State Space Research Articles

Stabilisation in an infinite time horizon by homomorphically encrypted first-order controllers with regular Pisot poles

It has been previously found that partially homomorphic encryption based controllers cannot operate in an infinite time horizon, unless all elements of their state matrices are integer numbers. Considering this fact and the results of a recent research revealing the role of Pisot numbers to act as the poles of integer state matrix based state space models involving no unstable pole-zero cancellation, the present paper aims to introduce some classes of realisations implementing first-order discrete-time controllers, which can be used in an infinite time horizon in encrypted control systems. These classes of controller realisations are obtained based on sequences approaching to limit points of positive Pisot numbers settled in the range ( 1 , 2 ) . An analytical procedure is also suggested to find the exact range of the controller gain for ensuring the closed-loop stability.

The Boltzmann Equation and Its Place in the Edifice of Statistical Mechanics

It is customary to classify approaches in statistical mechanics (SM) as belonging either to Boltzmanninan SM (BSM) or Gibbsian SM (GSM). It is, however, unclear how the Boltzmann equation (BE) fits into either of these approaches. To discuss the relation between BE and BSM, we first present a version of BSM that differs from standard presentation in that it uses local field variables to individuate macro-states, and we then show that BE is a special case of BSM thus understood. To discuss the relation between BE and GSM, we focus on the BBGKY hierarchy and note the version of the BE that follows from the hierarchy is “Gibbsian” only in the minimal sense that it operates with an invariant measure on the state space of the full system.

Adaptive compensation for multi-axial real-time hybrid simulation via nonlinear parameter estimation

For Real-time hybrid simulation (RTHS) to be stable and accurate, it is essential to address the time desynchronization issue between the numerical and physical substructures. Desynchronization is primarily caused by time delays, inherent dynamics of the control plant, system uncertainties, and noises. While existing adaptive compensators have shown effective tracking performance in single-input single-output (SISO) RTHS, their effectiveness in multi-input multi-output (MIMO) RTHS has not been fully demonstrated. MIMO-RTHS presents additional challenges due to its larger solution space, and significant dynamic coupling between actuators. To address these challenges, this study introduces an adaptive compensation framework for MIMO-RTHS. The proposed framework utilizes a control law based on the inverse dynamics of the control plant, incorporating real-time adaptive parameter updates through Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF) methods. Both the transfer function (TF) and discrete-time state-space (SS) models of the plant are employed in distinct parameter estimation cases. The performance of the proposed compensation is validated through a multi-axial RTHS (maRTHS) benchmark problem. Extensive simulations on the maRTHS incorporating various earthquake inputs, sensor noise, and model uncertainties, demonstrated an excellent tracking performance and strong robustness across four parameter estimation cases (EKF-TF, UKF-TF, EKF-SS, and UKF-SS). The use of UKF with SS model (UKF-SS) achieved superior performance, effectively managing nonlinearities and noise without requiring low-pass filtering.

MasterPlan: A Reinforcement Learning Based Scheduler for Archive Storage

With the sheer volume of data in today’s world, archive storage systems play a significant role in persisting the cold data. Due to stringent cost concerns, one popular design is to organize disks into groups and periodically switch them to be powered on for serving user requests. Scheduling thus becomes critical for both CapEx and performance. Unfortunately, field results indicate that existing schedulers can be often suboptimal. Our further analysis suggests that the main reason is the mismatch between the ever-changing workloads and the fixed set of coarsely-configured parameters in current heuristic-based schedulers. In this paper, we propose MasterPlan , a reinforcement learning (RL) based scheduler for archive storage systems. By identifying the unique characteristics of archive storage service, we design a state space and reward function for the RL agent. MasterPlan includes a continuous action encoding approach to guarantee efficient exploration, and a meta adaptation module to extract features of workload series. Experiments show that MasterPlan can achieve 1.25 × throughput, 2.16 × 99 th latency and 1.47 × power draw improvement compared to existing solutions.

