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Distributed consensus tracking for linear multiagent systems (MASs) with directed switching topologies and a dynamic leader is investigated in this paper. By fully considering the special feature of Laplacian matrices for topology candidates, several new classes of multiple Lyapunov functions (MLFs) are constructed in this paper for leader-following MASs with, respectively, an autonomous leader and a nonautonomous leader. Under the condition that each possible topology graph contains a spanning tree rooted at the leader node, some efficient criteria for achieving consensus tracking in the considered MASs are provided. Specifically, it is proven that consensus tracking in the closed-loop MASs can be ensured if the average dwell time for switching among different topologies is larger than a derived positive quantity and the control parameters in tracking protocols are appropriately designed. It is further theoretically shown that the present Lyapunov inequality based criteria for consensus tracking with an autonomous leader are much less conservative than the existing ones derived by the $M$ -matrix theory. The results are then extended to the case where the topology graph only frequently contains a directed spanning tree as the MASs evolve over time. At last, numerical simulations are performed to illustrate the effectiveness of the analytical analysis and the advantages of the proposed MLFs. [ABSTRACT FROM AUTHOR]

This paper addresses the distributed estimation problem in a set membership framework. The agents of a network collect measurements which are affected by bounded errors, thus implying that the unknown parameters to be estimated belong to a suitable feasible set. Two distributed algorithms are considered, based on projections of the estimate of each agent onto its local feasible set. The main contribution of the paper is to show that such algorithms are asymptotic interpolatory estimators, i.e., they converge to an element of the global feasible set, under the assumption that the feasible set associated to each measurement is convex. The proposed techniques are demonstrated on a distributed linear regression estimation problem. [ABSTRACT FROM AUTHOR]

This paper studies the delay consensus margin and its bounds for second-order multiagent systems to achieve robust consensus with respect to uncertain delays varying within a range. This paper attempts to answer the question: What is the largest delay range within which a control protocol is able to achieve and maintain the consensus? We consider second-order agents with unstable poles, which communicate over an undirected network topology, and derive explicit bounds on the delay consensus margin. The results show that the consensuability robustness of such unstable agents depends on the pole locations of the agents, as well as on the eigenratio of the network graph. [ABSTRACT FROM AUTHOR]

In this paper, the robustness to model mismatch of a preexisting collocated boundary adaptive feedback law is investigated. This control law was originally designed for an antidamped pure wave partial differential equation (PDE). Actuation and measurements are located at the same boundary. Adaptive terms account for uncertain parameters located at the antidamped boundary, opposite to the collocated actuation and measurement. By extending and transforming the system state using, in particular, backstepping, this paper establishes that this controller is robust to sufficiently small in-domain damping. In particular, both stability and attractivity (convergence) are established similarly as in the nominal case. Note moreover that, assuming that some parameters are known, the exponential stability to an attractor holds. Simulations are performed to illustrate the interest of this study to attenuate mechanical vibrations in an oil-drilling context. [ABSTRACT FROM AUTHOR]

This paper is concerned with the power system state estimation (PSSE) problem that aims to find the unknown operating point of a power network based on a given set of measurements. We first study the power flow (PF) problem as an important special case of PSSE. PF is known to be nonconvex and NP-hard in the worst case. To this end, we propose a set of semidefinite programs (SDPs) with the property that they all solve the PF problem as long as the voltage angles are relatively small. Associated with each SDP, we explicitly characterize the set of all the complex voltages that can be recovered via that convex problem. As a generalization, the design of an SDP problem that recovers multiple nominal points and a neighborhood around each point is also cast as a convex program. The results are, then, extended to the PSSE problem, where the measurements used in the PF problem are subject to noise. A two-term objective function is employed for each convex program developed for the PSSE problem: 1) the first term accounting for the nonconvexity of the PF equations and 2) other one for estimating the noise levels. An upper bound on the estimation error is derived with respect to the noise level, and the proposed techniques are demonstrated on multiple test systems, including a 9241-bus European network. Although the focus of this paper is on power networks, yet the developed results apply to every arbitrary state estimation problem with quadratic measurement equations. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The goal of this paper is to develop balancing theory for the linear time-varying (LTV) symmetric systems. To this end, first, we extend the concept of symmetry in terms of the dual system. Then, we define the cross Gramian for the LTV systems. For LTV symmetric systems, we establish a connection among the controllability, observability, and cross Gramians. In particular, if one of these three Gramians is obtained, the other two Gramians can be constructed. Based on this fact, we show that the symmetry structure is preserved under balanced truncation if the Hankel singular values are pointwise distinct. [ABSTRACT FROM AUTHOR]

