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The problem is considered to find the time-optimal control that transfers a fourth-order system that consists of a double integrator and a harmonic oscillator, coupled by one control channel, between two arbitrary states. That fourth-order system is equivalent to the Hill-Clohessy-Wiltshire model of the relative dynamics of an orbiting spacecraft in proximity of a second spacecraft on a circular reference orbit, subjected to a thrust parallel to the orbital velocity vector and having time-continuous amplitude. A new method is here introduced to determine the time-optimal control problem stated above. This method combines two previously discovered optimal control synthesis methods: the method by Romano and Curti (2020), that enables to find (analytically, in some case) the optimal control transferring a general Linear Time Invariant Normal system between two arbitrary states; and, the method by Belousova and Zarkh (1996), that enables to find the optimal control transferring a fourth-order system consisting of a double integrator and a harmonic oscillator, coupled by one control channel, from an arbitrary initial state to the origin of the state space, if the optimal control is a priori known, that transfers the same system from a reference state to the origin. The here proposed combined method utilizes two phases. During the first phase, a number of reference minimum-time controls are obtained that transfer the system from specific reference states to the state space origin; this is achieved by exploiting Pontryagin's principle together with back-propagation from the origin of the state space. During the second phase, a search is run along a particular curve in the state space (named extremal search path) that depends on the boundary states of the problem at hand. In particular, a minimum-time control problem is iteratively solved to find the optimal control history that steers the system from a state on that curve to the origin, by exploiting Belousova and Zarkh method, until a particular state is found which satisfies an equivalency condition that, as demonstrated by Romano and Curti, guarantees that the optimal control history pertaining to the problem of transferring the system from that state to the origin is the same optimal control history that transfers the system between the arbitrarily set initial and final states. The new results, substantiated by numerical experiments, have both a theoretical and a practical value, as they could be applied for the optimal guidance of spacecraft performing autonomous proximity maneuvers. [ABSTRACT FROM AUTHOR]

Summary: In this work, two state estimation methods are proposed for a class of discrete‐time descriptor linear systems subject to bounded uncertainties. First, we propose set‐valued estimator algorithm using symmetric boxes to compute rigorous bounds of the system states. The observer gains are calculated using L∞$$ {L}_{\infty } $$ norm to attenuate the effects of the uncertainties and to improve the accuracy of the proposed estimator. Second, to obtain tighter state enclosures, zonotopic set computation are developed instead of interval analysis to design a new set‐valued state estimation algorithm. The performances of the proposed state estimation approaches are highlighted on different illustrative examples. [ABSTRACT FROM AUTHOR]

Summary: A novel method of an adaptive linear quadratic (LQ) regulation of uncertain continuous linear time‐invariant systems is proposed. Such an approach is based on the direct self‐tuning regulators design framework and the exponentially stable adaptive control technique developed earlier by the authors. Unlike the known solutions, a procedure is proposed to obtain a non‐overparametrized regression equation (RE) with respect to the unknown controller parameters from an initial RE of the LQ‐based reference tracking control system. On the basis of such result, an adaptive law is proposed, which under mild regressor finite excitation condition provides monotonous convergence of the LQ‐controller parameters to an adjustable set of their true values, which bound is defined only by the machine precision. Using the Lyapunov‐based analysis, it is proved that the mentioned law guarantees the exponential stability of the closed‐loop adaptive optimal control system. The simulation examples are provided to validate the theoretical contributions. [ABSTRACT FROM AUTHOR]

Accurate short-term load forecasting (STLF) is essential for power grid systems to ensure reliability, security and cost efficiency. Thanks to advanced smart sensor technologies, time-series data related to power load can be captured for STLF. Recent research shows that deep neural networks (DNNs) are capable of achieving accurate STLP since they are effective in predicting nonlinear and complicated time-series data. To perform STLP, existing DNNs use time-varying dynamics of either past load consumption or past power correlated features such as weather, meteorology or date. However, the existing DNN approaches do not use the time-invariant features of users, such as building spaces, ages, isolation material, number of building floors or building purposes, to enhance STLF. In fact, those time-invariant features are correlated to user load consumption. Integrating time-invariant features enhances STLF. In this paper, a fuzzy clustering-based DNN is proposed by using both time-varying and time-invariant features to perform STLF. The fuzzy clustering first groups users with similar time-invariant behaviours. DNN models are then developed using past time-varying features. Since the time-invariant features have already been learned by the fuzzy clustering, the DNN model does not need to learn the time-invariant features; therefore, a simpler DNN model can be generated. In addition, the DNN model only learns the time-varying features of users in the same cluster; a more effective learning can be performed by the DNN and more accurate predictions can be achieved. The performance of the proposed fuzzy clustering-based DNN is evaluated by performing STLF, where both time-varying features and time-invariant features are included. Experimental results show that the proposed fuzzy clustering-based DNN outperforms the commonly used long short-term memory networks and convolution neural networks. [ABSTRACT FROM AUTHOR]

