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In this paper, we investigate a continuous-time linear quadratic stochastic optimal control (LQSOC) problem in an infinite horizon, where diffusion and drift terms of the corresponding stochastic system depend on both state and control variables. In light of the stochastic control theory, this LQSOC problem is reduced to solving a generalised algebraic Riccati equation (GARE). With the help of an existing model-based value iteration (VI) algorithm, we propose two data-driven VI algorithms to solve the GARE. The first one relies on transforming the stochastic system into a deterministic control system first and then solving the LQSOC problem by the data of the deterministic system. Consequently, this algorithm does not need the information of two system coefficients and has a lower algorithm complexity. The second algorithm directly uses the data generated by the stochastic system, and thus it circumvents the requirement of all system coefficients. We also provide convergence proofs of these two data-driven algorithms and validate these algorithms through two simulation examples. [ABSTRACT FROM AUTHOR]

Summary: This article considers the output regulation problem of continuous‐time linear systems subject to input saturation in the scenario that the system dynamics are unknown. Based on the low‐gain technique and the output feedback technique, we construct an output feedback control law to solve the output regulation problem with input saturation. Since the system dynamics are unknown, we estimate the feedback and feedforward terms in the control law with a two‐step data‐driven method. An output feedback adaptive dynamic programming algorithm is proposed to estimate the feedback term. An online updating algorithm based on output tracking error is proposed to estimate the feedforward term directly without solving the output regulation equations. Both algorithms don't rely on the measurement of the internal states of the exosystem and the original system. We show that the input saturation caused by the iterative feedforward gain matrix in the online updating algorithm doesn't affect the convergence of the algorithm. With these two data‐driven algorithms, the control law doesn't rely on the dynamics anymore. The low‐gain control law obtained by the model‐free method prevents input saturation from occurring and hence solves the output regulation problem. Finally, a numerical example is provided to validate the theoretical results. [ABSTRACT FROM AUTHOR]

The paper is concerned with inheritance of density of orbits from a continuous time system to its time discretizations. We prove that for a two-sided minimal flow on a rather general topological space, there is a residual set of times such that, for every such time $ t $, the corresponding time-$ t $ homeomorphism inherits two-sided minimality. An analogous result is proved for one-sided minimal semiflows.Apart from trivial implications, in noncompact spaces there is no relation between two-sided, forward, and backward minimality of flows and homeomorphisms. This is not difficult to demonstrate for flows by appropriate examples. It has not been known how to provide corresponding examples of homeomorphisms. Using the results mentioned above, we are able to do so.As another application, we prove a continuous time analogue of Gottschalk's Theorem on spaces which do not admit minimal maps. [ABSTRACT FROM AUTHOR]

In this work we provide detailed estimates of maximal principal angles between subspaces and we analyse their smoothness for smoothly varying subspaces. This leads to a new definition of angular values for linear dynamical systems in continuous time. We derive some of their properties complementary to the theory of angular values developed in Beyn, et al. [Angular values of nonautonomous and random linear dynamical systems: Part I – fundamentals, SIAM J. Appl. Dyn. Syst. 21(2) (2022), pp. 1245–1286; Angular values of nonautonomous linear dynamical systems: Part II – reduction theory and algorithm, SIAM J. Appl. Dyn. Syst. 22(1) (2023), pp. 162–198] for discrete time systems. The estimates are further employed to establish upper semicontinuity of angular values for some parametric model examples of discrete and continuous type. [ABSTRACT FROM AUTHOR]

Abstract A practical fixed‐time composite learning control scheme, by combining dynamic regressor extension and mixing (DREM) parameter identification algorithm and adaptive dynamic surface control (DSC) technique, is proposed for a class of strict‐feedback non‐linear systems subjected to linear‐in‐parameters uncertainties and full‐state constraint. To address the problem of state constraint, a non‐linear transformation function is introduced to convert the originally constrained non‐linear system into an unconstrained one. Meanwhile, the hyperbolic tangent function is employed to avoid singularity issues that often appeared in the traditional fixed‐time (FXT) control designs. In order to relax the requirement of persistency of excitation condition, a modified FXT‐DREM parameter identification approach with an interval excitation condition is constructed by introducing a three‐layer transformation technique derived from the classical DREM algorithm. Then, the modified FXT‐DREM parameter identification algorithm is seamlessly integrated into the adaptive DSC framework, resulting in a composite‐learning control scheme. By employing Lyapunov stability analysis, the fixed‐time convergence of both the parameter estimation error and the trajectory tracking error is proved. Finally, the effectiveness of the proposed design is demonstrated through simulation test.

Summary Digital MemComputing machines (DMMs), which employ nonlinear dynamical systems with memory (time non‐locality), have proven to be a robust and scalable unconventional computing approach for solving a wide variety of combinatorial optimization problems. However, most of the research so far has focused on the numerical simulations of the equations of motion of DMMs. This inevitably subjects time to discretization, which brings its own (numerical) issues that would be otherwise absent in actual physical systems operating in continuous time. Although hardware realizations of DMMs have been previously suggested, their implementation would require materials and devices that are not so easy to integrate with traditional electronics. Addressing this, our study introduces a novel hardware design for DMMs, utilizing readily available electronic components. This approach not only significantly boosts computational speed compared to current models but also exhibits remarkable robustness against additive noise. Crucially, it circumvents the limitations imposed by numerical noise, ensuring enhanced stability and reliability during extended operations. This paves a new path for tackling increasingly complex problems, leveraging the inherent advantages of DMMs in a more practical and accessible framework. [ABSTRACT FROM AUTHOR]