NUMERICAL-ANALYTICAL METHOD OF DECOMPOSITION-AUTOCOMPENSATION FOR SOLVING THE SIGNAL RECOGNITION PROBLEM BASED ON INACCURATE OBSERVATIONS

A numerical-analytical method is developed to solve the problem of optimal recognition of a set of possible signals observed as an additive mixture containing not only a fluctuation observation error (with an unknown statistical distribution) but also a singular interference (with parametric uncertainty). The method allows for both the detection of signals present in the mixture and the estimation of their parameters within a specified quality criterion and associated constraints. The proposed method, based on the idea of generalized invariant-unbiased estimation of linear functional values, enables decomposition of the computational procedure and autocompensation of singular interference without resorting to the traditional expansion of the state space. Linear spectral decompositions in specified functional bases are used for the parametric finite-dimensional representation of signals and interference, while knowledge of the correlation matrix of the observation error is sufficient for error description. Random and systematic errors are analyzed, and an illustrative example is provided.

Touch-down condition control for the bipedal spring-mass model in walking

Behaviors of animal bipedal locomotion can be described, in a simplified form, by the bipedal spring-mass model. The model provides predictive power, and helps us understand this complex dynamical behavior. In this paper, we analyzed a range of gaits generated by the bipedal spring-mass model during walking, and proposed a stabilizing touch-down condition for the swing leg. This policy is stabilizing against disturbances inside and outside the same energy level and requires only internal state information. In order to generalize the results to be independent of size and dimension of the system, we nondimensionalized the equations of motion for the bipedal spring-mass model. We presented the equilibrium gaits (a.k.a fixed point gaits) as a continuum on the walking state space showing how the different types of these gaits evolve and where they are located in the state space. Then, we showed the stability analysis of the proposed touch-down control policy for different energy levels and leg stiffness values. The results showed that the proposed touch-down control policy can stabilize towards all types of the symmetric equilibrium gaits. Moreover, we presented how the peak leg force changes within an energy level and as it varies due to the type of the gait since peak force is important as a measurement of injury or damage risk on a robot or animal. Finally, we presented simulations of the bipedal spring-mass model walking on level ground and rough terrain transitioning between different equilibrium gaits as the energy level of the system changes with respect to the ground height. The analysis in this paper is theoretical, and thus applicable to further our understanding of animal bipedal locomotion and the design and control of robotic systems like ATRIAS, Cassie, and Digit.

Stochastic First-Order Methods for Average-Reward Markov Decision Processes

We study average-reward Markov decision processes (AMDPs) and develop novel first-order methods with strong theoretical guarantees for both policy optimization and policy evaluation. Compared with intensive research efforts in finite sample analysis of policy gradient methods for discounted MDPs, existing studies on policy gradient methods for AMDPs mostly focus on regret bounds under restrictive assumptions, and they often lack guarantees on the overall sample complexities. Toward this end, we develop an average-reward stochastic policy mirror descent method for solving AMDPs with and without regularizers and provide convergence guarantees in terms of the long-term average reward. For policy evaluation, existing on-policy methods suffer from suboptimal convergence rates as well as failure in handling insufficiently random policies due to the lack of exploration in the action space. To remedy these issues, we develop a variance-reduced temporal difference (VRTD) method with linear function approximation for randomized policies along with optimal convergence guarantees, and design an exploratory VRTD method that resolves the exploration issue and provides comparable convergence guarantees. By combining the policy evaluation and policy optimization parts, we establish sample complexity results for solving AMDPs under both generative and Markovian noise models. It is worth noting that when linear function approximation is utilized, our algorithm only needs to update in the low-dimensional parameter space, and thus can handle MDPs with large state and action spaces. Funding: T. Li and G. Lan were supported in part by the National Science Foundation [Grant CCF-1909298] and the Office of Navel Research [Grant N00014-20-1-2089].