This paper presents the design and analysis of Switched Fractional Order Model Reference Adaptive Controllers (SFOMRAC) for Multiple Input Multiple Output (MIMO) linear systems with unknown parameters. The proposed controller uses adaptive laws whose derivation order switches between a fractional order and the integer order, according to a certain level of control error. The switching aims to use fractional orders when the control error is larger to improve transient response and system performance during large disturbed states, and to obtain smoother control signals, leading to a better control energy usage. Then, it switches to the integer order when the control error is smaller to improve steady state. Boundedness of all the signals in the scheme is analytically proved, as well as convergence of the control error to zero. Moreover, these properties are extended to the case when system states are affected by a bounded non-parametric disturbance. Simulation studies are carried out using different representative plants to be controlled, showing that fractional orders and switching error levels can be found in most of the cases, such as when SFOMRAC achieves a better balance among control energy and system performance than the non-switched equivalent strategies. [ABSTRACT FROM AUTHOR]

An application of moving-horizon strategy for nonlinear systems with possible outliers in measurements is addressed. With the increased success of movinghorizon strategy in the state estimation for linear systems with outliers acting on the measurement, investigating the nonlinear approach is highly required. In this paper we applied the nonlinear version which has been presented in the literature in term of discrete-time linear time-invariant systems, where the applied strategy considers minimizing a least-squares functions in which each measure possibly contaminated by outlier is left out in turn and the lowest cost is propagated. The moving horizon filter effectiveness as compared with the extended Kalman filter is shown by means of simulation example and estimation error comparison. The moving horizon filter shows the feature of resisting outliers with robust estimation. [ABSTRACT FROM AUTHOR]

This article presents a chance‐constrained tube‐based model predictive control (MPC) method for tracking linear time‐invariant systems based on data‐driven uncertainty sets. By defining the terminal admissible set to consider all the possible steady‐states and reformulating the stochastic tube‐based MPC framework, the proposed method can systematically hedge against the impact of uncertainties and ensure tracking for all reachable operating setpoints. To reduce the conservatism of control performance while enlarging the feasible region, a data‐driven polyhedral uncertainty set is constructed by using the principal component analysis technique, which can effectively capture correlations among uncertain variables. Since state constraint violations in a certain probability are allowed, a probability uncertainty set is constructed by using statistic limit and cutting plane methods to formulate a stochastic tube to ensure constraint satisfaction. The recursive feasibility and stability can be guaranteed if the uncertainties are bounded. The effectiveness of the proposed method is verified by numerical examples and tracking problems of a thickening process. [ABSTRACT FROM AUTHOR]

This paper addresses a problem of optimal error quantification in the framework of robust control theory in the 1 setup. The upper bounds of biased external disturbance and the gains of coprime factor perturbations in a discrete-time linear time invariant SISO plant are assumed to be unknown. The computation of optimal data-consistent upper bounds under a known bias of external disturbance has been simplified to linear programming. This allows for the computation of optimal estimates in real-time and their application to achieve optimal robust steady-state tracking even when facing an unknown bias in the external disturbance. The presented results have been illustrated through computer simulations. [ABSTRACT FROM AUTHOR]

Impulse responses (IRs) estimation of multi-input acoustic systems is a prerequisite for many audio applications. In this paper, an adaptive identification problem based on the Autostep algorithm is extended to the simultaneous estimation of room IRs for multiple input single output linear time invariant systems without any a priori information. To do so, the proposed algorithm is initially evaluated in a simulated room with several sound sources active at the same time. Finally, an experimental validation is proposed for the cases of a semi-anechoic chamber and an arbitrary room. Special attention is dedicated to the algorithm convergence behavior, considering different meta parameters settings. Results are eventually compared with the other normalized version of the least mean square algorithm. [ABSTRACT FROM AUTHOR]