Quantum trajectory techniques have been used in the theory of open systems as a starting point for numerical computations and to describe the monitoring of a quantum system in continuous time. We extend this technique to develop a general approach to the dynamics of quantum/classical hybrid systems. By using two coupled stochastic differential equations, we can describe a classical component and a quantum one which have their own intrinsic dynamics and which interact with each other. A mathematically rigorous construction is given, under the restriction of having a Markovian joint dynamics and of involving only bounded operators on the Hilbert space of the quantum component. An important feature is that, if the interaction allows for a flow of information from the quantum component to the classical one, necessarily the dynamics is dissipative. We show also how this theory is connected to a suitable hybrid dynamical semigroup, which reduces to a quantum dynamical semigroup in the purely quantum case and includes Liouville and Kolmogorov–Fokker–Planck equations in the purely classical case. Moreover, this semigroup allows to compare the proposed stochastic dynamics with various other proposals based on hybrid master equations. Some simple examples are constructed in order to show the variety of physical behaviors which can be described; in particular, a model presenting hidden entanglement is introduced. [ABSTRACT FROM AUTHOR]

In this paper, passive control and H ∞ state feedback based on non-fragile observer are presented for a class of uncertain, nonlinear and input time-delay systems. Firstly, taking uncertainties, nonlinearities and input time-delay into account, non-fragile observer and controller are designed and the perturbations of controller gain and observer gain are processed. Secondly, for the dynamic disturbances, an appropriate non-fragile state feedback controller based on the observation is selected to prove that the states of closed-loop system can be passive and stabilized with H ∞ performance for continuous time system. Moreover, the problems such as time-delay are handled in virtue of Lyapunov method and linear matrix inequalities (LMIs). Finally, the simulation results demonstrate the validity of the proposed control design method. [ABSTRACT FROM AUTHOR]

The possibility to anticipate critical transitions through detecting loss of resilience has attracted attention in many fields. Resilience indicators rely on the mathematical concept of critical slowing down, which means that a system recovers more slowly from external perturbations when it gets closer to tipping point. This decrease in recovery rate can be reflected in rising autocorrelation and variance in data. To test whether resilience is changing, resilience indicators are often calculated using a moving window in long, continuous time series of the system. However, for some systems, it may be more feasible to collect several high-resolution time series in short periods of time, i.e., in bursts. Resilience indicators can then be calculated to detect a change of resilience between such bursts. Here, we compare the performance of both methods using simulated data and showcase the possible use of bursts in a case study using mood data to anticipate depression in a patient. With the same number of data points, the burst approach outperformed the moving window method, suggesting that it is possible to downsample the continuous time series and still signal an upcoming transition. We suggest guidelines to design an optimal sampling strategy. Our results imply that using bursts of data instead of continuous time series may improve the capacity to detect changes in resilience. This method is promising for a variety of fields, such as human health, epidemiology, or ecology, where continuous monitoring can be costly or unfeasible. [ABSTRACT FROM AUTHOR]

In this paper, the problem of fault estimation (FE) and fault‐tolerant control (FTC) for a class of systems with dynamic event‐triggered mechanism (ETM) and time delay in a network environment is studied. To shorten the time between events and minimize the amount of data transmitted, this paper introduces dynamic variables within the ETM. In order to ensure the interval between the system state and its estimation, a fault/state estimation observer considering time delay is designed, which improves the reliability and security of the system. On this basis, a fault‐tolerant controller considering time delay is constructed to compensate the impact of faults on the system. The observer, controller, and ETM are co‐designed to maintain system performance. By making full use of the information between subsystems, a continuous time interconnection systems is constructed and the cooperative control mechanism is redesigned on the basis of the above system. Through theoretical analysis, it has been demonstrated that Zeno phenomenon does not exist in the ETM in this paper. Finally, the main results are verified by numerical simulation, and the validity of the conclusions is demonstrated. [ABSTRACT FROM AUTHOR]

Differing from the response control in civil and engineering applications, the excitation in a closed-loop sensing system is unknown and the control is designed to balance and measure the unknown excitation in real time. In this paper, a novel optimal force-balance control for a closed-loop sensing system with time delay is proposed. By introducing the errors between the control force and the unknown input as new variables, the force-balance control problem is transformed into a response minimization one with a time delay. Then, the discretization method is applied, and the continuous time system with time delay is converted into an extended discrete system without time delay, from which the analytical expression of the optimal force-balance control force is obtained. To illustrate the effectiveness of the proposed control, the optimal control of a practical quartz flexible force-balance accelerometer (FBA) is solved as an application. Numerical results show that the proposed control can realize the accurate measurement of wide-band random acceleration signals with a time delay of up to 10 times of control period. Besides, the proposed control can also significantly inhibit the vibration response of the FBA while guaranteeing measurement accuracy, which will benefit the obtaining of a large dynamic measurement range as a sensing application. [ABSTRACT FROM AUTHOR]

We introduce a novel technique for producing several families of distributions: the alpha-log-power transformed method. The novelty of our new approach lies in the fact that it adds one new shape parameter and was not derived from any established parent model. Some examples of the new family are presented. Also, some important statistical properties of the new family are studied. The maximum likelihood estimation approach is utilized to estimate the model parameters of the new family. To evaluate the performance of the estimators, Monte Carlo simulation is conducted using some arbitrary baseline distributions namely the Weibull, Burr-XII and Pareto distribution. Two real datasets are used to empirically show the potential significance and applicability of the alpha log power transformed Weibull. The alpha log power transformed Weibull is a very competitive model for characterizing observations in survival analysis. [ABSTRACT FROM AUTHOR]

