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This paper is concerned with the input-to-state stability (ISS) and stochastic input-to-state stability (SISS) of impulsive stochastic nonlinear systems. By constructing a general SISS-Lyapunov function, which takes the exponential SISS-Lyapunov function as a special case, the ISS criteria are obtained respectively, for destabilizing and stabilizing impulses. It should be stressed that we impose the average dwell-time (ADT) condition for destabilizing impulses and reverse average dwell-time (RADT) condition for stabilizing impulses to restrain the occurrence of impulses, which extends the fixed dwell-time condition in recent literature. Moreover, the ADT and RADT conditions in this paper correspond to the average impulsive interval method in most existing results under exponential ISS-Lyapunov condition. As a subsequent result, the ISS and SISS of impulsive stochastic interconnected systems on networks are also studied by the Lyapunov method and graph-theoretical technique. Finally, several illustrative examples together with their numerical simulations are provided to demonstrate theoretical

This paper is concerned with the problem of exponential stability for semi-Markov jump stochastic nonlinear systems. It is well known that the semi-Markov chain is an extension of the Markov chain, whose sojourn time distribution depends on the current and next state, and is no longer limited to the exponential distribution. However, in existing works, the independence and the distribution function limitation are imposed on the sojourn time of semi-Markov jump systems. In this paper, by developing a new stochastic analysis method, the problem of exponential stability is investigated for semi- Markov jump stochastic nonlinear systems without additional constraints for the sojourn time. In addition, mode-dependent linear comparable relationships are assumed among Lyapunov like functions, which can effectively reduce the conservatism caused by mode-independent case. Two examples are presented to demonstrate the effectiveness of the proposed results.

The problems discussed in this paper are motivated by general ratio consensus algorithms, introduced by Kempe, Dobra, and Gehrke (2003) in a simple form as the push-sum algorithm, later extended by B\'en\'ezit et al. (2010) under the name weighted gossip algorithm. We consider a communication protocol described by a strictly stationary, ergodic, sequentially primitive sequence of non-negative matrices, applied iteratively to a pair of fixed initial vectors, the components of which are called values and weights defined at the nodes of a network. The subject of ratio consensus problems is to study the asymptotic properties of ratios of values and weights at each node, expecting convergence to the same limit for all nodes. The main results of the paper provide upper bounds for the rate of the almost sure exponential convergence in terms of the spectral gap associated with the given sequence of random matrices. It will be shown that these upper bounds are sharp. Our results complement previous results of Picci and Taylor (2013) and Iutzeler, Ciblat and Hachem (2013).

This paper addresses the problems of establishing structural stability and the L2 gain of 2D mixed continuous-discrete-time systems. The first contribution is to show that Lyapunov functions quadratically dependent on the frequency are exact for establishing structural stability. This is particularly important since the existing works that exploit Lyapunov functions provide a much larger upper bound on the dependence on the frequency or other parameters. The second contribution is to propose a novel linear matrix inequality (LMI) necessary and sufficient condition for establishing the existence of such Lyapunov functions. It is shown, analytically and through several examples, for both best and worst cases, that the numerical complexity of this novel condition is much smaller than that of the existing methods. The third contribution is to show that the proposed methodology can be used to establish upper bounds on the L2 gain, in particular, deriving a novel necessary and sufficient LMI condition based on Lyapunov functions quadratically dependent on the frequency. Lastly, the paper presents the generalization of the proposed methodology to non-mixed 2D systems.

This paper is concerned with the design of a feedback control based on past states in order to make a given unstable hybrid stochastic differential equation (SDE) to be stable in distribution (stabilisation in distribution). This is the first paper in this direction. Under the global Lipschitz condition on the coefficients of the given unstable hybrid SDE, we will show that the stabilisation in distribution can be achieved by linear delay feedback controls. In particular, we discuss how to design the feedback controls in two structure cases: state feedback and output injection.

In this paper we propose an observer for a class of Lipschitz nonlinear systems affected by time-varying and known measurement delays which is an improvement of the one presented in [9]. Under the assumption that the delay function is piece-wise continuous and differentiable we prove that exponential convergence to zero of the observation error can be achieved with any desired decay rate, by suitably tuning a gain vector. The delay bound achieved with the observer proposed here is less conservative than the one obtained in [9], as confirmed by numerical tests. For the sake of brevity, in this paper only one-step observers are considered. However, a cascade observer can be arranged to cope with arbitrarily long delays.