In this paper, we present a framework for risk-sensitive model predictive control (MPC) of linear systems affected by stochastic multiplicative uncertainty. Our key innovation is to consider a time-consistent, dynamic risk evaluation of the cumulative cost as the objective function to be minimized. This framework is axiomatically justified in terms of time-consistency of risk assessments, is amenable to dynamic optimization, and is unifying in the sense that it captures a full range of risk preferences from risk neutral (i.e., expectation) to worst case. Within this framework, we propose and analyze an online risk-sensitive MPC algorithm that is provably stabilizing. Furthermore, by exploiting the dual representation of time-consistent, dynamic risk measures, we cast the computation of the MPC control law as a convex optimization problem amenable to real-time implementation. Simulation results are presented and discussed. [ABSTRACT FROM AUTHOR]

This paper presents an extension of the reinforcement learning algorithms to design suboptimal control sequences for multiple performance functions in continuous-time systems. The first part of the paper provides the theoretical development and studies the required conditions to obtain a state-feedback control policy that achieves Pareto optimal results for the multiobjective performance vector. Then, a policy iteration algorithm is proposed that takes into account practical considerations to allow its implementation in real-time applications for systems with partially unknown models. Finally, the multiobjective linear quadratic regulator problem is solved using the proposed control scheme and employing a multiobjective optimization software to solve the static optimization problem at each iteration. [ABSTRACT FROM AUTHOR]

This paper studies the optimal output-feedback control of a linear time-invariant system where a stochastic event-based scheduler triggers the communication between the sensor and the controller. The primary goal of the use of this type of scheduling strategy is to provide significant reductions in the usage of the sensor-to-controller communication and, in turn, improve energy expenditure in the network. In this paper, we aim to design an admissible control policy, which is a function of the observed output, to minimize a quadratic cost function while employing a stochastic event-triggered scheduler that preserves the Gaussian property of the plant state and the estimation error. For the infinite horizon case, we present analytical expressions that quantify the tradeoff between the communication cost and control performance of such event-triggered control systems. This tradeoff is confirmed quantitatively via numerical examples. Besides, numerical simulations justify that the event-triggered control provides better quadratic control performance than the (traditional) periodic time-triggered control at the same average sampling rate. [ABSTRACT FROM AUTHOR]

This paper presents reduction theorems for stability, attractivity, and asymptotic stability of compact subsets of the state space of a hybrid dynamical system. Given two closed sets $\Gamma _1 \subset \Gamma _2 \subset \mathbb {R}^n$ , with $\Gamma _1$ compact, the theorems presented in this paper give conditions under which a qualitative property of $\Gamma _1$ that holds relative to $\Gamma _2$ (stability, attractivity, or asymptotic stability) can be guaranteed to also hold relative to the state space of the hybrid system. As a consequence of these results, sufficient conditions are presented for the stability of compact sets in cascade-connected hybrid systems. We also present a result for hybrid systems with outputs that converge to zero along solutions. If such a system enjoys a detectability property with respect to a set $\Gamma _1$ , then $\Gamma _1$ is globally attractive. The theory of this paper is used to develop a hybrid estimator for the period of oscillation of a sinusoidal signal. [ABSTRACT FROM AUTHOR]

We characterize the role played by memory when linear time-invariant systems interact. This study is of interest as the phenomenon that occurs in this setting is arguably the same phenomenon that governs some cascading failure and contagion effects in interconnected systems. We aim to later extend solutions presented in this paper to problems in other desired settings. The characterization relies on basic methods in homological algebra, and is reminiscent of the rank-nullity theorem of linear algebra. Interconnection of systems is first expressed as an exact sequence, then loss of memory causes a loss of exactness, and finally exactness is recovered through specific algebraic invariants of the systems that encode the role of memory. We thus introduce a new invariant, termed lag, of linear time-invariant systems and characterize the role of memory in terms of the lag. We discuss properties of the lag, and prove several results regarding the characterization. [ABSTRACT FROM AUTHOR]

This paper studies linear stochastic approximation (SA) algorithms and their application to multiagent systems in engineering and sociology. As main contribution, we provide necessary and sufficient conditions for convergence of linear SA algorithms to a deterministic or random final vector. We also characterize the system convergence rate, when the system is convergent. Moreover, differing from non-negative gain functions in traditional SA algorithms, this paper considers also the case when the gain functions are allowed to take arbitrary real numbers. Using our general treatment, we provide necessary and sufficient conditions to reach consensus and group consensus for first-order discrete-time multiagent system over random signed networks and with state-dependent noise. Finally, we extend our results to the setting of multidimensional linear SA algorithms and characterize the behavior of the multidimensional Friedkin–Johnsen model over random interaction networks. [ABSTRACT FROM AUTHOR]