Fish production integrates changes in biomass from growth, reproduction, and mortality, and is a useful indicator for fisheries management. However, calculation of fish production has been limited by the intensive requirements for data on abundance, biomass, age structure, and vital rates, and so it is uncommon to find estimates of fish production for wetlands. We developed an approach to directly estimate production that is suitable for data-limited systems: a continuous time model of production describing individual growth over short time intervals with continuous time models of abundance and biomass over longer timescales. We applied this model for 18 Great Lakes coastal wetlands (GLCWs) on Lake Ontario, including Big Island Wetland (BIW). In BIW, most species were dominated in abundance and biomass by younger cohorts and, as a result, these young, fast-growing individuals contributed disproportionately to fish production. In total, BIW produced 336.1 kg·ha·year of fish and the other 17 neighbouring ranged between 447.7 and 1119.9 kg·ha·year. These are some of the first estimates of fish production for GLCWs, highlighting their value for managing Great Lakes fisheries. [ABSTRACT FROM AUTHOR]

The investigation examines the continuous system as one of the two most common forms of migrant data-gathering today. The system is defined as a set of tools that obtains migration data on changes in the registration of the place of previous residence within the country or immigration record, including the total number of individuals entering or leaving the country and the type of visa issued to them. The strengths of the continuous system are noted, which lie in its ability to generate data on a regular basis and be useful to the authorities at the national level during the management of migration challenges and forecasting of various processes. The factors that influence the rejection of this data-gathering form today are highlighted, such as: 1) difficulty of conducting a comparative analysis between countries; 2) blurring of the entry category, which makes its unification problematic; 3) issues with monitoring of persons with unsettled (legal) status; 4) lack of recording of undocumented individuals in the continuous record of migrants; 5) system bias in focusing on emigration, ignoring the dimension of immigration. The idea about the lower level of use of the continuous system in our time due to the need for large financial resources, technological support, real agreement and coordination of joint actions between the governments of national states is substantiated as an unlikely scenario, taking into account the political, economic, cultural and social, etc. differentiation in the world. Attention is paid to the issue of prospects for the implementation of a continuous data-gathering system in the future based on the analysis of recent research and changes in the status of migration in the context of sustainable development. It is emphasized that, given the current challenges, the form will be used in the future, continuously recording data on displaced persons, but not claiming primacy in the process of systematizing information on global flows of migrants. [ABSTRACT FROM AUTHOR]

There has been a great deal of interest in the last few years for neural networks (NNs) with values in multidimensional domains. The most popular models are complex-valued neural networks (CVNNs), followed by quaternion-valued neural networks (QVNNs), and, more recently, by Clifford-valued neural networks (ClVNNs). However, also very recently, a different type of NNs were put forward, namely octonion-valued neural networks (OVNNs). OVNNs are defined on the 8D octonion algebra, and they are not a special type of ClVNNs, because Clifford numbers are associative, whereas octonions are not. Moreover, beside the complex and quaternion algebras, the only other normed division algebra over the reals is the algebra of octonions, which makes OVNNs a direct generalization of CVNNs and QVNNs from this point of view, raising interest for applications handling high-dimensional data. On the other hand, systems defined on time scales were proposed as a generalization of both discrete time and continuous time systems, or any type of hybrid combination between the two. Finally, time delays appear as a consequence of implementing NNs in real life circuits. Taking all these into consideration, this paper studies the fundamental properties of exponential stability and exponential synchronization for OVNNs with leakage and mixed delays defined on time scales. In order to avoid the problems raised by the non-associativity of the octonion algebra, the OVNN model is decomposed into a real-valued one. Then, two different Lyapunov-type functionals are defined and the particularities of time scale calculus are used in order to deduce sufficient conditions expressed as scalar and linear matrix inequalities (LMIs) for the exponential stability of the proposed models, based on Halanay-type inequalities suitable for time scale systems. Afterwards, a state feedback controller is used to deduce sufficient criteria given as scalar inequalities and LMIs for the exponential synchronization of the same type of models. The generality of the model, given by the definition on the algebra of octonions, the use of different types of delays, and the definition on time scales represent an important advantage. Also, for less general models, it is possible to particularize the obtained results. With the aim to demonstrate each of the paper's four theorems, four numerical examples are provided. [ABSTRACT FROM AUTHOR]

A practical fixed‐time composite learning control scheme, by combining dynamic regressor extension and mixing (DREM) parameter identification algorithm and adaptive dynamic surface control (DSC) technique, is proposed for a class of strict‐feedback non‐linear systems subjected to linear‐in‐parameters uncertainties and full‐state constraint. To address the problem of state constraint, a non‐linear transformation function is introduced to convert the originally constrained non‐linear system into an unconstrained one. Meanwhile, the hyperbolic tangent function is employed to avoid singularity issues that often appeared in the traditional fixed‐time (FXT) control designs. In order to relax the requirement of persistency of excitation condition, a modified FXT‐DREM parameter identification approach with an interval excitation condition is constructed by introducing a three‐layer transformation technique derived from the classical DREM algorithm. Then, the modified FXT‐DREM parameter identification algorithm is seamlessly integrated into the adaptive DSC framework, resulting in a composite‐learning control scheme. By employing Lyapunov stability analysis, the fixed‐time convergence of both the parameter estimation error and the trajectory tracking error is proved. Finally, the effectiveness of the proposed design is demonstrated through simulation test. [ABSTRACT FROM AUTHOR]

The recent methods that guarantee the stability of the reduced-order models are Mihailov stability, improved Pade approximation and truncation, improved generalized pole clustering, moment matching and salp swarm optimization. Further, these methods could overcome the limitations such as non-uniqueness, pole clustering, gain adjustment and difficulty to maintain the dominant roots in the lower order system for non-minimum higher order plants. This research emphasizes the design of the proposed compensating algorithm by using an additional open loop zero for the stable reduced-order models of large-scale single-input single-output linear time-invariant continuous time systems. The results of the proposed algorithm are compared with the existing compensating methods and the design is validated and illustrated numerically. [ABSTRACT FROM AUTHOR]