International audience; This paper considers a particular parameter estimator for switched systems and analyzes its properties. The estimator in question is defined as the map from the data set to the solution set of an optimization problem where the to-be-optimized cost function is a sum of pointwise infima over a finite set of sub-functions. This is a hard nonconvex problem. The paper studies some fundamental properties of this problem such as uniqueness of the solution or boundedness of the estimation error regardless of computational considerations. The interest of the analysis is to lay out the main influential properties of the data on the performance of this (ideal) estimator.

This paper deals with strong structural controllability of linear systems. In contrast to existing work, the structured systems studied in this paper have a so-called zero/nonzero/arbitrary structure, which means that some of the entries are equal to zero, some of the entries are arbitrary but nonzero, and the remaining entries are arbitrary (zero or nonzero). We formalize this in terms of pattern matrices whose entries are either fixed zero, arbitrary nonzero, or arbitrary. We establish necessary and sufficient algebraic conditions for strong structural controllability in terms of full rank tests of certain pattern matrices. We also give a necessary and sufficient graph theoretic condition for the full rank property of a given pattern matrix. This graph theoretic condition makes use of a new color change rule that is introduced in this paper. Based on these two results, we then establish a necessary and sufficient graph theoretic condition for strong structural controllability. Moreover, we relate our results to those that exists in the literature, and explain how our results generalize previous work., 11 pages, 6 Figures

Given an unstable hybrid stochastic differential equation (SDE), can we design a feedback control, based on the discrete-time observations of the state at times $0, \tau, 2\tau, \ldots$ , so that the controlled hybrid SDE becomes asymptotically stable? It has been proved that this is possible if the drift and diffusion coefficients of the given hybrid SDE satisfy the linear growth condition. However, many hybrid SDEs in the real world do not satisfy this condition (namely, they are highly nonlinear) and there is no answer to the question, yet if the given SDE is highly nonlinear. The aim of this paper is to tackle the stabilization problem for a class of highly nonlinear hybrid SDEs. Under some reasonable conditions on the drift and diffusion coefficients, we show how to design the feedback control function and give an explicit bound on $\tau$ (the time duration between two consecutive state observations), whence the new theory established in this paper is implementable.

This paper addresses the stability issue of a class of delayed switched cascade nonlinear systems consisting of separate subsystems and coupling terms between them. Some global and local asymptotic stability sufficient conditions are proposed, drawing stability conclusion of the overall cascade system from those of separate systems. These results essentially rely on the following observation: For a general delayed switched nonlinear system being asymptotically stable, the trajectories of the perturbed system asymptotically approach zero if so does the perturbation. This observation is one of the main results in this paper.

Most existing results about modeling and characterizing Gaussian Markov, reciprocal, and conditionally Markov (CM) processes assume nonsingularity of the processes. This assumption makes the analysis easier, but restricts application of these processes. This paper studies, models, and characterizes the general (singular/nonsingular) Gaussian CM (including reciprocal and Markov) sequence. For example, to our knowledge, there is no dynamic model for the general (singular/nonsingular) Gaussian reciprocal sequence in the literature. We obtain two such models from the CM viewpoint. As a result, the significance of studying reciprocal sequences from the CM viewpoint is demonstrated. The results of this paper unify singular and nonsingular Gaussian CM (including reciprocal and Markov) sequences and provide tools for their application. An application of CM sequences in trajectory modeling with a destination is discussed, and illustrative examples are presented.

This is a companion paper of [Mixed equilibrium solution of time-inconsistent stochastic linear-quadratic problem, SIAM J. Control Optim. , vol. 57, no. 1, 533–569, 2019], where general theory has been established to characterize the open-loop equilibrium control, feedback equilibrium strategy and mixed equilibrium solution for a time-inconsistent stochastic linear-quadratic problem. This note is, on the one hand, to test the developed theory of that paper and on the other hand to push the solvability of multiperiod mean-variance portfolio selection. A nondegenerate assumption, which is popular in the existing literature about multiperiod mean-variance portfolio selection, has been removed in this note; and neat conditions have been obtained to characterize the existence of equilibrium solutions.