Assessing the Impact of Geopolitical Risk on Longevity Bond Pricing: Insights from Bayesian Multivariate Regression

AbstractThis paper investigates the multivariate pricing of coupon longevity bonds (CLBs) using the Fama–French–Lee–Carter (FF–LC) five-vector model in the framework of Bayesian integrated nested Laplace approximation (INLA) in the presence of geopolitical risk (GPR). The variance-covariance and correlation matrices are utilized to capture the interdependence between factors. We prove the generalization of multivariate Bayesian INLA with the basic probability assignment which is utilized as a posterior uncertainty belief associated with the GPR uncertainty category (a rich representation of GPR uncertainty) that is an element of the frame of discernment in the CLB posterior estimation. INLA Bayesian principal component analysis (INLA-BPCA) is applied to the model prediction parameters generating a multivariate normally distributed posterior. The deviance information criterion (DIC) assesses optimal factor selection. The results show that the BPCA posterior gains a feature that allows for a balance between the goodness-of-fit and complexity in hierarchical model selection by incorporating the retained principal components (or the effective number of parameters) from the DIC formula. Furthermore, it is also evident in our results, that the DIC outperforms the Bayesian information criterion (BIC), and Watanabe–Akaike information criterion (WAIC). The DIC is more suitable for Bayesian-based parametric models with high complexity. Lastly, the INLA-BPCA-DIC is applied to select the best longevity factors that yield a low longevity price of risk for insurers and practitioners, to attenuate the risks associated with investing in CLBs in the presence of geopolitical uncertainty shocks.

From high-dimensional committors to reactive insights.

Transition path theory (TPT) offers a powerful formalism for extracting the rate and mechanism of rare dynamical transitions between metastable states. Most applications of TPT either focus on systems with modestly sized state spaces or use collective variables to try to tame the curse of dimensionality. Increasingly, expressive function approximators such as neural networks and tensor networks have shown promise in computing the central object of TPT, the committor function, even in very high-dimensional systems. That progress prompts our consideration of how one could use such a high-dimensional function to extract mechanistic insights. Here, we present and illustrate a straightforward but powerful way to track how individual dynamical coordinates evolve during a reactive event. The strategy, which involves marginalizing the reactive ensemble, naturally captures the evolution of the dynamical coordinate's distribution, not just its mean reactive behavior.

Cancellation of the ZEDE law in Honduras and international investment law issues

Purpose In 2013, Honduras Congress passed the Zones for Employment and Economic Development (ZEDE) Organic Law, along with some constitutional changes, to create ZEDEs, which are essentially special economic zones with some unique features. Prospera Honduras Inc., a company with substantial United States investment, invested in Honduras relying on the ZEDE Organic Law and the Free Trade Agreement between Central America, the Dominican Republic and the United States of America (CAFTA-DR). In 2022, Honduras cancelled the ZEDE Organic Law, allegedly harming Prospera Honduras Inc.’s investments. Prospera and some other foreign investors have initiated an investor-state arbitration against Honduras for several alleged breaches of CAFTA-DR provisions. Honduras has remained silent and decided not to participate in the arbitration. This paper aims to examine whether the cancellation of the ZEDE Organic Law gives rise to international investment law obligations under the CAFTA-DR. Design/methodology/approach This is a doctrinal research and contains qualitative analysis. Findings The article concludes that CAFTA-DR preserves some regulatory space for host states; therefore, it would be wrong to assume that the arbitral decision in Prospera Inc. and others v. Honduras will favour only the foreign investors. This article also argues that, drawing insights from this dispute, future International Investment Agreements should better preserve Indigenous people’s rights. Moreover, the host states should reconsider whether they intend International Investment Agreements (IIAs) to apply to special economic zones in future. Originality/value There is no existing scholarly work examining the international investment law issues relating to the cancellation of ZEDEs in Honduras. Therefore, the findings of this article will be novel.