Abstract This paper extends the characteristic ratio approach using novel inequalities to ensure zero/low overshoot for linear‐time‐invariant systems with zeros. The extension provided by this paper is based on the maximally‐flatness property of a transfer function, where the square‐magnitude of the transfer function is ensured to be a low‐pass filter. In order to be able to design low‐order/fixed structure controllers, a partial pole‐assignment approach is used instead of the full pole‐assignment used in the Characteristic Ratio Assignment (CRA) method. The developed inequalities and additional stability conditions are combined into an optimization problem using time domain restrictions when necessary. Although the method given in the paper is general, particular inequalities are developed for PI and PI‐PD controller cases, due to their frequent use in industrial applications. Similarly, First‐Order‐Plus‐Delay‐Time (FOPDT) and Second‐Order‐Plus‐Delay‐Time (SOPDT) systems are considered specifically, since most of the practical systems can be approximated by one of these types. The study is extended to plants with uncertainties where a theorem is developed to decrease computation time dramatically. The benefits of the proposed methods are demonstrated by several examples.

This paper extends the characteristic ratio approach using novel inequalities to ensure zero/low overshoot for linear‐time‐invariant systems with zeros. The extension provided by this paper is based on the maximally‐flatness property of a transfer function, where the square‐magnitude of the transfer function is ensured to be a low‐pass filter. In order to be able to design low‐order/fixed structure controllers, a partial pole‐assignment approach is used instead of the full pole‐assignment used in the Characteristic Ratio Assignment (CRA) method. The developed inequalities and additional stability conditions are combined into an optimization problem using time domain restrictions when necessary. Although the method given in the paper is general, particular inequalities are developed for PI and PI‐PD controller cases, due to their frequent use in industrial applications. Similarly, First‐Order‐Plus‐Delay‐Time (FOPDT) and Second‐Order‐Plus‐Delay‐Time (SOPDT) systems are considered specifically, since most of the practical systems can be approximated by one of these types. The study is extended to plants with uncertainties where a theorem is developed to decrease computation time dramatically. The benefits of the proposed methods are demonstrated by several examples. [ABSTRACT FROM AUTHOR]

This article investigates the policy iteration (PI) method for the discounted optimal control (DOC) problem of continuous‐time linear systems. We show the properties and convergence of the PI method. The theory analysis shows that the convergence of PI can be ensured without requiring the initial admissible control gain. The convergence rate of the PI method is provided. An iteration‐termination criterion is established for detecting the stability of the closed‐loop system under the control gain obtained by executing PI. Two kinds of data‐driven implementations are constructed without using prior information of the system dynamics. A simulation example is presented to validated the properties of the PI method. [ABSTRACT FROM AUTHOR]

This article features the composite disturbance estimation and non-fragile hybrid-triggered control problems for continuous-time repeated scalar nonlinear systems prone to external disturbances. Priorly, the proportional integral observer comprising of both proportional and integral loops is incorporated to obtain better state estimations. Further, the external disturbance weakening the system performance is carefully estimated by deploying an improved equivalent-input-disturbance technique. Then, the availed disturbance estimate is blended into the control algorithm to exterminate the influence of the disturbance acting upon the proffered system. Next, a hybrid-triggered control comprised of a transition among event and time triggered paradigms are considered to reduce the network transmittance and also to simultaneously enhances the system outcomes. On top of that, the perturbations in controller gain matrix are taken into concern in order to make the controller more resilient towards redundant changes. Following that, utilising the Lyapunov theory, we obtain the mean-square asymptotic stability requirements for the developed system with the use of linear matrix inequalities and configure the gain matrices. Successively, the credibility of the synthesised control system is portrayed by exhibiting two numerical examples. [ABSTRACT FROM AUTHOR]

This paper investigates the linear quadratic regulator (LQR) problem for continuous-time linear systems with redundant control inputs. The LQR control problem has been widely studied, but due to technical difficulties, there is little advance in the study of adding input redundancies. To address this problem, a convergent matrix series, the limit of a monotonically decreasing sequence, is first presented as an upper bound of the symmetric positive definite solution of a class of continuous algebraic Riccati equations (CAREs). Compared with the existing studies on this topic, the obtained bounds are more precise. Moreover, by utilising these upper bounds in the LQR problem of adding input redundancies, a class of sufficient conditions is presented to decrease the quadratic performance index. Finally, the corresponding numerical examples are given to illustrate the effectiveness of our results and compare them with the existing results. Meanwhile, some simulation experiments show that systems with redundant control inputs have good control performance. [ABSTRACT FROM AUTHOR]

Intermittent control stands as a valuable strategy for resource conservation and cost reduction across diverse systems. Nonetheless, prevailing research is intractable to address the challenges posed by robust optimal intermittent control of nonlinear input-affine systems with unmatched uncertainties. This paper aims to fill this gap. Initially, we introduce an enhanced finite-time intermittent control approach to ensure stability within nonlinear dynamic systems harboring bounded errors. A neural networks (NNs) state observer is constructed to estimate system information. Subsequently, an optimal intermittent controller that operates within a finite time span, guaranteeing system stability by employing the Hamilton–Jacobi–Bellman (HJB) methodology. Furthermore, we devise an output information-based event-triggered intermittent (ETI) approach rooted in the robust adaptive dynamic programming (ADP) algorithm, furnishing an optimal intermittent control law. In this process, a critic NNs is introduced to estimate the cost function and optimal intermittent controller. Simulation results show that our proposed method is superior to existing intermittent control strategies. • We study the robust intermittent affine control system with unmatched uncertainties. • In contrast to the existing ET ADP, we introduce a novel intermittent ET ADP. • The proposed optimal output intermittent control show better control performance. [ABSTRACT FROM AUTHOR]