In this paper, we propose two iterative algorithms to identify transfer functions of two-dimensional (2-D) systems. The proposed algorithms are modifications of the 2-D adaptive Fourier decomposition (AFD) and weak pre-orthogonal adaptive Fourier decomposition (W-POAFD). 2-D AFD and W-POAFD are newly established adaptive representation theories for multivariate functions utilizing, respectively, the product-TM system and the product-Szego dictionary. The proposed algorithms give rise to rational approximations with real coefficients to transfer functions. Owing to the modified maximal selection principles, the algorithms achieve a fast convergence rate $\boldsymbol {O(n^{-\frac{1}{2}})}$ . To use 2-D AFD and W-POAFD for system identification not only the theory is revised, but also the practical algorithm codes are provided. Experimental examples show that the proposed algorithms give promising results. The theory and algorithms studied in this paper are valid for any ${n}$ -D case, ${n\geq 2}$ .

In this paper, we study attitude synchronization for elements in the unit sphere in $\mathbb {R}^{\scriptscriptstyle {\scriptscriptstyle {3}}}$ and for elements in the three-dimensional (3-D) rotation group, for a network with switching topology. The agents’ angular velocities are assumed to be the control inputs, and a switching control law for each agent is devised that guarantees synchronization, provided that all elements are initially contained in a region, which we identify later in the paper. The control law is decentralized and it does not require a common orientation frame among all agents. We refer to synchronization of unit vectors in $\mathbb {R}^{\scriptscriptstyle {3}}$ as incomplete synchronization, and of 3-D rotation matrices as complete synchronization. Our main contribution lies in showing that these two problems can be analyzed under a common framework, where all agents’ dynamics are transformed into unit vectors dynamics on a sphere of appropriate dimension.

This paper is concerned with the problem of energy-to-peak stochastic stability (EPSS) of two-dimensional (2-D) Roesser systems in the presence of state time-varying delays and multiplicative noises. First, a scheme that ensures a 2-D stochastic time-delay system is stochastically stable with an attenuation performance is proposed. The scheme presented in this paper can be regarded as an extension of the Lyapunov–Krasovskii functional method for 2-D stochastic time-delay systems, focusing on the EPSS problem. The proposed scheme is then utilized to derive delay-dependent EPSS conditions in terms of tractable linear matrix inequalities. A numerical example is given to illustrate the effectiveness of the derived stability conditions.

This paper investigates the existence of nonimpulsive unique solution and stochastic stability problems for the discrete-time linear rectangular descriptor Markov jump systems at two cases. For every case, the sufficient and necessary conditions, in terms of strict linear matrix inequalities, are eventually proposed to guarantee that the discrete-time linear rectangular descriptor Markov jump systems are column (row) regular, column (row) causal, stochastically stable, and have a unique solution. In addition, some assumptions are introduced to ensure that there is no impulse in the solution at the instant when the Markov process jumps. Moreover, the concrete procedures on how to apply the results obtained in this paper are presented as well. Finally, an example is provided to demonstrate the effectiveness of the results.

In this paper, we address the so-called Liouville control problem for discrete-time SISO linear systems in the class of Gaussian distributions. In particular, we propose a systematic procedure for the characterization of a dynamic output feedback policy that will transfer the output of the system, which is a known Gaussian random variable, to a goal Gaussian distribution after a finite number of stages. In the proposed approach, the Liouville control problem is reduced to two decoupled (finite-dimensional) quadratic programs, one of which is subject to a single affine constraint, which is a convex program, whereas the other one is subject to a single quadratic equality constraint. Despite the fact that the second optimization problem is not convex, one can characterize its exact solution via a systematic procedure without resorting to convex relaxation techniques, which may yield suboptimal or even infeasible solutions to the original (nonconvex) optimization problem. Finally, we present numerical simulations that illustrate the key ideas of this paper.

Recently, Thompson sampling has been shown to achieve good theoretical performance guarantees for stochastic control problems with parameter uncertainty when the state, control, and parameter spaces are all finite. Much less is known however about the performance of Thompson sampling when applied to continuous or more general spaces, which constitutes an important class of problems in practice. In this paper, we study Thompson sampling when applied to a broad class of average cost stochastic control problems where the state, control, and parameter spaces are all general measurable spaces. The main contributions of our paper are establishing theoretical performance guarantees for Thompson sampling as measured by: first, expected posterior sampling error; and second, average per period regret.

This paper proposes a less conservative stability criterion for discrete-time Lur'e systems with sector and slope restrictions by constructing a novel Lyapunov functional. Compared with the Lyapunov functional in the literature, this paper fully utilizes the sector and slope restrictions in our Lyapunov functional, which includes integral terms involved with the sector restriction of the nonlinearities $\phi (y_{i})$ and $\phi (y_{i+1})$ , integral terms involved with the slope restriction between $\phi (y_{i})$ and $\phi (y_{i+1})$ , and a quadratic term with an augmented vector related to available vectors for representing upper and lower bounds of all integral terms. The positive definiteness of a matrix appearing in the quadratic term can be relaxed by utilizing the lower bounds of all integral terms. Based on the Lyapunov functional, an improved stability criterion is derived in terms of linear matrix inequalities. Numerical examples show the effectiveness of the proposed criterion.