This work investigates a state estimation problem for linear time-invariant systems based on polarized measurement information from event sensors. To enable estimator design, a new notion of observability, namely,\epsilon-observability is defined with the precision parameter\epsilon which relates to the worst-case performance of inferring the initial state, based on which a criterion is developed to test the\epsilon-observability of discrete-time linear systems. Utilizing multisensor polarity data from event sensors and the implicit information hidden in event-triggering conditions at no-event instants, an iterative event-triggered state estimator is designed to evaluate a set containing all possible values of the state. The proposed estimator is built by outer approximation of intersecting ellipsoids that are predicted from previous state estimates and the ellipsoids inferred from received polarity information of event sensors as well as the event-triggering protocol; the estimated regions of the state derived from multisensor event measurements are fused together, the sizes of which are proved to be asymptotically bounded. Distributed implementation of the estimation algorithm utilizing a two-layer processor network of hierarchy architecture is discussed, and the temporal computational complexity of the algorithm implemented in centralized and distributed ways is analyzed. The efficiency of the proposed event-triggered state estimator is verified by numerical experiments. [ABSTRACT FROM AUTHOR]

In this paper we prove that stabilisability is a static output feedback (SOF) invariant, for scalar and multivariable systems. Then we examine scalar stabilisability, from an invariant viewpoint. We prove that the signature of Hermite's Bezoutian is constant within certain intervals that we call critical, and we give a very simple algebraic stabilisability criterion, consisted of a finite number of stability checks, one for each critical interval. We establish the validity of this criterion with Routh, Hurwitz and Lyapunov methods. We prove that the winding number of the Nyquist plot around points of the real axis, is constant within critical intervals. We correlate the stabilisability within critical intervals with the stability of corresponding critical polynomials defined at their limits. Finally, we discuss why our findings constitute a decisive step towards the analytical solution for the persisting problem of static output feedback stabilizability of linear time invariant multivariable systems. [ABSTRACT FROM AUTHOR]

We consider a class of linear time invariant systems with control delay and additive disturbances. A state predictive feedback method is first applied to compensate the actuator delay. In this way, a closed loop system free of delay is achieved. It allows to ensure input‐to‐state‐stability of the closed loop system. Applications are given for the lateral‐directional stability of an airplane with two controls, on the aileron and on the rudder, in correlation with compliance with some regulatory flight conditions. [ABSTRACT FROM AUTHOR]

For arbitrary multiple‐input multiple‐output linear time invariant systems with unknown inputs this article provides sufficient conditions to estimate linear functionals of the state variables. When the unknown input is uniformly bounded these conditions are strictly weaker than the classical conditions for functional unknown input observers, well‐known in the literature, and generalize previous results using discontinuous differentiators. Furthermore, a general methodology is proposed to design functional observers, that are able to estimate the functionals, when possible, exactly and in finite‐time or fixed‐time. Instead of using a cascade of Luenberger observers and high‐order sliding‐mode differentiators, standard in the literature for this problem, a bi‐homogeneous observer of reduced order is proposed in the article. Proofs of the convergence are provided using smooth Lyapunov functions and an academic example illustrates the behavior of the proposed observer for a system not tractable with the available methods. [ABSTRACT FROM AUTHOR]

This article presents a new observer design approach for linear time invariant multivariable systems subject to unknown inputs. The design is based on a transformation to the so‐called special coordinate basis (SCB). This form reveals important system properties like invertability or the finite and infinite zero structure. Depending on the system's strong observability properties, the SCB allows for a straightforward unknown input observer design utilizing linear or nonlinear observers design techniques. The chosen observer design technique does not only depend on the system properties, but also on the desired convergence behavior of the observer. Hence, the proposed design procedure can be seen as a unifying framework for unknown input observer design. [ABSTRACT FROM AUTHOR]

The paper focuses on energy modelling that involves a concatenated structure of a linear time‐invariant system. A block‐structured (BS) technique was adopted for a nonlinear system identification. Using the superimposition principle, the model mapped the thermodynamic state variables as an indirect function of time to the output function. The available energy and degradation of solar radiation are determined through a black box model. For testing and validation purposes, a solar collector with recirculating air was considered. The basic principle is to establish a relation between state variables and the performance parameters, without invoking the conventional thermodynamic relationship between them. The output of the model was compared with the validation data to ensure whether or not there was any affinity between them. The sigmoidal, wavenet, and polynomial forms of nonlinearity provided a good fit to the experimental dataset. The mean absolute percentage error encountered while estimating the collector efficiency was noticed to vary from −4.85 × 10−03% to 1.22 × 10−03%. Similarly, it falls in the domain of −4.73 × 10−04% to 7.78 × 10−02% for the second law efficiency. The maximum heat loss rate (BS model) obtained across the first and second passages of the solar air collector was 235.41 and 218.19 W at the air mass flow rate of 8.10 g/s, which is congruent to the validation dataset. [ABSTRACT FROM AUTHOR]