The fact that VCO-ADCs produce noise-shaped quantization noise suggests that a link between frequency modulation and Sigma-Delta modulation should exist. The connection between a VCO-ADC and a first-order Sigma-Delta modulator has been already explained using Pulse Frequency Modulation. In this article, we attempt to extend this explanation to a generic Sigma-Delta modulator. We show that the link between Sigma-Delta modulation and Pulse Frequency Modulation relies in a sampling invariance property that defines the equivalence between both entities. This equivalence property, allows to go beyond the white quantization noise model of a Sigma-Delta modulator, revealing the origin of some nonlinear phenomena. We first predict spurious tones which cannot be explained by circuit non linearity. Multi-bit and single-bit modulators are shown to belong to a same generic class of systems. Finally, quantizer overload is analyzed using our model. The results are applied to Continuous-Time Sigma-Delta modulators of orders one, two and three and then extended to a generic case. [ABSTRACT FROM AUTHOR]

This paper studies a control problem of continuous time Lur'e systems involving input quantization (for the output of the controller) and output quantization (for the output of the plant). When the output of one quantization operator becomes directly the input of the other one, the nested quantization is produced, which is difficult for the design of the systems. Based on spherical polar coordinate quantizer, a quantization method with finite data rate is proposed for handling the nested quantization. In addition, both the quantization errors and Lur'e‐type nonlinearity are converted to sector bound uncertainties that are modeled by norm bounded uncertain matrices, which facilitates the design of the systems. Owing to the quantization error the resulting closed‐loop system is described by a discontinuous right‐hand side differential equation and the notion of Krasovskii solution is adopted for the equation. By Krasovskii solution the update rule of the quantization region is designed to ensure the convergence to the origin of the system with the nested quantization and avoid the quantizer saturation. Further, since the quantizers cannot quantize the controller output and the system output directly, we develop an optimalization problem for each quantizer to obtain the estimates of the outputs of the plant and the controller. Finally, a method is presented to achieve the parameters of the controller. [ABSTRACT FROM AUTHOR]

In this paper we would like to address the classical optimization problem of minimizing a proper, convex and lower semicontinuous function via the second order in time dynamics, combining viscous and Hessian-driven damping with a Tikhonov regularization term. In our analysis we heavily exploit the Moreau envelope of the objective function and its properties as well as Tikhonov regularization properties, which we extend to a nonsmooth case. We introduce the setting, which at the same time guarantees the fast convergence of the function (and Moreau envelope) values and strong convergence of the trajectories of the system to a minimal norm solution—the element of the minimal norm of all the minimizers of the objective. Moreover, we deduce the precise rates of convergence of the values for the particular choice of parameters. Various numerical examples are also included as an illustration of the theoretical results. [ABSTRACT FROM AUTHOR]

Abstract The definition of scaled p‐norm and its properties are given here. Compared with the norm‐normalized sign function, using scaled p‐norm in the controller design can not only achieve the time‐synchronized stability of non‐linear dynamic systems, but also improve the convergence rate of the system. Besides, the scaled p‐norm is applied to design the consensus protocol for multi‐agent systems, which enables the states of all agents to achieve fast time‐synchronized consensus. The simulation results demonstrate the superiority of this method in improving the convergence rate of the system.

We consider the problem of partitioning a set of items into unlabeled subsets so as to optimize an additive objective, i.e., the objective function value of a partition is equal to the sum of the contribution of each subset. Under an arbitrary objective function, this family of problems is known to be an N P -complete combinatorial optimization problem. We study this problem under a broad family of objective functions characterized by elementary symmetric polynomials, which are "building blocks" to symmetric functions. By analyzing a continuous relaxation of the problem, we identify conditions that enable the use of a reformulation technique in which the set partitioning problem is cast as a more tractable network flow problem solvable in polynomial-time. We show that a number of results from the literature arise as special cases of our proposed framework, highlighting its generality. We demonstrate the usefulness of the developed methodology through a novel and timely application of quarantining heterogeneous populations in an optimal manner. Our case study on real COVID-19 data reveals significant benefits over conventional measures in terms of both spread mitigation and economic impact, underscoring the importance of data-driven policies. [ABSTRACT FROM AUTHOR]

Continuous-time state-space models (SSMs) are flexible tools for analysing irregularly sampled sequential observations that are driven by an underlying state process. Corresponding applications typically involve restrictive assumptions concerning linearity and Gaussianity to facilitate inference on the model parameters via the Kalman filter. In this contribution, we provide a general continuous-time SSM framework, allowing both the observation and the state process to be non-linear and non-Gaussian. Statistical inference is carried out by maximum approximate likelihood estimation, where multiple numerical integration within the likelihood evaluation is performed via a fine discretization of the state process. The corresponding reframing of the SSM as a continuous-time hidden Markov model, with structured state transitions, enables us to apply the associated efficient algorithms for parameter estimation and state decoding. We illustrate the modelling approach in a case study using data from a longitudinal study on delinquent behaviour of adolescents in Germany, revealing temporal persistence in the deviation of an individual's delinquency level from the population mean. [ABSTRACT FROM AUTHOR]

Summary: This article aims to address state and sensor fault estimation issue for a class of continuous‐time nonlinear switched systems, modelled as Takagi‐Sugeno (T‐S) models with nonlinear consequent parts and subject to L2$$ {L}_2 $$ norm bounded disturbances. This modelling approach helps to prevent Unmeasured Premise Variables (UPVs) problem. The primary contribution of this study consists of proposing robust H∞$$ {H}_{\infty } $$ asynchronous switched observers to simultaneously estimate state and sensor faults under state‐dependent switching. Based on a candidate multiple Lyapunov function, the design of the proposed observer is formulated in terms of Linear Matrix Inequalities (LMIs) conditions. These conditions are dwell‐time‐independent and less conservative compared with similar previous studies, thanks to some usual relaxation techniques and the incremental quadratic constraints applied on unmeasured nonlinear consequent parts. Another contribution consists to perform the estimation of the attraction domain of the estimation error using an optimization procedure. In order to illustrate the effectiveness of the proposed design approach, two simulation examples are considered. The first one concerns the conservatism reduction brought by our proposal compared with previous studies, while the second one is dedicated to show through an illustrative example the performance of the proposed switched T‐S observers under mismatching switching laws. [ABSTRACT FROM AUTHOR]

