Decomposition Of State Space Research Articles

Stabilization of bilinear systems with distributed delays using the Banach state space decomposition method

Stabilization of bilinear systems with distributed delays using the Banach state space decomposition method

A parallel algorithm for reliability assessment of multi-state flow networks based on simultaneous finding of all multi-state minimal paths and performing state space decomposition

This article presents a new efficient method for reliability evaluation of two-terminal Multi-state Flow Networks (MFNs). Indirect State Space Decomposition (SSD) methods are usually more efficient than direct SSD methods. However, indirect SSD methods require searching for all d-MPs/d-MCs. The presented method requires only an MFN, a system demand requirement d, and the probability distributions of states of components as an input. The presented algorithm uses a partition technique to decompose a state space into smaller and distinct subspaces. The algorithm tries to determine a d-flow with a lower bound for each subspace. If a flow exists and it is a d-MP, the algorithm computes the probability that a capacity vector belongs to this subspace and is bounded below by the d-MP and decomposes this subspace into smaller subspaces. For all subspaces without d-MP, the presented algorithm uses parallel computations and the SSD method to compute the probability that a capacity vector belongs to this subspace and is bounded below by a d-MP. The numerical experiments show that the efficiency of the presented method improves in comparison with other indirect SSD methods if the number of available logical processes and the number of d-MPs increase.

Dynamic robot routing optimization: State–space decomposition for operations research-informed reinforcement learning

There is a growing interest in implementing artificial intelligence for operations research in the industrial environment. While numerous classic operations research solvers ensure optimal solutions, they often struggle with real-time dynamic objectives and environments, such as dynamic routing problems, which require periodic algorithmic recalibration. To deal with dynamic environments, deep reinforcement learning has shown great potential with its capability as a self-learning and optimizing mechanism. However, the real-world applications of reinforcement learning are relatively limited due to lengthy training time and inefficiency in high-dimensional state spaces. In this study, we introduce two methods to enhance reinforcement learning for dynamic routing optimization. The first method involves transferring knowledge from classic operations research solvers to reinforcement learning during training, which accelerates exploration and reduces lengthy training time. The second method uses a state–space decomposer to transform the high-dimensional state space into a low-dimensional latent space, which allows the reinforcement learning agent to learn efficiently in the latent space. Lastly, we demonstrate the applicability of our approach in an industrial application of an automated welding process, where our approach identifies the shortest welding pathway of an industrial robotic arm to weld a set of dynamically changing target nodes, poses and sizes. The suggested method cuts computation time by 25% to 50% compared to classic routing algorithms.

Multi-synchronization of coupled multi-stable memristive Cohen–Grossberg neural networks with mixed time-delays

This paper investigates the multi-synchronization issue for a class of coupled multi-stable memristive Cohen–Grossberg neural networks with both additive time delays and distributed delays. First, the multi-stability of the isolated subnetwork with a general class of activation function is analyzed. By employing state-space decomposition, M-matrix and fixed point theory, some sufficient conditions are deduced to ensure that each subnetwork of the coupled networks has (r+1)n locally exponential stable equilibrium states. In the scenario where the time delays are continuously differentiable, a unique Lyapunov–Krasovskii function is established and some sufficient conditions are derived for the coupled system to achieve multi-synchronization under feedback control. Additionally, in circumstances where the time delays are immeasurable or discontinuous, a new feedback controller is constructed based on the system’s model parameters, and a delay-independent finite-time multi-synchronization criterion is proposed. Finally, three numerical examples are provided to illustrate the effectiveness of the proposed methods.

Optimal distributed time-varying formation control for second-order multiagent systems: LQR-based method

The optimal leaderless and leader-following time-varying formation (TVF) control problems for second-order multiagent systems (MASs) are investigated, where two optimal TVF control protocols are proposed to achieve the desired formations as well as minimize the comprehensive optimization function that contain the cooperative performance index and the control energy index. For leaderless case, the optimal formation control problem is reformulated as an infinite-time state regulator problem by employing the state space decomposition method, which is subject to specified constraints on energy and performance indices, and the analytic criterion for optimal TVF achievability is subsequently proposed. Then, the results of optimal leaderless TVF control are extended to the leader-following case with switching topologies, where the main challenge is changed to find the optimal controller rather than the optimal gain matrix, and the optimal value of the comprehensive index is accurately determined. Finally, two simulation cases are proposed to validate the effectiveness of the theoretical results, and comparisons with previous works are presented to expound the optimality of the proposed formation control method.