This paper provides a parametrization of optimal anisotropic controllers for linear discrete time invariant systems. The controllers to be designed are limited by causal dynamic output-feedback control laws. The obtained solution depends on several adjustable parameters that determine the specific type of controller, and is of the form of a system of the Riccati equations relating to a -optimal controller for a system formed by a series connection of the original system and the worst-case generating filter corresponding to the maximum value of the mean anisotropy of the external disturbance. [ABSTRACT FROM AUTHOR]

This paper investigates a combined H∞$$ {H}_{\infty } $$ and anti‐disturbance control problem for a class of semi‐Markovian jump nonlinear systems with constant time delay, and both modeled and unmodeled disturbances. In particular, the modeled disturbance is thought to be produced by a nonlinear exogenous system and is estimated by introducing a mode‐dependent nonlinear disturbance observer. The desired controller for the addressed system is then proposed, which consists of two components: (i) state feedback, which ensures the system's stochastic stability by attenuating the unmodeled disturbance; and (ii) disturbance estimate, which compensates for the modeled disturbance effect. Following that, a novel mode‐dependent asymmetric Lyapunov‐Krasovskii functional is used to derive the sufficient conditions for the existence of the proposed controller and disturbance observer. The developed theoretical results are supported by three numerical examples that demonstrate the utility of the proposed design method. [ABSTRACT FROM AUTHOR]

Petrochemical and dairy industries, waste management, and paper manufacturing fall under the category of process industries where flow and liquid control are essential. Even when liquids are mixed or chemically treated in interconnected tanks, the fluid and flow should constantly be observed and controlled, especially when dealing with nonlinearity and imperfect plant models. In this study, we propose a nonlinear dynamic multiple-input multiple-output (MIMO) plant model. This model is then transformed through linearization, a technique frequently utilized in the analysis and modeling of fractional processes, and decoupling for decentralized fixed-structure H-infinity robust control design. Simulation tests based on MATLAB and SIMULINK are subsequently executed. Numerous assessments are conducted to evaluate tracking performance, external disturbance rejection, and plant parameter fluctuations to gauge the effectiveness of the proposed model. The objective of this work is to provide a framework that anticipates potential outcomes, paving the way for implementing a reliable controller synthesis for MIMO-connected tanks in real-world scenarios. [ABSTRACT FROM AUTHOR]

We develop original models to study interacting agents in financial markets and in social networks. Within these models, randomness is vital as a form of shock or news that decays with time. Agents learn from their observations and learning ability to interpret news or private information in time-varying networks. Under general assumptions on the noise, a limit theorem is developed for the generalized averaging framework for certain type of conditions governing the learning. In this context, the agents' beliefs (properly scaled) converge in distribution that is not necessarily normal. Fresh insights are gained not only from proposing a new setting for social learning models but also from using different techniques to study discrete-time random linear dynamical systems. [ABSTRACT FROM AUTHOR]

We present a novel physics-informed system identification method to construct a passive linear time-invariant system. In more detail, for a given quadratic energy functional, measurements of the input, state, and output of a system in the time domain, we find a realization that approximates the data well while guaranteeing that the energy functional satisfies a dissipation inequality. To this end, we use the framework of port-Hamiltonian (pH) systems and modify the dynamic mode decomposition, respectively, operator inference, to be feasible for continuous-time pH systems. We propose an iterative numerical method to solve the corresponding least-squares minimization problem. We construct an effective initialization of the algorithm by studying the least-squares problem in a weighted norm, for which we present the analytical minimum-norm solution. The efficiency of the proposed method is demonstrated with several numerical examples. [ABSTRACT FROM AUTHOR]

An axiomatic development of control systems theory can systematize important concepts. The current research article is dedicated to the investigation and comparison of two axiomatic approaches to the analysis of discrete linear time-invariant systems affected by external random disturbances. The main goal of this paper is to explore axiomatics of an anisotropy-based theory in comparison with axiomatics of a spectral entropy approach in detail. It is demonstrated that the use of the spectral entropy approach is mathematically rigorous, which allows one to prove that the minimal disturbance attenuation level in terms of an anisotropy-based control theory provides the desired performance that is not only for ergodic signals. As a result, axiomatics of the spectral entropy approach allows one to rigorously prove that anisotropy-based controllers can be used to guarantee the desired disturbance attenuation level, not only for stationary random sequences, but also for a wider set of input random signals. [ABSTRACT FROM AUTHOR]