This paper crowns efforts, made by its author, aiming in showing and proving that the current formula for calculation of the spectra of output signals at A/D converters requires a correcting factor in it. A number of partial results obtained and published in the last years are referred to here. They paved the way to a fully satisfactory and correct result; it is presented in this work. The corrected formula for spectrum calculation is derived using a description of the output signal of an A/D converter by means of the so-called Dirac comb, however not in a direct form, but with taking into account physical reality. In addition, the paper contains a number of interpretative remarks, comments, and explanations - clarifying those matters that have so far been omitted in analyses of the sampling process, despite the fact that they raised various types of doubts. [ABSTRACT FROM AUTHOR]

This work uses the entropy-regularized relaxed stochastic control perspective as a principled framework for designing reinforcement learning (RL) algorithms. Herein, an agent interacts with the environment by generating noisy controls distributed according to the optimal relaxed policy. The noisy policies, on the one hand, explore the space and hence facilitate learning, but, on the other hand, they introduce bias by assigning a positive probability to nonoptimal actions. This exploration-exploitation trade-off is determined by the strength of entropy regularization. We study algorithms resulting from two entropy regularization formulations: the exploratory control approach, where entropy is added to the cost objective, and the proximal policy update approach, where entropy penalizes policy divergence between consecutive episodes. We focus on the finite horizon continuous-time linear-quadratic (LQ) RL problem, where a linear dynamics with unknown drift coefficients is controlled subject to quadratic costs. In this setting, both algorithms yield a Gaussian relaxed policy. We quantify the precise difference between the value functions of a Gaussian policy and its noisy evaluation and show that the execution noise must be independent across time. By tuning the frequency of sampling from relaxed policies and the parameter governing the strength of entropy regularization, we prove that the regret, for both learning algorithms, is of the O √N) (up to a logarithmic factor) over N episodes, matching the best known result from the literature. [ABSTRACT FROM AUTHOR]

We construct a marginally stable linear switching system in continuous time, in four dimensions, and with three switching states, which is exponentially stable with respect to constant switching laws and which has a unique Barabanov norm, but such that the Barabanov norm fails to be strictly convex. This resolves a question of Chitour, Gaye, and Mason. [ABSTRACT FROM AUTHOR]

This study examined the control problem of continuous‐time nonlinear systems under a sample‐and‐hold control structure. A new integral‐type double self‐triggered (ST) model predictive control (MPC) approach is developed by combining a novel ST strategy with MPC, which significantly decreases the sampling frequency of the system, saving computation/communication resources. In contrast to the traditional ST strategy, two integral‐type self‐triggering mechanisms are designed based on the mode of the state and the integral of the difference between the optimal and actual states. In addition, the integral‐type double ST‐MPC algorithm is developed, and the feasibility and stability of the closed‐loop system are rigorously demonstrated. Finally, the effectiveness and superiority of the proposed algorithm are verified by comparing the simulation results with those of existing ST‐MPC methods. [ABSTRACT FROM AUTHOR]

This paper proposes a recursive delta-operator-based subspace identification method with fixed data size. The majority of existing subspace identification methods are constrained to discrete-time systems because of the disparity in Hankel matrices. Additionally, due to the storage cost, LQ-factorization and singular value decomposition in identification methods are best suited for batch processing rather than online identification. The continuous-time systems are transformed into state space models based on the delta-operator to address these issues. These models approach the original systems when the sampling interval approaches zero. The size of the data matrices is fixed to reduce the computing load. By fading the impact of past data on future data, the amount of data storage can be decreased. The effectiveness of the proposed method is illustrated by the continuous stirred tank reactor system. [ABSTRACT FROM AUTHOR]

This paper presents a closed-loop continuous-time subspace identification method using prior information. Based on a rational inner function, a generalized orthonormal basis can be constructed, and the transformed noises have ergodicity features. The continuous-time stochastic system is converted into a discrete-time stochastic system by using generalized orthogonal basis functions. As is known to all, incorporating prior information into identification strategies can increase the precision of the identified model. To enhance the precision of the identification method, prior information is integrated through the use of constrained least squares, and principal component analysis is adopted to achieve the reliable estimate of the system. Moreover, the identification of open-loop models is the primary intent of the continuous-time system identification approaches. For closed-loop systems, the open-loop subspace identification methods may produce biased results. Principal component analysis, which reliably estimates closed-loop systems, provides a solution to this problem. The restricted least-squares method with an equality constraint is used to incorporate prior information into the impulse response following the principal component analysis. The input–output algebraic equation yielded an optimal multi-step-ahead predictor, and the equality constraints describe the prior information. The effectiveness of the proposed method is provided by numerical simulations. [ABSTRACT FROM AUTHOR]