Coexistence of locally multistable equilibrium points for [formula omitted]-neuron delayed quaternion-valued neural networks with continuous piecewise nonlinear activation functions

This article investigates the coexistence of multistable equilibrium points (EPs) for n-neuron delayed quaternion-valued neural networks (DQVNNs) in which the continuous and piecewise nonlinear functions are used as the activation functions. Using the state space decomposition technique, Brouwer’s fixed point theorem, and Lagrange’s mean value theorem, some novel sufficient conditions have been derived to ensure the coexistence of 54n EPs in which 34n of them are locally stable. Furthermore, in this scientific contribution, positively invariant sets have been estimated which actually turned out to be quite challenging for the activation functions of the designed DQVNNs. Finally, some comparisons and convincing simulations with the application to associative memory of DQVNNs are given to verify the theoretical results at the end of this article.

Constructing the Oseledets decomposition with subspace growth estimates

The semi-invertible version of Oseledets’ multiplicative ergodic theorem providing a decomposition of the underlying state space of a random linear dynamical system into fast and slow spaces is deduced for a strongly measurable cocycle on a separable Banach space. This work is a much shorter means of obtaining this general version of the theorem, using measurable growth estimates on subspaces for linear operators combined with a modified version of Kingman’s subadditive ergodic theorem.

A generic impulsive controller for Hamiltonian time-independent systems

In a recent work Briozzo (2021) the author introduced an impulsive Floquet controller for periodic orbits in time-periodic Hamiltonian systems, which expresses the control law analytically in terms of the linearized dynamics about the reference orbit and makes full use of the center manifold enhancing performance by minimizing the energy of the actual orbit in the co-moving frame of the reference one. The purpose of the present work is to introduce an equivalent controller for Hamiltonian linear time-periodic systems obtained by linearization of a general time-independent Hamiltonian one about a periodic orbit, so incorporating the presence of a shear manifold associated to energy conservation and the ensuing non-isolation of periodic orbits. Like its preceding version, the controller defines a target subspace akin to the sliding surface of sliding mode controllers, onto which the system state vector is repeatedly sent by control impulses, and is generic in the sense that the target subspace and the control law are explicitly given for any possible decomposition of state space into a shear manifold and saddle, centre, or saddle-focus ones.

STATE SPACE DECOMPOSITION AND CLASSIFICATION OF TERM STRUCTURE SHAPES IN THE TWO-FACTOR VASICEK MODEL

In this paper, we analyze the shapes of forward curves and yield curves that can be attained in the two-factor Vasicek model. We show how to partition the state space of the model, such that each partition is associated to a particular shape (normal, inverse, humped, etc.). The partitions and the corresponding shapes are determined by the winding number of a single curve with possible singularities and self-intersections, which can be constructed as the envelope of a family of lines. Building on these results, we classify possible transitions between term structure shapes, give results on attainability of shapes conditional on the level of the short rate, and propose a simple method to determine the relative frequency of different shapes of the forward curve and the yield curve.

A deep encoder-decoder framework for identifying distinct ligand binding pathways.

The pathway(s) that a ligand would adopt en route to its trajectory to the native pocket of the receptor protein act as a key determinant of its biological activity. While Molecular Dynamics (MD) simulations have emerged as the method of choice for modeling protein-ligand binding events, the high dimensional nature of the MD-derived trajectories often remains a barrier in the statistical elucidation of distinct ligand binding pathways due to the stochasticity inherent in the ligand's fluctuation in the solution and around the receptor. Here, we demonstrate that an autoencoder based deep neural network, trained using an objective input feature of a large matrix of residue-ligand distances, can efficiently produce an optimal low-dimensional latent space that stores necessary information on the ligand-binding event. In particular, for a system of L99A mutant of T4 lysozyme interacting with its native ligand, benzene, this deep encoder-decoder framework automatically identifies multiple distinct recognition pathways, without requiring user intervention. The intermediates involve the spatially discrete location of the ligand in different helices of the protein before its eventual recognition of native pose. The compressed subspace derived from the autoencoder provides a quantitatively accurate measure of the free energy and kinetics of ligand binding to the native pocket. The investigation also recommends that while a linear dimensional reduction technique, such as time-structured independent component analysis, can do a decent job of state-space decomposition in cases where the intermediates are long-lived, autoencoder is the method of choice in systems where transient, low-populated intermediates can lead to multiple ligand-binding pathways.

Multistability of Dynamic Memristor Delayed Cellular Neural Networks With Application to Associative Memories.