Frequent transitions in self-assembly across the evolution of a central metabolic enzyme

Many enzymes assemble into homomeric protein complexes comprising multiple copies of one protein. Because structural form is usually assumed to follow function in biochemistry, these assemblies are thought to evolve because they provide some functional advantage. In many cases, however, no specific advantage is known and, in some cases, quaternary structure varies among orthologs. This has led to the proposition that self-assembly may instead vary neutrally within protein families. The extent of such variation has been difficult to ascertain because quaternary structure has until recently been difficult to measure on large scales. Here, we employ mass photometry, phylogenetics, and structural biology to interrogate the evolution of homo-oligomeric assembly across the entire phylogeny of prokaryotic citrate synthases – an enzyme with a highly conserved function. We discover a menagerie of different assembly types that come and go over the course of evolution, including cases of parallel evolution and reversions from complex to simple assemblies. Functional experiments in vitro and in vivo indicate that evolutionary transitions between different assemblies do not strongly influence enzyme catalysis. Our work suggests that enzymes can wander relatively freely through a large space of possible assembly states and demonstrates the power of characterizing structure-function relationships across entire phylogenies.

Disturbance decoupling controller design of switched Boolean control networks in recursion

This paper studies the disturbance decoupling problem (DDP) of switched Boolean control networks (SBCNs) by the methodology of recursion. All the state nodes of the original SBCNs are split into two parts based on whether or not the state node influences the outputs. By driving the part of state nodes which influence the outputs to the largest control invariant set, the concept of DDP in recursion is proposed. Using the algebraic state space representation (ASSR) method, both mode-independent and mode-dependent state feedback controllers are constructed to solve the DDP in recursion of SBCNs. Furthermore, based on the obtained mode-independent state feedback DDP controllers, the mode-independent output feedback controllers are designed for the DDP in recursion of SBCNs.

Exact likelihood for inverse gamma stochastic volatility models

We obtain a novel analytic expression of the likelihood for a stationary inverse gamma stochastic volatility (SV) model. This allows us to obtain the maximum likelihood estimator for this nonlinear non‐Gaussian state space model. Further, we obtain both the filtering and smoothing distributions for the inverse volatilities as mixtures of gammas, and therefore, we can provide the smoothed estimates of the volatility. We show that by integrating out the volatilities the model that we obtain has the resemblance of a GARCH in the sense that the formulas are similar, which simplifies computations significantly. The model allows for fat tails in the observed data. We provide empirical applications using exchange rates data for seven currencies and quarterly inflation data for four countries. We find that the empirical fit of our proposed model is overall better than alternative models for four countries currency data and for two countries inflation data.

BLESS Behavior Correctness Proof as ConvincingVerification Artifact

Safety-critical cyber-physical systems require evidence they are indeed safe. In practice, such evidence is results of system tests. Unfortunately, tests can only demonstrate the presence of software errors, not their absence, and can practically cover a tiny fraction of system state space. Valiant efforts to formally verify program correctness have either been excruciatingly difficult (theorem proving) or incomplete (static analysis, model checking, SAT or SMT solving). The BLESS Methodology was created specifically for engineers in industry to formally verify software controlling machines. The BLESS Methodology transforms programs that control machines, annotated with assertions to form proof outlines, into deductive proofs that every possible program execution will conform to its specification. To the extent that cyber-physical system specifications have been validated to express system safety and performance, a deductive proof can be a convincing argument to a person of program correctness. This paper uses a simple safety-critical system to argue that behavior correctness proof under the BLESS Methodology is a convincing verification artifact in addition to customary testing.

Generalized synchronization in the presence of dynamical noise and its detection via recurrent neural networks.

Given two unidirectionally coupled nonlinear systems, we speak of generalized synchronization when the responder "follows" the driver. Mathematically, this situation is implemented by a map from the driver state space to the responder state space termed the synchronization map. In nonlinear times series analysis, the framework of the present work, the existence of the synchronization map amounts to the invertibility of the so-called cross map, which is a continuous map that exists in the reconstructed state spaces for typical time-delay embeddings. The cross map plays a central role in some techniques to detect functional dependencies between time series. In this paper, we study the changes in the "noiseless scenario" just described when noise is present in the driver, a more realistic situation that we call the "noisy scenario." Noise will be modeled using a family of driving dynamics indexed by a finite number of parameters, which is sufficiently general for practical purposes. In this approach, it turns out that the cross and synchronization maps can be extended to the noisy scenario as families of maps that depend on the noise parameters, and only for "generic" driver states in the case of the cross map. To reveal generalized synchronization in both the noiseless and noisy scenarios, we check the existence of synchronization maps of higher periods (introduced in this paper) using recurrent neural networks and predictability. The results obtained with synthetic and real-world data demonstrate the capability of our method.