Carbon dots (CDs) are a new class of nanomaterials exhibiting high biocompatibility, water solubility, functionality, and tunable fluorescence (FL) property. Due to the limitations of batch hydrothermal synthesis in terms of low CDs yield and long synthesis duration, this work aimed to increase its production capacity through a continuous flow reactor system. The influence of temperature and time was first studied in a batch reactor for glucose, xylose, sucrose and table sugar precursors. CDs synthesized from sucrose precursor exhibited the highest quantum yield (QY) (175.48%) and the average diameter less than 10 nm (~6.8 ± 1.1 nm) when synthesized at 220°C for 9 h. For a flow reactor system, the best condition for CDs production from sucrose was 1 mL min−1 flow rate at 280°C, and 0.2 MPa pressure yielding 53.03% QY and ~ 6.5 ± 0.6 nm average diameter (6.6 mg min−1 of CDs productivity). CDs were successfully used as ciprofloxacin (CP) nanocarrier for antimicrobial activity study. The cytotoxicity study showed that no effect of CDs on viability of L-929 fibroblast cells was detected until 1000 µg mL−1 CDs concentration. This finding demonstrates that CDs synthesized via a flow reactor system have a high zeta potential and suitable surface properties for nano-theranostic applications. In this work, we focused on a scaled-up production of CDs from various sugar monomers from a batch hydrothermal synthesis to a continuous flow microreactor system. From the result, the novelties of the work are as follows: Successful CDs' production with high capacity of 6.6 mg CDs min−1 was achieved from sucrose in a continuous system at the reaction time of only 4.4 min at moderate temperature (280–350°C) and pressure (<2 MPa). The developed process was greatly superior than the process in a batch reactor which provided only 0.19 mg CDs min−1 when the reaction time was 9 or 12 h. The produced CDs were subsequently used as in vitro antimicrobial drug nanocarrier due to its high zeta potential indicating its high stability in aqueous solution, thus led to enhanced CP loading capacity. The pH-controlled released of CP from CP@CDs conjugates worked efficiently toward gram-positive and gram-negative bacterial strains, namely, Staphylococcus aureus, Escherichia coli and Pseudomonas aeruginosa. In vitro cytotoxicity against mammalian fibroblast cells (L-929 cells) was also carried on. The findings demonstrated that CDs potentially serve as a new type of nanocarrier with good functionality, FL properties and markedly high biocompatibility for further nanomedicine and nanotherapeutic. Their utilization is potentially combined with photonic property such as bioimaging for rapid in vivo monitoring of targeted intracellular drug-release toward specific cells, sensitive neurodegeneration detection as well as photo-responsive anti-inflammatory wound healing application. [ABSTRACT FROM AUTHOR]

Abstract This paper designs a finite‐time convergence protocol and an event‐triggered control protocol based on Zero‐Gradient‐Sum (ZGS) algorithm under stochastic switching undirected topology, respectively, which greatly expands the theory of continuous‐time distributed optimization algorithms. With finite‐time stability and Lyapunov stability analysis, it is illustrated that the proposed method can finite‐time converge to the optimal solution of distributed unconstrained convex optimization problem and overcome the disturbances of the switching communication networks. In addition, the event‐triggered mechanism can effectively reduce the network burden and communication cost as well as avoid Zeno behaviour. Finally, two numerical simulations verify the advantages and effectiveness of these methods.

A new approach to the transformations of the matrices of linear continuous-time systems to their canonical forms with desired eigenvalues is proposed. Conditions for the existence of solutions to the problems were given and illustrated by simple numerical examples. [ABSTRACT FROM AUTHOR]

• This paper investigates the finite-time and fixed-time input-to-state stability of impulsive nonlinear systems. • Both cases of stable/unstable continuous dynamics and impulses are studied by unified ADT conditions. • The Lyapunov functions with time-varying linear/nonlinear rates are utilized to handle the twofold effect of impulses. • It determines that the stable nonlinear systems are robust against hybrid impulses with multiple jump maps. In this paper, we investigate the finite-time and fixed-time input-to-state stability of impulsive nonlinear systems involving hybrid impulses which have time-dependent multiple jump maps. Under unified average dwell-time conditions, several criteria for finite-time and fixed-time input-to-state stability are established by virtue of the Lyapunov function with linear rate and nonlinear rate of jump maps. It shows that, when the finite/fixed-time input-to-state stable continuous systems are subject to hybrid impulses, the finite-time and fixed-time input-to-state stability can be ascertained under the requirement that the accumulative effect of hybrid impulses is non-destabilizing or the accumulative effect of hybrid impulses is destabilizing and the impulses are not activated too frequently. Finally, the effectiveness of theoretical results is verified by two numerical examples and an application example about an axisymmetric circular spacecraft. [ABSTRACT FROM AUTHOR]

We demonstrate how developmental theories may be instantiated as statistical models, using hierarchical continuous‐time dynamic systems. This approach offers a flexible specification and an often more direct link between theory and model parameters than common modeling frameworks. We address developmental theories of the relation between the academic competencies of mathematics and language, using data from the online learning system Mindsteps. We use ability estimates from 160,164 observation occasions, across N = 4623 3rd to 9th grade students and five ability domains. Model development is step‐by‐step from simple to complex, with ramifications for theory and modeling discussed at each step. [ABSTRACT FROM AUTHOR]

Aiming at the carrier landing control problem of the fixed-wing unmanned aerial vehicle (UAV) with model uncertainties and external disturbances, a discrete-time fuzzy flight control (DFFC) strategy is proposed to improve the flight performance by utilizing a discrete-time disturbance observer (DTDO) and the prescribed performance control (PPC) method in this paper. Firstly, the continuous time system model with uncertainties and disturbances is transformed into a discrete-time model by Euler approximation method and then the model uncertainties are approximated by the fuzzy logic system (FLS). Then, a DTDO based on the FLS is designed to estimate and compensate the disturbances caused by the deck motion and airwake, and the DFFC method is developed with the assistance of the discrete-time dynamic surface control and the PPC method. Notably, the designed DTDO by introducing FLS further improves the robustness of the system. Preciously, the application of the PPC ensures that the UAV can track the reference glide trajectory within the specified performance range. At last, the stability of the system is proved by Lyapunov theory, and the effectiveness and supremacy of the DFFC are illustrated via the simulation comparison and analysis. [ABSTRACT FROM AUTHOR]