This paper concerns the stabilization problem for an underactuated robot called the Pendubot. Relying on a computational algorithm which is based on various results of the 'polynomial matrix approach', we propose an output-feedback-based internally stabilizing controller to stabilize the Pendubot at the unstable vertical upright position. The algorithm utilizes results for the solution of polynomial matrix Diophantine equations required for the computation and parameterization of proper 'denominator assigning' and internally stabilizing controllers for linear time invariant multivariable systems and reduces the problem to that of the solution of a set of numerical linear equations. The controller presented uses only the measured output which consists of the angles of the two links and does not require knowledge of the angular velocities which are usually not directly measurable. Comparative simulations are carried out to verify the good performance of the proposed controller. Finally, experimental results are provided to demonstrate the validity and feasibility of the proposed method. [ABSTRACT FROM AUTHOR]

In the present paper we consider the problem of estimating the multidimensional power spectral density which describes a second-order stationary random field from a finite number of covariance and generalized cepstral coefficients. The latter can be framed as an optimization problem subject to multidimensional moment constraints, i.e., to search a spectral density maximizing an entropic index and matching the moments. In connection with systems and control, such a problem can also be posed as finding a multidimensional shaping filter (i.e., a linear time-invariant system) which can output a random field that has identical moments with the given data when fed with a white noise, a fundamental problem in system identification. In particular, we consider the case where the dimension of the random field is greater than two for which a satisfying theory is still missing. We propose a multidimensional moment problem which takes into account a generalized definition of the cepstral moments, together with a consistent definition of the entropy. We show that it is always possible to find a rational power spectral density matching exactly the covariances and approximately the generalized cepstral coefficients, from which a shaping filter can be constructed via spectral factorization. In plain words, our theory allows us to construct a well-posed spectral estimator for any finite dimension. [ABSTRACT FROM AUTHOR]

Control laws can be constructed in systems design by introducing parameters to obtain good system performance or robustness. Cai et al., in their paper 'Design of LPV controller for morphing aircraft using inexact scheduling parameters', establish a linear parameter-varying model for a morphing aircraft by Jacobian linearization. With such a model, Cai et al. investigate the design problem of gain-scheduled output-feedback controllers by using inexact scheduling parameters for morphing aircraft during the wing transition process. [Extracted from the article]

This article is concerned with the identification of time‐varying systems. Differently from the conventional polynomial approximation approaches, the changing laws of the time‐varying parameters are considered to build the identification model for the time‐varying systems. Specifically, the concept of the invariant matrix is put forward to characterize the time‐varying parameters and to establish the state‐space model with regard to the system parameters. Then this article proposes a stacked state estimation algorithm to achieve the time‐varying parameter estimation. Moreover, for the purpose of enhancing the computational efficiency, a detached state estimation algorithm is proposed by reducing the dimension of the state vector to reconstruct the state equation. Finally, a numerical simulation example is employed to demonstrate the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

This article deals with abstract linear time invariant controlled systems of parabolic type. In [9], with A. Benabdallah, we introduced the block moment method for scalar control operators. The principal aim of this method is to compute the minimal time needed to drive an initial condition (or a space of initial conditions) to zero, in particular in the case when spectral condensation occurs. The purpose of the present article is to push forward the analysis to deal with any admissible control operator. The considered setting leads to applications to one dimensional parabolic-type equations or coupled systems of such equations. With such admissible control operator, the characterization of the minimal null control time is obtained thanks to the resolution of an auxiliary vectorial block moment problem (i.e. set in the control space) followed by a constrained optimization procedure of the cost of this resolution. This leads to essentially sharp estimates on the resolution of the block moment problems which are uniform with respect to the spectrum of the evolution operator in a certain class. This uniformity allows the study of uniform controllability for various parameter dependent problems. We also deduce estimates on the cost of controllability when the final time goes to the minimal null control time. We illustrate how the method works on a few examples of such abstract controlled systems and then we deal with actual coupled systems of one dimensional parabolic partial differential equations. Our strategy enables us to tackle controllability issues that seem out of reach by existing techniques. [ABSTRACT FROM AUTHOR]

