals are transmitted to the plant over a set of parallel communication channels with possible packet dropout. Our goal is to analytically describe intrinsic constraints among channel packet dropout probabilities and the plant’s characteristics in the mean-square stabilizability of the system. It turns out that this is a very hard problem. Here, we focus on the case in which the plant has relative degree one and each non-minimum zero of the plant is only associated with one of control input channels. Then, the admissible region of packet dropout probabilities in the mean-square stabilizability of the system is obtained. Moreover, a set of hyper-rectangles in this region is presented in terms of the plant’s non-minimum phase zeros, unstable poles and Wonham decomposition forms which is related to the structure of controllable subspace of the plant. A numerical example is presented to illustrate the fundamental constraints in the mean-square stabilizability of the networked system.

Corrections to “Outage Analysis for Decode-and-Forward Multirelay Systems Allowing Intra-Link Errors”

In [1] , we derived an analytical expression for the outage probability of decode-and-forward (DF) multirelay systems that allow for intra-link errors (IE). To this end, we relied upon the admissible rate region of a binary many-help-one problem with independently degraded helpers, which we believed to have obtained in [2] . Unfortunately, later on we realized that the admissible rate region in [2] is incorrect, and thus so is the resulting DF-IE outage probability in [1] .

Integration of Robotic Vision and Tactile Sensing for Wire-Terminal Insertion Tasks

This paper reports the development of a manipulation system for electric wires, implemented by means of a commercial gripper installed on an industrial manipulator and equipped with cameras and suitably designed tactile sensors. The purpose of this system is the execution of wire insertion on commercial electromechanical components. The synergy between computer vision and tactile sensing is necessary because, in a real environment, the tight spaces very often prevent the possibility to use the vision system, also when the same task is performed by a human being. A novel technique to speed up the generation of training data sets for convolutional neural networks (CNNs) is proposed. Therefore, this technique is used to train a CNN in order to detect small objects (such as wire terminals). Moreover, aiming to prevent faults during the task and to interact with the environment safely, several machine learning approaches are used to produce an affordable output from the tactile sensor. The proposed approach shows how a cheap sensor embedded with suitable intelligence can provide information comparable to a more expensive force sensor. Note to Practitioners —This paper was motivated by the lack of commercial solution for the automatic cabling of switchgears. Existing approaches to this problem are in some way limited to specific large-scale products or simple layouts. This paper investigated a robust and flexible solution, based on the exploitation of multiple sensors and machine learning algorithms, for wire detection, grasping, and connection. The proposed approach is characterized by simple design and self-tuning capabilities, and it can be easily employed on a wide range of switchgear layouts thanks to the large workspace of the manipulator. Experimental results show that the proposed system is able to achieve a 95% success rate within a realistic admissible region. In the future research, we will integrate the proposed solution with an electromechanical component localization module and a terminal fastening system to evaluate the performance on the real production line.

A Fault Tolerant Control Scheme Using the Feasible Constrained Control Allocation Strategy

This paper investigates the necessity of feasibility considerations in a fault tolerant control system using the constrained control allocation methodology where both static and dynamic actuator constraints are considered. In the proposed feasible control al-location scheme, the constrained model predictive control (MPC) is employed as the main controller. This considers the admissible region of the control allocation problem as its constraints. Using the feasibility notion in the control allocation problem provides the main controller with information regarding the actuator′s status, which leads to closed loop system performance improvement. Several simulation examples under normal and faulty conditions are employed to illustrate the effectiveness of the proposed methodology. The main results clearly indicate that closed loop performance and stability characteristics can be significantly degraded by neglecting the actuat-or constraints in the main controller. Also, it is shown that the proposed strategy substantially enlarges the domain of attraction of the MPC combined with the control allocation as compared to the conventional MPC.

Geographic wayfinders and space-time algebra

Time Geography is a framework for describing reachable points in a (static) spatio-temporal environment. While originally devised to facilitate reasoning about an individual's or a population's living conditions, it was later adapted to many other applications. A wayfinder is an entity that moves through a space-time continuum with possible obstacles. We show how to model the pertinent notions in relational algebra (and, more abstractly, in modal semirings) with box and diamond operators. Admissible or undesired regions can be described as Boolean combinations of primitive regions such as the set of all points reachable by forward or backward movement from a given region or starting point. To derive results about the region blocked by the union of two regions we introduce an abstract algebraic view of coordinates that is largely independent of dimensional and metric aspects and thus very general. Moreover, the approach lends itself quite well to machine-supported proofs.

Influence of the Change in the Galactic-Nucleosynthesis Rate before the Formation of Solar System on the Determination of Age of The Universe

The dependence of the region of physically admissible values of uranium-thorium isotope ratios on the short-term change in nucleosynthesis rate, which increases just before the formation of the Solar system, is studied. An additional admissible region associated with the presence of the isotope 244Pu and the effect of this region on the calculation of the age of the Universe, TU, are considered within galactic-nucleosynthsis theory. The size of the admissible region and its dependence on the short-term increase in the rate of heavy-element production (enhancement of nucleosynthsis) before the formation of the Solar System is discussed along with the consistency of the predictions for the above ratios with the region of admissible values. It is shown that an enhancement of nucleosynthesis is necessary for attaining agreement between the calculated ratios of cosmochronometer nuclei and the region of admissible values, but this enhancement should not lead to an increase in the abundances of heavy elements that is greater than 1 to 3% of the total amount of synthesized heavy elements.