Recently, dynamic memristor (DM)-cellular neural networks (CNNs) have received widespread attention due to their advantage of low power consumption. The previous works showed that DM-CNNs have at most 318 equilibrium points (EPs) with n=16 cells. Since time delay is unavoidable during the process of information transmission, the goal of this article is to research the multistability of DM-CNNs with time delay, and, meanwhile, to increase the storage capacity of DM-delay (D)CNNs. Depending on the different constitutive relations of memristors, two cases of the multistability for DM-DCNNs are discussed. After determining the constitutive relations, the number of EPs of DM-DCNNs is increased to 3n with n cells by means of the appropriate state-space decomposition and the Brouwer's fixed point theorem. Furthermore, the enlarged attraction domains of EPs can be obtained, and 2n of these EPs are locally exponentially stable in two cases. Compared with standard CNNs, the dynamic behavior of DM-DCNNs shows an outstanding merit. That is, the value of voltage and current approach to zero when the system becomes stable, and the memristor provides a nonvolatile memory to store the computation results. Finally, two numerical simulations are presented to illustrate the effectiveness of the theoretical results, and the applications of associative memories are shown at the end of this article.

Convexification of Queueing Formulas by Mixed-Integer Second-Order Cone Programming: An Application to a Discrete Location Problem with Congestion

Mixed-integer second-order cone programs (MISOCPs) form a novel class of mixed-integer convex programs, which can be solved very efficiently as a result of the recent advances in optimization solvers. This paper shows how various performance metrics of M/G/1 queues can be modeled by different MISOCPs. To motivate the reformulation method, it is first applied to a challenging stochastic location problem with congestion, which is broadly used to design socially optimal service systems. Three different MISOCPs are developed and compared on different sets of benchmark test problems. The new formulations efficiently solve very large-size test problems that cannot be solved by the two existing methods developed based on linear programming within reasonable time. The superiority of the conic reformulation method is next shown over a state-space decomposition method recently used to solve an assignment problem in queueing systems. Finally, the general applicability of the method is shown for similar optimization problems that use queue-theoretic performance measures to address customer satisfaction and service quality.

Reliability evaluation of all-user terminals in LEO satellite communication network based on modular reduction

LEO satellite communication network has a large number of satellites distributed in low orbits, which leads to multiple coverage of many areas on the ground. It is hard work to describe and evaluate the reliability of LEO satellite communication network. To solve this problem, the reliability of all-user terminals in LEO satellite communication network is defined, and the corresponding reliability evaluation method is proposed in the paper. Due to the large scale of the interstellar network, a modular reduction algorithm using the modular network instead of the original network for state decomposition is proposed in this paper. Case study shows that the calculation time of the proposed method is equivalent to 6.28% of the original state space decomposition algorithm. On this basis, the reliability of LEO satellite communication network is further analyzed. It is found that the reliability of LEO satellite network was more sensitive to the reliability of Inter-Satellite link and the satisfaction of global coverage in the early stage, and it is more sensitive to the reliability of the satellite in the later stage. The satellite-ground link has a relatively constant impact on of LEO satellite network.

Formation control for networked multiagent systems with a minimum energy constraint

Minimum-energy formation achievement problems for networked multiagent systems are investigated, where information networks with leaderless and leader-follower structures are respectively addressed and information networks are randomly switching. The critical feature of this work is that the energy constraint is minimum in the sense of the linear matrix inequality, but limited-budget control and guaranteed-cost control cannot realize a minimum-energy formation. Firstly, the leaderless minimum-energy formation control problem is converted into an asymptotic stability one via a nonsingular transformation and state space decomposition, and based on linear matrix inequality techniques, sufficient conditions for analysis and design of leaderless minimum-energy formation achievement are proposed, respectively, which can be solved by the generalized eigenvalue method. Then, main results of minimum-energy formation achievement of leaderless networked multiagent systems are extended leader-follower networked multiagent systems, where the asymmetric property of the leader-follower information network is well dealt with by two nonsingular transformations. Finally, two simulation examples are shown to verify the main results for minimum-energy formation achievements of leaderless and leader-follower networked multiagent systems, respectively.