Within the set of stochastic, indecomposable, aperiodic (SIA) matrices, the class of Sarymsakov matrices is the largest known subset that is closed under matrix multiplication, and more critically whose compact subsets are all consensus sets. This paper shows that a larger subset with these two properties can be obtained by generalizing the standard definition for Sarymsakov matrices. The generalization is achieved by introducing the notion of the SIA index of a stochastic matrix, whose value is 1 for Sarymsakov matrices, and then exploring those stochastic matrices with larger SIA indices. In addition to constructing the larger set, this paper introduces another class of generalized Sarymsakov matrices, which contains matrices that are not SIA, and studies their products. Sufficient conditions are provided for an infinite product of matrices from this class, converging to a rank-one matrix. Finally, as an application of the results just described and to confirm their usefulness, a necessary and sufficient combinatorial condition, the “avoiding set condition,” for deciding whether or not a compact set of stochastic matrices is a consensus set is revisited. In addition, a necessary and sufficient combinatorial condition is established for deciding whether or not a compact set of doubly stochastic matrices is a consensus set.

In this paper, the locally fixed-time and globally fixed-time $\mathcal {H}_{\infty }$ control problems for the port-controlled Hamiltonian (PCH) systems are investigated via the interconnection and damping assignment passivity-based control (IDA-PBC) technique. Compared with finite-time stabilization, where the convergence time of the closed-loop system's states relies on the initial values, the settling time of fixed-time stabilization can be adjusted to achieve desired equilibrium point regardless of initial conditions. The concepts of fixed-time $\mathcal {H}_{\infty }$ control, fixed-time stability region (or region of attraction), and fixed-time stability boundary are presented in this paper, and the criterions of globally fixed-time attractivity of a prespecified locally fixed-time stability region are obtained. Combining the locally fixed-time stability of an equilibrium point and the globally fixed-time attractivity of a prespecified fixed-time stability region, the globally fixed-time $\mathcal {H}_{\infty }$ control problem of PCH system is effectively solved. Two novel control laws are designed to deal with the globally fixed-time $\mathcal {H}_{\infty }$ control problem, and the conservativeness in estimating the settling time is also briefly discussed. An illustrative example shows that the theoretical results obtained in this paper work very well in the fixed-time $\mathcal {H}_{\infty }$ control design for PCH systems.

We study in this paper, a class of constrained linear-quadratic (LQ) optimal control problem formulations for the scalar-state stochastic system with multiplicative noise, which has various applications, especially in the financial risk management. The linear constraint on both the control and state variables considered in our model destroys the elegant structure of the conventional LQ formulation and has blocked the derivation of an explicit control policy so far in the literature. We successfully derive in this paper, the analytical control policy for such a class of problems by utilizing the state separation property induced from its structure. We reveal that the optimal control policy is a piecewise affine function of the state and can be computed offline efficiently by solving two coupled Riccati equations. Under some mild conditions, we also obtain the stationary control policy for an infinite time horizon. We demonstrate the implementation of our method via some illustrative examples and show how to calibrate our model to solve dynamic constrained portfolio optimization problems.

This paper investigates the distributed computation of the well-known linear matrix equation in the form of $AXB = F$, with the matrices A, B, X, and F of appropriate dimensions, over multi-agent networks from an optimization perspective. In this paper, we consider the standard distributed matrix-information structures, where each agent of the considered multi-agent network has access to one of the sub-block matrices of A, B, and F. To be specific, we first propose different decomposition methods to reformulate the matrix equations in standard structures as distributed constrained optimization problems by introducing substitutional variables; we show that the solutions of the reformulated distributed optimization problems are equivalent to least squares solutions to original matrix equations; and we design distributed continuous-time algorithms for the constrained optimization problems, even by using augmented matrices and a derivative feedback technique. Moreover, we prove the exponential convergence of the algorithms to a least squares solution to the matrix equation for any initial condition., This paper has been submitted to TAC

The paper revisits Aizerman and Kalman conjectures for absolute stability through the lens of a novel graphical interpretation. Even though these conjectures have been proven false, such a graphical interpretation suggests natural ways to introduce additional conditions in order to obtain new valid absolute stability criteria. As an illustration, the paper proves a new absolute stability criterion obtained by the iterative application of a variation of the circle criterion.