Search-Detect-Track Sensor Allocation for Geosynchronous Space Objects

The initiation of tracks for newly discovered objects presents unique challenges in space situational awareness. Recent work explores the use of admissible regions to initialize filters for space object tracking; however, these methods require follow-on measurements to refine the initial admissible region solution. This paper presents an approach to the joint search and track problem, designed to allow a single sensor to build and maintain a catalog of objects without requiring an a priori estimate.

Mathematical modelling of the reaction of condensation telomerization and the investigation of the model

A mathematical model of the distribution of mixture components in the equilibrium condensation telomerization is developed depending on the ratio of the amounts of monomers and telogen, as well as the number of HX as regulating parameters, the computer implementation of the model is carried out, and its study is carried out by numerical simulation. The model is based on the well-known schematic diagram of the flow of the condensation telomerization process under the assumption of equal reactivity of the same functional groups (Flory principle). Based on the analysis of the flow pattern of the process, 6 structural elements are identified, reproducible at each stage associated with an increase in the degree of polymerization based on 4 basic components. It is proved that the equilibrium concentrations of these elements, depending on the polymerization degree, depend on the equilibrium concentration of products with a degree of polymerization 1 and are described by infinite geometric progression with the same denominator. According to the physical content of the task, this progression must be convergent. Equations of material balance of components are contained in the form of a system with 4 equations containing infinite sums. It is possible to minimize these sums using the properties of geometric progressions and to obtain a closed system with 4 nonlinear equations for the equilibrium concentrations of the base components. The Monte Carlo method is used to study the features of the numerical solution of the system of equations of the model. It is found that with a random choice of initial approximations of solutions from an admissible region, the system contains 4 roots, of which 2 contain positive and negative components and are false, and 2 have completely positive components. A valid criterion for finding a real root has a physical meaning based on the calculation of the denominator of a geometric progression. The possibilities of practical use of the model are discussed

On-board passive-image based non-cooperative space object capture window estimation

This paper proposes a novel capture window estimation framework for non-cooperative space object capture mission. The proposed approach is developed by taking into account the following facts: 1) only one monocular camera onboard the capturer satellite is available; 2) the a-priori knowledge of resident space objects (RSOs) is strictly limited; 3) the capture window estimation framework is independent from the capture modes. The relative state between the observed space object and capturer is formulated in a probabilistic manner through solving the admissible region from passive-images. Then, the probability and probability rate of a target entering the capture zone are efficiently characterized, leading to a complete RSO capture window estimation architecture. Finally, the entire algorithm is validated by a Monte Carlo simulation and an experimental trial, results from which demonstrate the effectiveness of the proposed approach in terms of estimation accuracy and reliability.

Parallel initial orbit determination using angles-only observation pairs

We propose a type of admissible-region analysis for track initiation in multi-satellite problems when angles are the primary observable. Pairs of optical observations are used to calculate candidate orbits via a Lambert solver by hypothesizing range values. The method is attractive because it allows multiple levels of parallelization of the track-initiation process. Orbital element partitions are introduced to divide the admissible region into smaller search spaces to be processed on individual computer nodes. For a specified rectangular partition in the space of orbital elements, constraints are developed to bound the values of range that will lead to initial orbit hypotheses (data association hypotheses) associated with that partition. These bounds allow us to parallelize the generation of candidate orbits, because each element-space partition can be handled independently of the others. Several constraints are developed and shown to limit the range pair hypotheses effectively to the constrained admissible region based on the orbital element partitions. Examples are provided to highlight the topology of the proposed constraints.

Distortion Bounds for Source Broadcast Problems

This paper investigates the joint source-channel coding problem of sending a memoryless source over a memoryless broadcast channel. An inner bound and several outer bounds on the admissible distortion region are derived, which respectively generalize and unify several existing bounds. As a consequence, we also obtain an inner bound and an outer bound for the degraded broadcast channel case. When specialized to the Gaussian or binary source broadcast, the inner bound and outer bound not only recover the best known inner bound and outer bound in the literature, but also generate some new results. Besides, we also extend the inner bound and outer bounds to the Wyner-Ziv source broadcast problem, i.e., source broadcast with side information available at decoders. Some new bounds are obtained when specialized to the Wyner-Ziv Gaussian and Wyner-Ziv binary cases.

Flexible Look-Ahead Dispatch Realized by Robust Optimization Considering CVaR of Wind Power

In this study, a novel approach for look-ahead dispatch (LAD) considering large-scale wind power integration is proposed. An index designated the conditional value-at-risk of wind power (CVaR-WP) is introduced to evaluate the risk of wind power accommodation. A flexible LAD model is developed to balance the operational costs and the CVaR-WP based on robust optimization (RO). According to the proposed model, the base points, participation factors, and flexible capacity of automatic generation control units are co-optimized. In addition, a reasonable admissible region of wind power on each node can be obtained correspondingly. An efficient algorithm based on the big-M method and the decomposition method is presented to solve the resulting bilinear programing model. The proposed approach combines the advantages of RO and stochastic programing, which can avoid the overconservativeness of RO while maintaining its high computing efficiency. Test results illustrate the effectiveness and efficiency of the proposed approach.