Finite-time stability of singular switched systems with a time-varying delay based on an event-triggered mechanism

<abstract><p>In this paper, the finite-time stability (FTS) of singular switched systems that have time-varying delays and perturbations is investigated. First, the concept of the FTS of time-varying delay singular switched systems is given, and a specific event-triggered mechanism is proposed. Then, a state feedback mechanism is proposed based on the event-triggered mechanism. Second, using the L-K function and state space decomposition, adequate criteria for the FTS of singular switched systems are found. Sufficient requirements are also presented for meeting the finite-time stable $ H_\infty $ performance index $ \gamma $.</p></abstract>

Guaranteed-Cost Consensus Control for High-Dimensional Multi-Agent Systems With Input Delays and Parameter Uncertainties

In this paper, the problem of consensus control is investigated for a kind of multi-agent systems (MAS) in high-dimensional form. Both the nonlinear dynamics and norm-bound uncertainties are taken into account, which makes the model more comprehensive than those in existing literature. By employing the related error (between each agent and its neighbors) and considering the time-varying input delay, the consensus protocol is constructed to force agents to close to the consensus dynamical function. An augmented closed-loop system is established by taking use of properties of Laplacian matrix and the state space decomposition method. A few of sufficient criteria are gained with the help of feasible solutions for linear matrix inequalities. The asymptotical stability of error system is realized and the upper-bound is obtained for the cost function consisting of both the consensus regulation performance and the control energy consumption. An illustrative example and the corresponding simulations are given for verifying the validity of our results.

A Fast ISAR Tomography Technique for Fully Polarimetric 3-D Imaging of Man-Made Targets

The 3-D inverse synthetic aperture radar (ISAR) tomography is an enabling technique for applications such as the exact diagnosis of scattering mechanisms for complex targets. Nevertheless, current ISAR tomography solutions still suffer from problems such as the great computational complexity and optimal utilization of the signatures acquired from limited baselines. In this work, we propose a fast ISAR tomography technique for fully polarimetric 3-D imaging of man-made targets. A stack of 2-D complex-valued images with different baselines and polarizations is first obtained through a phase error calibration (PEC) process and graphic processing unit accelerated polarimetric filtered backprojection. A polarimetric state-space decomposition (P-SSD) algorithm is then developed which could provide joint 3-D reconstruction results with low computational complexity. Examples from both numerical multibaseline data for the Sandia laboratories implementation of cylinders (SLICY) benchmark model and the outdoor range dataset collected by the Georgia Tech Research Institute (GTRI) are presented to demonstrate the superior performance and the usefulness of the proposed technique.

A generic impulsive controller for hamiltonian linear time-periodic systems

This work introduces an impulsive controller for Hamiltonian linear time-periodic systems obtained by linearization of a general time-periodic Hamiltonian one about a periodic orbit. The controller defines a target subspace akin to the sliding surface of sliding mode controllers, onto which the system state vector is periodically sent by control impulses, and is generic in the sense that the target subspace and the control law are explicitly given for any possible decomposition of state space into saddle, centre, or saddle-focus sub-manifolds. The novel treatment of the center manifold minimizes the system energy on it ensuring damping of oscillatory motions, which is proved crucial for controllability.

A multistate network approach for reliability evaluation of unmanned swarms by considering information exchange capacity

An unmanned swarm is a group of numerous unmanned ground or aerial vehicles performing tasks in a self-organized and self-adaptive manner to achieve an overall mission objective. Efficient and reliable information exchange among the agents is essential for the unmanned swarm to accomplish the mission. Thus, it is important to provide an accurate reliability model and a corresponding efficient method of evaluation for the unmanned swarm information exchange network (USIEN). In this paper, we develop a multistate network model for the reliability evaluation of USIEN that considers the capacity for information exchange. We propose an overall reliability metric to evaluate the reliability of USIEN under certain missions. In addition, an improved fast state-space decomposition (SSD) bounding algorithm with a reliability threshold for approximating the proposed reliability metric is developed. Results and comparisons with extant studies show that the proposed model and metric lead to a more realistic method to evaluate the reliability of USIEN. Efficiency investigations indicate that the proposed algorithm provides an efficient approximation of reliability for the large unmanned swarm. The proposed model and metric can be used to support mission planning and the design of an unmanned swarm.

Pinning multisynchronization of delayed fractional-order memristor-based neural networks with nonlinear coupling and almost-periodic perturbations

This paper concerns the multisynchronization issue for delayed fractional-order memristor-based neural networks with nonlinear coupling and almost-periodic perturbations. First, the coexistence of multiple equilibrium states for isolated subnetwork is analyzed. By means of state-space decomposition, fractional-order Halanay inequality and Caputo derivative properties, the novel algebraic sufficient conditions are derived to ensure that the addressed networks with arbitrary activation functions have multiple locally stable almost periodic orbits or equilibrium points. Then, based on the obtained multistability results, a pinning control strategy is designed to realize the multisynchronization of the N coupled networks. By the aid of graph theory, depth first search method and pinning control law, some sufficient conditions are formulated such that the considered neural networks can possess multiple synchronization manifolds. Finally, the multistability and multisynchronization performance of the considered neural networks with different activation functions are illustrated by numerical examples.