In this paper, we propose a control law for the almost-global asymptotic tracking (AGAT) of a smooth reference trajectory for a fully actuated simple mechanical system (SMS) evolving on a Riemannian manifold that can be embedded in a Euclidean space. The existing results on tracking for an SMS are either local, or almost global, only in the case the manifold is a Lie group. In the latter case, the notion of a configuration error is naturally defined by the group operation and facilitates a global analysis. However, such a notion is not intrinsic to a Riemannian manifold. In this paper, we define a configuration error followed by error dynamics on a Riemannian manifold, and then, prove the AGAT. The results are demonstrated for a spherical pendulum, which is an SMS on $S^2$ and for a particle moving on a Lissajous curve in $\mathbb {R}^3$ .

This paper deals with the certification problem for robust quadratic stability, robust state convergence, and robust quadratic performance of linear systems that exhibit bounded rates of variation in their parameters. We consider both continuous-time (CT) and discrete-time (DT) parameter-varying systems. In this paper, we provide a uniform method for this certification problem in both cases and we show that, contrary to what was claimed previously, the DT case requires a significantly different treatment compared to the existing CT results. In the established uniform approach, quadratic Lyapunov functions, that are affine in the parameter, are used to certify robust stability, robust convergence rates, and robust performance in terms of linear matrix inequality feasibility tests. To exemplify the procedure, we solve the certification problem for $\mathscr{L}_2$-gain performance both in the CT and the DT cases. A numerical example is given to show that the proposed approach is less conservative than a method with slack variables., 8 pages, 3 figures

Mathematically, the Rayleigh quotient is defined as the quadratic function of a symmetric matrix and a nonzero (usually unconstrained) variable vector. In this paper, we consider the constrained Rayleigh quotient, in which the variable vector has the orthogonality constraint, i.e., it is constrained to be orthogonal to a nonzero vector, this nonzero vector is called the orthogonality-constraint vector (or abbreviated as the OC-vector) for the variable vector. The matrix for the Rayleigh quotient is an eigen-balanced (EB) Laplacian matrix. A tighter lower bound of the constrained Rayleigh quotient has many implications in mathematics as well as in cooperative control problems. The main contributions in this paper are as follows: First, we provide the greatest lower bound (or the infimum) of the constrained Rayleigh quotient with respect to a general OC-vector and the EB Laplacian matrix, whose results are novel and better than the existing results. Then, we interpret the physical meaning of our results in an insightful geometric form and characterize the properties of the results. Finally, as an example to illustrate the merit of the tighter lower bound of the constrained Rayleigh quotient, we consider the scale of the agents driving by a fundamental consensus protocol, and show that the convergence rate of the agents’ scale is characterized by the greatest lower bound of the constrained Rayleigh quotient.

In this paper, a control technique is presented for an undamped, pinned–pinned Euler–Bernoulli beam with control inputs and bounded disturbances on one boundary. The control strategy drives the system to its origin at an arbitrary exponential rate in the presence of the disturbances. This is achieved in two main steps. First, a backstepping transformation is used to convert the marginally stable Euler–Bernoulli beam system to a new form that has an exponentially stable homogeneous form. Control inputs are needed to fully convert the system to this form; however, since they are distorted by unknown bounded disturbances, the next step implements a sliding mode controller to account for them. The proposed sliding manifolds require a combination of classical and “second order” techniques in order to avoid discontinuous chattering on the physical system. Therefore, the continuous sliding mode controllers developed return the beam to its origin at an arbitrary exponential rate, and do so in the presence of unknown bounded disturbances on the boundary. The main contributions of this paper with respect to previous backstepping designs for the Euler–Bernoulli beam are that all three of the following goals are accomplished together: (i) steady-state position is the origin, (ii) decay rate has no theoretical restrictions, and (iii) is robust to bounded disturbances.