The fundamental lemma by Jan C. Willems and co-workers is deeply rooted in behavioral systems theory and it has become one of the supporting pillars of the recent progress on data-driven control and system analysis. This tutorial-style paper combines recent insights into stochastic and descriptor-system formulations of the lemma to further extend and broaden the formal basis for behavioral theory of stochastic linear systems. We show that series expansions – in particular Polynomial Chaos Expansions (PCE) of L 2 -random variables, which date back to Norbert Wiener's seminal work – enable equivalent behavioral characterizations of linear stochastic systems. Specifically, we prove that under mild assumptions the behavior of the dynamics of the L 2 -random variables is equivalent to the behavior of the dynamics of the series expansion coefficients and that it entails the behavior composed of sampled realization trajectories. We also illustrate the short-comings of the behavior associated to the time-evolution of the statistical moments. The paper culminates in the formulation of the stochastic fundamental lemma for linear time-invariant systems, which in turn enables numerically tractable formulations of data-driven stochastic optimal control combining Hankel matrices in realization data (i.e. in measurements) with PCE concepts. [ABSTRACT FROM AUTHOR]

Synchrophasor data provide unprecedented opportunities for inferring power system dynamics, such as estimating voltage angles, frequencies, and accelerations along with power injection at all buses. Aligned to this goal, this work puts forth a novel framework for learning dynamics after small-signal disturbances by leveraging Gaussian processes (GPs). We extend results on learning of a linear time-invariant system using GPs to the multi-input multi-output setup. This is accomplished by decomposing power system dynamics into a set of single-input single-output linear systems with narrow frequency pass bands. The proposed learning technique captures time derivatives in continuous time, accommodates data streams sampled at different rates, and can cope with missing data and heterogeneous levels of accuracy. While Kalman filter-based approaches require knowing all system inputs, the proposed framework handles readings of system inputs, outputs, their derivatives, and combinations thereof collected from an arbitrary subset of buses. Relying on minimal system information, it further provides uncertainty quantification in addition to point estimates of system dynamics. Numerical tests verify that this technique can infer dynamics at non-metered buses, impute and predict synchrophasors, and locate faults under linear and non-linear system models under ambient and fault disturbances. [ABSTRACT FROM AUTHOR]

This paper considers a discrete-time linear time invariant system in the presence of Gaussian disturbances/noises and sparse sensor attacks. First, we propose an optimal decentralized multi-sensor information fusion Kalman filter based on the observability decomposition when there is no sensor attack. The proposed decentralized Kalman filter deploys a bank of local observers who utilize their own single sensor information and generate the state estimate for the observable subspace. In the absence of an attack, the state estimate achieves the minimum variance, and the computational process does not suffer from the divergent error covariance matrix. Second, the decentralized Kalman filter method is applied in the presence of sparse sensor attacks as well as Gaussian disturbances/noises. Based on the redundant observability, an attack detection scheme by the χ 2 test and a resilient state estimation algorithm by the maximum likelihood decision rule among multiple hypotheses, are presented. The secure state estimation algorithm finally produces a state estimate that is most likely to have minimum variance with an unbiased mean. Simulation results on a motor controlled multiple torsion system are provided to validate the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

We present a novel problem formulation for model-free data-driven fault diagnosis, in which possible faults are diagnosed simultaneously to identifying the linear time-invariant system. This problem is practically relevant for systems whose model cannot be identified reliably prior to diagnosing possible faults, for instance when operating conditions change over time, when a fault is already present before system identification is carried out, or when the system dynamics change due to the presence of the fault. A computationally attractive solution is proposed by solving the problem using unconstrained convex optimization, where the objective function consists of three terms of which two are non-differentiable. An additional recursive implementation based on a proximal algorithm is presented in order to solve the optimization problem online. The numerical results on a buck converter show the application of the proposed solution both offline and online. [ABSTRACT FROM AUTHOR]

Linear time-invariant systems are very popular models in system theory and applications. A fundamental problem in system identification that remains rather unaddressed in extant literature is to leverage commonalities amongst related systems to estimate their transition matrices more accurately. To address this problem, we investigate methods for jointly estimating the transition matrices of multiple systems. It is assumed that the transition matrices are unknown linear functions of some unknown shared basis matrices. We establish finite-time estimation error rates that fully reflect the roles of trajectory lengths, dimension, and number of systems under consideration. The presented results are fairly general and show the significant gains that can be achieved by pooling data across systems, in comparison to learning each system individually. Further, they are shown to be robust against moderate model misspecifications. To obtain the results, we develop novel techniques that are of independent interest and are applicable to similar problems. They include tightly bounding estimation errors in terms of the eigen-structures of transition matrices, establishing sharp high probability bounds for singular values of dependent random matrices, and capturing effects of misspecified transition matrices as the systems evolve over time. [ABSTRACT FROM AUTHOR]