The definition of scaled p‐norm and its properties are given here. Compared with the norm‐normalized sign function, using scaled p‐norm in the controller design can not only achieve the time‐synchronized stability of non‐linear dynamic systems, but also improve the convergence rate of the system. Besides, the scaled p‐norm is applied to design the consensus protocol for multi‐agent systems, which enables the states of all agents to achieve fast time‐synchronized consensus. The simulation results demonstrate the superiority of this method in improving the convergence rate of the system. [ABSTRACT FROM AUTHOR]

Traffic flow forecasting is a critical task for intelligent transportation systems. However, the existed forecasting can only be conducted at certain time steps, because the data are discretely collected at these time steps. In contrast, traffic flow evolves in real time via a continuous manner in real world. Therefore, an ideal forecasting paradigm should be performed at arbitrary time steps instead of only at these certain time steps. Considering the forecasting time steps will no longer be restricted by these time steps, we call such paradigm as temporal super-resolution forecasting. In this paper, we incorporate the idea of neural ordinary differential equations (neural ODEs) to handle the problem, modeling the change rate of traffic flow on the urban road. Therefore, due to the continuous nature of ordinary differential equations, the traffic flow at arbitrary time steps can be forecasted by performing definite integral for the change rate. The urban road is usually regarded as a network, and the change rate of which can be described by continuous-time network dynamics, we parameterize the network dynamics of the traffic flow to quantify the change rate. On these foundations, we propose spatial-temporal continuous dynamics network to complete the temporal super-resolution forecasting task. Extensive experiments on public traffic flow datasets illustrate that our model can achieve high accuracy on temporal super-resolution forecasting, while ensuring its performance on conventional experimental settings at these certain time steps. [ABSTRACT FROM AUTHOR]

This paper addresses the time‐regularization event‐triggered H∞$$ {H}_{\infty } $$ control problem for a class of continuous‐time switched systems with frequent asynchronism and external disturbances. In the system, both the system state and the switching information are transmitted to the controller only at the event‐triggered sampling instants, which may cause the occurrence of asynchronous switching behavior. To solve the problem, we first propose a time‐regularization event‐triggered mechanism, which not only avoids Zeno behavior efficaciously, but also allows the system to switch multiple times in the holding interval. Then, based on the time‐regularization event‐triggered mechanism, the error system is modeled as a sampled switched delay system with augmented switching signal. After that, sufficient conditions for the exponentially stability and weighted H∞$$ {H}_{\infty } $$ performance of the switched system under average dwell time are derived by constructing multiple switching Lyapunov functions. Finally, a circuit example is given to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Parametric continuous-time analysis often entails derivations of continuous-time models from predefined discrete formulations. However, undetermined convergence rates of frequency-dependent parameters can result in ill-defined continuous-time limits, leading to modeling discrepancy, which impairs the reliability of fitting and forecasting. To circumvent this issue, we propose a simple solution based on functional data analysis (FDA) and truncated Taylor series expansions. It is demonstrated through a simulation study that our proposed method is superior—compared with misspecified parametric methods—in fitting and forecasting continuous-time stochastic processes, while the parametric method slightly dominates under correct specification, with comparable forecast errors to the FDA-based method. Due to its generally consistent and more robust performance against possible misspecification, the proposed FDA-based method is recommended in the presence of modeling discrepancy. Further, we apply the proposed method to predict the future return of the S&P 500, utilizing observations extracted from a latent continuous-time process, and show the practical efficacy of our approach in accurately discerning the underlying dynamics. [ABSTRACT FROM AUTHOR]

In this paper, the problem of sliding mode preview repetitive control (SMPRC) for continuous-time nonlinear systems is proposed. First, an augmented delay system is constructed, in which the output of the modified repetitive controller is taken as a part of the augmented state vector. The augmented delay system is then transformed into the controllable canonical form by using state and linear transformations. To introduce preview compensation, a virtual optimal preview control (PC) law is designed for the uncontrollable subsystem. Next, a sliding mode control (SMC) law is cooperated with the virtual optimal PC law to ensure the robustness of the overall system in the presence of uncertainties and external disturbances. Stability of the proposed controller is also proved. Finally, the numerical simulation results demonstrate the effectiveness of the proposed method. Abbreviations: LQR: linear quadratic regulator; MRC: modified repetitive control; PC:preview control; PRC: preview repetitive control; RC: repetitive control; SFC: statefeedback control; SMC: sliding mode control; SMPRC: sliding mode preview repetitivecontrol. [ABSTRACT FROM AUTHOR]

We investigate the reinsurance contract and investment strategy problem between an insurer and a reinsurer under the continuous-time framework. For the reinsurance contract design, the joint interests of the insurer and the reinsurer are considered. That is, the insurer determines the claim risk sharing strategy, and the reinsurer determines the reinsurance price. The insurer and the reinsurer can invest in the common risk-free asset and different risky assets to increase their respective wealths. The competition between the insurer and the reinsurer is quantified through the relative performance. Both the insurer and the reinsurer aim at maximizing the expected value of the terminal pay-off while minimizing its variance. By using the stochastic optimal control technique, we derive analytically the optimal time-consistent investment strategy and obtain the optimal reinsurance contract. Finally, the influences of model parameters on the optimal reinsurance contract and time-consistent investment strategy are examined through numerical experiments. [ABSTRACT FROM AUTHOR]

In this paper for linear discrete time switched systems, the problem of existence of a common solution to Stein inequalities is considered. A sufficient condition for robust Schur stability of a matrix polyope by using Schur complement lemma and a necessary and sufficient condition for the existence of a common solution of Stein equation are given. As in the case of continuous time systems, the problem of existence of a common solution is reduced to a convex optimization one. An efficient solution algorithm which requires solving a linear minimax problem at each step is suggested. The algorithm is supported with a number of examples from the literature and observed that the method desired results fastly. [ABSTRACT FROM AUTHOR]