This paper is concerned with the problem of continuous-time nonlinear filtering of stochastic processes evolving on connected Riemannian manifolds without boundary. The main contribution of this paper is to derive the feedback particle filter (FPF) algorithm for this problem. In its general form, the FPF is shown to provide an intrinsic description of the filter that automatically satisfies the geometric constraints of the manifold. The particle dynamics are encapsulated in a Stratonovich stochastic differential equation that retains the feedback structure of the original (Euclidean) FPF. The implementation of the filter requires a solution of a Poisson equation on the manifold, and a numerical algorithm is described for this purpose. For the special case when the manifold is a matrix Lie group, explicit formulae for the filter are derived, using the matrix coordinates. Filters for two example problems are presented: the attitude estimation problem on $SO(3)$ and the robot localization problem in $SE(3)$ . Comparisons are also provided between the FPF and popular algorithms for attitude estimation, namely the multiplicative extended Kalman filter (EKF), the invariant EKF, the unscented quaternion estimator, the invariant ensemble Kalman filter, and the bootstrap particle filter. Numerical simulations are presented to illustrate these comparisons.

The topic of this paper is the backstepping-based solution of the robust state feedback regulation problem for general linear heterodirectional hyperbolic systems with spatially varying coefficients. Thereby, a large class of outputs is considered, i.e., mixed distributed and pointwise in-domain or boundary outputs. The state feedback regulator design is based on the $\boldsymbol {p}$ -copy internal model principle. This results in a stabilization problem for a cascade of $\boldsymbol {m+p}$ boundary controlled transport partial differential equations (PDEs) with $\boldsymbol {p}$ ordinary differential equations (ODEs). For this, a systematic backstepping approach is presented, in which all design equations are explicitly solvable in backstepping coordinates. Furthermore, the solvability conditions for the considered output regulation problem can be evaluated in closed form utilizing the plant transfer behavior. Robust output regulation is verified for nondestabilizing model uncertainties and unknown disturbance input locations. A $\boldsymbol {4 \times 4}$ hyperbolic system with uncertain transport velocities and couplings in the transport PDEs illustrates the results of this paper.

The main aim of this paper is to provide an analysis of gradient descent ( $\text{GD}$ ) algorithms with gradient errors that do not necessarily vanish, asymptotically. In particular, sufficient conditions are presented for both stability (almost sure boundedness of the iterates) and convergence of $\text{GD}$ with bounded (possibly) nondiminishing gradient errors. In addition to ensuring stability, such an algorithm is shown to converge to a small neighborhood of the minimum set, which depends on the gradient errors. It is worth noting that the main result of this paper can be used to show that $\text{GD}$ with asymptotically vanishing errors indeed converges to the minimum set. The results presented herein are not only more general when compared to previous results, but our analysis of $\text{GD}$ with errors is new to the literature to the best of our knowledge. Our work extends the contributions of Mangasarian and Solodov, Bertsekas and Tsitsiklis, and Tadic and Doucet. Using our framework, a simple yet effective implementation of $\text{GD}$ using simultaneous perturbation stochastic approximations, with constant sensitivity parameters, is presented. Another important improvement over many previous results is that there are no “additional” restrictions imposed on the step sizes. In machine learning applications where step sizes are related to learning rates, our assumptions, unlike those of other papers, do not affect these learning rates. Finally, we present experimental results to validate our theory.

In this paper, the problem of estimation is considered for a class of processes involving solidifying materials. These processes have natural nonlinear infinite-dimensional representations, and measurements are only available at particular points in the caster, each corresponding to a single discrete-in-time boundary measurement in the Stefan problem partial differential equation (PDE) mathematical model. The results for two previous estimators are summarized. The first estimator is based on the Stefan problem, using continuous instead of discrete-in-time boundary measurements. The second estimator employs a process model that is more detailed than the Stefan Problem, but with no output injection to reduce estimation error, other than model calibration. Both of these estimation frameworks are extended in the current paper to a more realistic sensing setting. First, an estimator is considered that uses the Stefan Problem under some simplifying but practically justified assumptions on the unknowns in the process. The maximum principle for parabolic PDEs is employed to prove that online calibration using a single discrete-in-time temperature measurement can provide removal of the estimation error arising due to mismatch of a single unknown parameter in the model. Although unproven, this result is then shown in simulation to apply to the more detailed process model.

This paper develops the fundamentals of optimal-tuning periodic-gain fractional delayed state feedback control for a class of linear fractional-order periodic time-delayed systems. Although there exist techniques for the state feedback control of linear periodic time-delayed systems by discretization of the monodromy operator, there is no systematic method to design state feedback control for linear fractional periodic time-delayed (FPTD) systems. This paper is devoted to defining and approximating the monodromy operator for a steady-state solution of FPTD systems. It is shown that the monodromy operator cannot be achieved in a closed form for FPTD systems, and hence, the short-memory principle along with the fractional Chebyshev collocation method is used to approximate the monodromy operator. The proposed method guarantees a near-optimal solution for FPTD systems with fractional orders close to unity. The proposed technique is illustrated in examples, specifically in finding optimal linear periodic-gain fractional delayed state feedback control laws for the fractional damped Mathieu equation and a double inverted pendulum subjected to a periodic retarded follower force with fractional dampers, in which it is demonstrated that the use of time-periodic control gains in the fractional feedback control generally leads to a faster response.