For a graph G, an Italian dominating function is a function f:V(G)→{0,1,2} such that for each vertex v∈V(G) either f(v)≠0, or ∑u∈N(v)f(u)≥2. If a family F={f1,f2,…,ft} of distinct Italian dominating functions satisfy ∑ti=1fi(v)≤2 for each vertex v, then this is called an Italian dominating family. In [L. Volkmann, The {R}oman {{2}}-domatic number of graphs, Discrete Appl. Math. 258 (2019), 235--241], Volkmann defined the Italian domatic number of G, dI(G), as the maximum cardinality of any Italian dominating family. In this same paper, questions were raised about the Italian domatic number of regular graphs. In this paper, we show that two of the conjectures are false, and examine some exceptions to a Nordhaus-Gaddum type inequality. [ABSTRACT FROM AUTHOR]

A dominating set D of a graph G=(V,E) is called a certified dominating set of G if |N(v)∩(V∖D)| is either 0 or at least 2 for all v∈D. The certified domination number γcer(G) is the minimum cardinality of a certified dominating set of G. In this paper, we prove that the decision problem corresponding to γcer(G) is NP-complete for split graphs, star convex bipartite graphs, comb convex bipartite graphs and planar graphs. We also prove that it is linear time solvable for chain graphs, threshold graphs and bounded tree-width graphs. [ABSTRACT FROM AUTHOR]

A modified reduction order is proposed for the LTI boiler system from the pole clustering method to reduce the higher-order system which yields an exact system model also to minimize the complexity involved in traditional methods. This approach is used to compute the reduced-order system from the combined method of cluster and Routh-Padé approximation techniques that are to achieve the effective formulated reduced-order system, and the method is explained through a numerical example. To evaluate the higher-order system from the new technique, the results of the proposed method are compared with other recently developed order reduction techniques like pole clustering, optimization algorithm, minimum variance, least square and recursive least square. The comparison results show that the proposed method is a powerful and stable method for linear time invariant boiler system. [ABSTRACT FROM AUTHOR]

The study of linear time invariant descriptor systems has intimately been related to the study of matrix pencils. It is true that a large number of systems can be reduced to the study of differential (or difference) systems, |$S\left ({F,G} \right)$|⁠ , $$\begin{align*} & S\left({F,G}\right): F\dot{x}(t) = G{x}(t) \left(\text{or the dual, } F{x}(t) = G\dot{x}(t)\right), \end{align*}$$ and $$\begin{align*} & S\left({F,G}\right): Fx_{k+1} = Gx_k \left(\text{or the dual, } Fx_k=Gx_{k+1}\right)\!, F,G \in{\mathbb{C}^{m \times n}}, \end{align*}$$ and their properties can be characterized by homogeneous matrix pencils, |$sF - \hat{s}G$|⁠. Based on the fact that the study of the invariants for the projective equivalence class can be reduced to the study of the invariants of the matrices of set |${\mathbb{C}^{k \times 2}}$| (for |$k \geqslant 3$| with all |$2\times 2$| -minors non-zero) under the extended Hermite equivalence , in the context of the bilinear strict equivalence relation, a novel projective transformation is analytically derived. [ABSTRACT FROM AUTHOR]

This article studies the practical prescribed time sampled-data control problem for input-constrained linear time invariant continuous time systems. By using the solution to a parametric Lyapunov equation, a bounded linear time-varying (LTV) sampled-data controller is designed to solve such a problem. In addition, stability analysis and performance analysis of the closed-loop sampled-data control system are presented by using the methodology of scalarization. Finally, the developed LTV sampled-data state controller is utilized to the whole physical simulation system of air-bearing testbed and experimental results verify the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper introduces a new reduction method for linear time-invariant continuous and discrete-time systems. The method is created considering only the effect of the dominance pole to get the reduced-order model. The denominator coefficient of reduced order model (ROM) is obtained by conserving the dominant poles of a higher order system while the numerator polynomial of the reduced model is found by comparing the original system transfer function with the transfer function of desired reduced order model. Five standard numeric examples are examined from literature considering single input single output (SISO) and discrete systems. To prove the validity, accuracy and simplicity of the proposed method, the results obtained are compared with other recent established and well-known techniques like Truncation and Routh Stability methods. [ABSTRACT FROM AUTHOR]