A novel method for solving dynamic flexible job-shop scheduling problem via DIFFormer and deep reinforcement learning

Due to the dynamic changes of manufacturing environments, heuristic scheduling rules are unstable in dynamic scheduling. Although meta-heuristic methods provide the best scheduling quality, their solution efficiency is limited by the scale of the problem. Therefore, a novel method for solving the dynamic flexible job-shop scheduling problem (DFJSP) via diffusion-based transformer (DIFFormer) and deep reinforcement learning (D-DRL) is proposed. Firstly, the DFJSP is modeled as a Markov decision process, where the state space is constructed in the form of the heterogeneous graph and the reward function is designed to minimize the makespan and maximize the machine utilization rate. Secondly, DIFFormer is used to encode the operation and machine nodes to better capture the complex dependencies between nodes, which can effectively improve the representation ability of the model. Thirdly, a selective rescheduling strategy is designed for dynamic events to enhance the solution quality of DFJSP. Fourthly, the twin delayed deep deterministic policy gradient (TD3) algorithm is adopted for training an efficient scheduling model. Finally, the effectiveness of the proposed D-DRL is validated through a series of experiments. The results indicate that D-DRL achieves better solution quality and higher solution efficiency when solving DFJSP instances.

An Efficient OCT Fingerprint Antispoofing Method Based on ResMamba

Optical coherence tomography (OCT), known for its noncontact and 3D imaging capabilities, has found widespread application in fingerprint antispoofing detection. However, the existing methods rely heavily on single-frame B-scan images, underutilizing the 3D spatial information inherent in OCT volume data. High computational costs further limit its practical applications. Thus, this study proposes an efficient fingerprint antispoofing method which leverages the spatial continuity of OCT volume data to enhance both the accuracy and computational efficiency. Using an OCT system, we collected 320 real fingerprints and 320 spoofed fingerprints. Then, to distinguish between genuine and spoofed fingerprints, we developed the proposed ResMamba model, which is based on an enhanced 3D convolutional network integrated with a state space model (SSM). We extracted regions of interest (ROIs) from B-scan images and segmented them into volume slices for training and classification. The experimental results demonstrate that ResMamba achieved a 0.56% error rate (ERR) and 99.22% area under the curve (AUC), with an inference time of just 11 ms. Furthermore, compared to the existing models, ResMamba effectively balances its accuracy, inference speed, and model size. Ablation studies confirm that integrating the SIC module enhances the model’s robustness. Overall, ResMamba offers an efficient and reliable fingerprint antispoofing solution, outperforming the traditional methods in terms of its accuracy and performance.

Formal error bounds for the state space reduction of Markov chains

Formal error bounds for the state space reduction of Markov chains

Spatio-temporal degradation model with graph neural network and structured state space model for remaining useful life prediction

Spatio-temporal degradation model with graph neural network and structured state space model for remaining useful life prediction

The utility of homomorphism concepts in simulation: building families of models from base-lumped model pairs

In this tutorial review paper we explain the concept of homomorphism and identify some principles that justify homomorphism construction based on the homogeneity of structure and coupling in systems with multiple components. We discuss some simple examples to show how these underlying justifying conditions can arise. Examples include brain simulation, combat attrition, and the greatly reduced computational complexity represented by Pascal’s triangle. Homomorphism is also shown to be fundamental for constructing approximate low-resolution models. Models that simplify complex time-demanding simulation models are often used as surrogate or metamodels in system optimization. However, such models are fitted typically to computationally derived response surfaces and not structurally related directly to the originals using homomorphisms as described here. Along these lines, we show how homomorphism plays an essential role in a novel approach being developed to strongly control tree expansion in state space explorations of stochastic system simulation.