In model predictive control ( MPC ), the control input is computed by solving a constrained finite-time optimal control ( CFTOC ) problem at each sample in the control loop. The main computational effort when solving the CFTOC problem using an active-set ( AS ) method is often spent on computing the search directions, which in MPC corresponds to solving unconstrained finite-time optimal control ( UFTOC ) problems. This is commonly performed using Riccati recursions or generic sparsity exploiting algorithms. In this paper, the focus is efficient search direction computations for AS type methods. The system of equations to be solved at each AS iteration is changed only by a low-rank modification of the previous one, and exploiting this structured change is important for the performance of AS -type solvers. In this paper, theory for how to exploit these low-rank changes by modifying the Riccati factorization between AS iterations in a structured way is presented. A numerical evaluation of the proposed algorithm shows that the computation time can be significantly reduced by modifying, instead of re-computing, the Riccati factorization. This speedup can be important for AS -type solvers used for linear, nonlinear, and hybrid MPC .

In this paper, we extend the stability theory on Kalman filtering with intermittent measurements from the scenario of one single sensor to the one of multiple sensors. Consider that a group of sensors take measurement of the states of a process and then send the data to a remote estimator. The estimator receives the measurements intermittently, which may be caused by the fact that the channels have packet dropouts or that the sensors schedule the data transmission stochastically. Based on the received measurements, the estimator computes the estimates of the process states by multi-sensor Kalman filtering. Because of the intermittent measurements, the estimator may be unstable. This stability issue is mainly investigated in this paper. A notion of transmission capacity, which is related to the communication rates of sensors, is proposed. It is shown that the expected estimation error covariance diverges for all feasible communication rates collections of the sensors when the transmission capacity is below a certain value; meanwhile, when the transmission capacity is above another certain value, there exists a feasible communication rates collection such that the expected estimation error covariance is bounded.

This paper explores optimal control problems with $l_1$ objectives involving linear discrete-time systems. These problems can be efficiently solved as linear programs. They also have previously been shown to yield sparse solutions, including idle or deadbeat solutions where the input or output is respectively zero along the entire control horizon. The main contribution of this paper is to derive conditions on the problem parameters that specify when idle or deadbeat solutions occur. These results, based on analyzing the dual problem, demonstrate how different types of sparse solutions result from the choice of the problem parameters and, as a consequence, may guide the design of controllers employing $l_1$ objectives.

This paper investigates a finite frequency ${H_{\infty }}$ deconvolution problem for single-input–single-output discrete-time systems. Motivated by the fact that many practical signals are located in a finite frequency range, this paper is focused on developing a design method for achieving better deconvolution performance over a finite frequency range. First, a finite frequency ${H_{\infty }}$ deconvolution problem is formulated such that the deconvolution specification is characterized by a modified $H_{\mathbf {\infty }}$ index associated with the corresponding finite frequency range. By an adapted generalized Kalman–Yakubovich–Popov lemma and an auxiliary vector approach, a matrix inequality condition is obtained for parameterizing a required deconvolution filter, based on which a simple iterative algorithm is then constructed for optimizing the filter performance. Multiobjective deconvolution is further discussed in the same framework. Compared with the traditional frequency weighting strategy, the proposed method can directly analyze and synthesize the deconvolution performance within finite frequency ranges, the advantage of which is demonstrated in a bandlimited signal recovery example.

In this paper, we apply Thompson sampling to a class of average reward stochastic control problems with parameter uncertainty. Specifically, we study an average reward stochastic control problem over an infinite horizon in which both the reward and state transition distributions are parameterized by an unknown parameter taking values in a finite space. The main result of this paper is a proof showing that Thompson sampling achieves a worst case average per period regret of $O(T^{-1})$ , which is asymptotically optimal.