We address the problem of determining optimal sensor precisions for estimating the states of linear time-varying discrete-time stochastic dynamical systems, with guaranteed bounds on the estimation errors. This is performed in the Kalman filtering framework, where the sensor precisions are treated as variables. They are determined by solving a constrained convex optimization problem, which guarantees the specified upper bound on the posterior error variance. Optimal sensor precisions are determined by minimizing the $l_1$ norm, which promotes sparseness in the solution and indirectly addresses the sensor selection problem. The theory is applied to realistic flight mechanics and astrodynamics problems to highlight its engineering value. These examples demonstrate the application of the presented theory to 1) determine redundant sensing architectures for linear time invariant systems, 2) accurately estimate states with low-cost sensors, and 3) optimally schedule sensors for linear time-varying systems. [ABSTRACT FROM AUTHOR]

Summary: In system identification, prior knowledge about the model structure may be available. However, imposing this structure on the identified model may be nontrivial. A new discrete‐time linear time‐invariant identification method is presented in the article that imposes prior knowledge of the degree of the common denominator of the system's transfer function matrix and the degrees of the numerators. First, a method is outlined for the solution in case of exact data. Then, this method is extended for noisy data in the output error setting. An initial estimate obtained by a subspace method is improved by a structured low‐rank approximation method. The performance of the method imposing the structure is compared on simulated data with the performance of classical identification methods that do not impose the structure. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the observation and stabilisation problems for a class of linear time-invariant systems, subject to unknown states, and network constraints, including time-delays and event-triggered sampling. A new type of event-triggered mechanism is proposed based on an appropriate storage function, which is chosen larger than the derivative of Lyapunov function. Thus, the convergence of the observer system is guaranteed by the negativity of this storage function. With the utilisation of LMI techniques and the designed novel event-triggered mechanism, as well as the utilisation of a Wirtinger-based inequality, only a slight over-estimation exists in the process of obtaining stability conditions, leading to reduced conservatism. With simulations of a mobile cart system, the effectiveness of this novel event-triggered mechanism is proven through a comparison with a classical event-triggered and also periodic time-triggered mechanisms. [ABSTRACT FROM AUTHOR]

This paper deals with an integrated algorithm for the approximation of higher dimensional system (HDS). Framework of this research is initiated by considering different higher order transfer functions of LTI system. Numerator as well as denominator coefficients of the corresponding lower dimensional model (LDM) are computed using dragonfly algorithm (DA) and Routh approximation (RA) respectively. The proposed technique is verified by considering standard test cases. Further, the performance accuracies are evaluated by comparing the step and frequency responses of HDS and LDM. [ABSTRACT FROM AUTHOR]

We consider a local version of the assignment problem for the dichotomy spectrum of linear continuous time-varying systems defined on the half-line. Our aim is to show that uniform complete controllability is a sufficient condition to place the dichotomy spectrum of the closed-loop system in an arbitrary position within some Hausdorff neighborhood of the dichotomy spectrum of the free system using an appropriate time-varying linear feedback. Moreover, we assume that the norm of the matrix of the linear feedback should be bounded from above by the Hausdorff distance between these two spectra with some constant multiplier. [ABSTRACT FROM AUTHOR]

The problem addressed in this paper is the optimal allocation of a CPU to a number of software control tasks. Each task is used to implement a feedback controller for a linear and time invariant system and is activated with a fixed period. On every periodic activation, the task executes a job, which collects the output of the system, and produces the control values after executing for a random computation time. If a job's duration exceeds a deadline, then the job is cancelled and the control values are not updated. The systems to be controlled are affected by process noise. Therefore the performance of each control loop can be evaluated through the steady-state covariance of the system's state, which depends on the probability with which the task implementing the controller drops its jobs. We show that by making a proper choice for the scheduling algorithm, this probability can be straightforwardly computed as a function of the scheduling parameters. This observation enables the construction of a very efficient procedure for finding the scheduling parameters that attain the optimal tradeoff between the performance of the different control loops. [ABSTRACT FROM AUTHOR]

This article investigates two On-policy and Off-policy Q-learning algorithms for time-varying linear discrete-time systems (DTSs) in the presence of complete dynamic uncertainties. To handle the challenge of time-varying description, the lifting method is employed to transform the original time-varying linear DTS into time-invariant linear DTS in the absence of the conventional controllability condition, which affects to the convergence of traditional Q-learning algorithms. Based on theoretical analysis of the structure in the obtained time-invariant linear DTS, On-policy and Off-policy algorithms are proposed to guarantee the convergence of Q-learning algorithms. Both On-policy and Off-policy Q-learning algorithms guarantee model-free consideration under the data collection. Especially, the Off-policy technique is able to develop the algorithm with high data efficiency because the collected data can be utilized again after each iteration. Finally, the simulation results of two-dimensional systems and spacecraft control systems are presented to validate the effectiveness of the two proposed control schemes. [ABSTRACT FROM AUTHOR]