In this paper, we investigate the decidability and complexity of the fault diagnosis problem in unbounded labeled Petri nets. First, we show that checking diagnosability for unbounded Petri nets is decidable. We present a new necessary and sufficient condition for diagnosability, which can be reduced to a model checking problem for unbounded Petri nets. Then, we show that checking diagnosability for unbounded Petri nets is EXPSPACE-complete. This complexity result is further extended to various subclasses of Petri nets. To the best of our knowledge, this is the first paper that establishes decidability and complexity results for diagnosability of unbounded Petri nets.

In this paper, the decentralized partially observable Markov decision process (Dec-POMDP) systems with discrete state and action spaces are studied from a gradient point of view. Dec-POMDPs have recently emerged as a promising approach to optimizing multiagent decision making in the partially observable stochastic environment. However, the decentralized nature of the Dec-POMDP framework results in a lack of shared belief state, which makes the decision maker impossible to estimate the system state based on local information. In contrast to the belief-based policy, this paper focuses on optimizing the decentralized observation-based policy, which is easily to be applied and does not have the sharing problem. By analyzing the gradient of the objective function, we have developed a centralized stochastic gradient policy iteration algorithm to find the optimal policy on the basis of gradient estimates from a single sample path. This algorithm does not need any specific assumption and can be applied to most practical Dec-POMDP problems. One numerical example is provided to demonstrate the effectiveness of the algorithm.

This paper is concerned with distributed learning and optimization in large-scale settings. The well-known fictitious play (FP) algorithm has been shown to achieve Nash equilibrium learning in certain classes of multiagent games. However, FP can be computationally difficult to implement when the number of players is large. Sampled FP (SFP) is a variant of FP that mitigates the computational difficulties arising in FP by using a Monte Carlo (i.e., sampling based) approach. Despite its computational advantages, a shortcoming of SFP is that the number of samples that must be drawn at each iteration grows without bound as the algorithm progresses. In this paper, we propose single sample FP (SSFP)—A variant of SFP in which only one sample needs to be drawn in each round of the algorithm. Convergence of SSFP to the set of Nash equilibria is proven. Simulation results show the performance of SSFP is comparable to that of SFP, despite drawing far fewer samples.

This paper is concerned with the stability (gain and phase) margin of networked dynamical systems, e.g., vehicles in formation, each of which has access to the state of its neighbors and subsequently uses a state feedback gain $F$ for a certain global objective such as attitude synchronization. Here, the network topology is directed and described by a generalized Laplacian matrix $L$ . An individual dynamical system can adopt its own state feedback control law such as a linear-quadratic-regulator controller for an ample stability margin, but it may lose the stability margin to a great extent when the same control strategy utilizing relative state information is used after being interconnected with other dynamical systems. This paper reveals and elaborates upon the following four facts: First, the stability margin after interconnection is quantified via the minimum singular value of a frequency-dependent matrix made up of $F$ and $L$ ; Second, the stability margin of a networked dynamical system having a pole at the origin is at most the inverse of the zero-eigenvalue sensitivity of $L$ ; Third, there exists an upper bound of the stability margin that has a computational merit, and asymptotically converges to the exact margin with respect to network size, probability of link existence, and control gain in a random network setting; and finally, $L$ can be designed to maximize the stability margin. Numerical examples are provided to demonstrate the elaboration.

In this paper, a unified framework is established to investigate both the quantized and the saturated control problems for a class of sampled-data systems under noisy sampling intervals. A random variable obeying the Erlang distribution is used to describe the noisy sampling intervals. In virtue of the matrix exponential, the sampled-data control system is transformed into an equivalent discrete-time stochastic system, and the aim of this paper is to design a quantized/saturated sampled-data controller such that the resulting discrete-time stochastic system is stochastically stable when the sampling error follows the Erlang distribution. In order to deal with the case of multiple control inputs, a confluent Vandermonde matrix approach is proposed in the design process. By using the Kronecker product operation and the matrix inequality techniques, the desired quantized/saturated controller gains are designed in terms of the solution to certain matrix inequalities. Finally, a simulation example is exploited to verify the effectiveness of the proposed design approach.

Consensus of a network with a directed acyclic graph, a directed graph with no directed cycles, is always guaranteed if it contains a spanning tree. This paper studies the effect of adding edges to a directed acyclic graph that may result in a directed cycle. It is shown that the effect on consensus performance of the whole network is only determined by a local subnetwork containing all the added edges. More specifically, both a one-dimensional (1-D) chain network and a 2-D grid network are investigated in this paper. It is proved that, when a reverse edge is added, the consensus performance is degraded by the amount only determined by the edge range, that is, independent of the network size or the location of the added edge.