The circle formation problem for a group of mobile agents with limited interaction range is addressed in this paper. Distributed switching control laws are developed for multiagent systems to form prescribed formations from any initial configurations on a circle. It is shown that the desired circle formation can be achieved if a parameter depending on the agents’ interaction range is larger than the prescribed angular distance from each agent to its immediate counterclockwise agent. When the agents’ interaction range is not sufficiently large, the formation error of each agent converges to a limit, and an upper bound and a lower bound on the limit value are provided. It is also shown that under the proposed control laws, the mobile agents’ spatial order on the circle is always preserved and thus collision between mobile agents is avoided. [ABSTRACT FROM AUTHOR]

This paper presents a systematic method to analyze the stability of systems with single delay in which the coefficient polynomials of the characteristic equation depend on the delay. Such systems often arise in, for example, life science and engineering systems. A method to analyze such systems was presented by Beretta and Kuang in a 2002 paper, but with some very restrictive assumptions. This paper extends their results to the general case with the exception of some degenerate cases. It is found that a much richer behavior is possible when the restrictive assumptions are removed. The interval of interest for the delay is partitioned into subintervals so that the magnitude condition generates a fixed number of frequencies as functions of the delay within each subinterval. The crossing conditions are expressed in a general form, and a simplified derivation for the first-order derivative criterion is obtained. Illustrative examples are also presented in this paper. [ABSTRACT FROM AUTHOR]

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 multiagent networks from an optimization perspective. In this paper, we consider the standard distributed matrix-information structures, where each agent of the considered multiagent network has access to one of the subblock 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. [ABSTRACT FROM AUTHOR]

In this paper, we consider the distributed filtering problem for continuous-time stochastic systems over sensor networks subject to Markovian switching topologies. Due to limited communication energy and bandwidth, an event-based communication scheme is proposed with the aim to decrease the transmission frequency. An individual triggering condition is put forward to regulate the communication rates for each component of the system state in order to better reflect the engineering requirements. The aim of this paper is to design a distributed filter over sensor networks with Markovian switching topologies such that the dynamics of the estimation error is exponentially mean-square bounded. It is shown that, with the proposed event-based distributed filtering algorithm, the exponential mean-square boundedness of the estimation errors is guaranteed if the sensor network is distributively detectable and the combined communication topology is strongly connected. A numerical example is presented to illustrate the usefulness of the developed algorithm. [ABSTRACT FROM AUTHOR]

In this paper, a full-order observer design method is proposed for port-Hamiltonian systems. The proposed method is based on the notion of contractive port-Hamiltonian systems. It is the first structure preserving observer design for a broad class of input-state-output port-Hamiltonian systems. The design procedure consists of solving a matching equation, similar to the Interconnection and Damping Assignment Passivity-Based Control (IDA-PBC) for controller design. The matching equation, as shown in the paper, has some closed-form solutions for general class of mechanical and electromechanical systems. As another feature of the proposed method, it is shown that the existence of solution of the corresponding matching equation for a linear port-Hamiltonian system is equivalent to the detectability property of that system. Upon these facts, the proposed method can be considered as a counterpart of IDA-PBC for observer design. Simulations for some benchmark examples, including ball and beam, magnetic levitation, and permanent magnetic synchronous motor, show the potency and applicability of the method. [ABSTRACT FROM AUTHOR]

This paper presents a small-gain result for large-scale interconnected systems composed of hybrid subsystems. It is assumed that the subsystems are input-to-output practically stable (IOpS) with offset and unboundedness observability (UO), and the interconnected system can be proved to be IOpS with offset and UO as long as the proposed small-gain condition is satisfied. If, moreover, the assumption of IOpS on the subsystems is reduced to input-to-output stability (IOS), then the interconnected system is IOS. [ABSTRACT FROM AUTHOR]

In this paper, we consider the identification of matrix state-space models (MSSM) of the following form: \begin{align*} \mathbf {X}(k+1) &= \mathbf {A}_2 \mathbf {X}(k) \mathbf {A}_1^T + \mathbf {B}_2 \mathbf {U}(k) \mathbf {B}_1^T \\ \mathbf {Y}(k) &= \mathbf {C}_2 \mathbf {X}(k) \mathbf {C}_1^T + \mathbf {E}(k) \end{align*} for all time dependent quantities and matrices of appropriate dimensions. Due to the large size of these matrices, vectorization does not allow the use of standard multivariable subspace methods such as N4SID or MOESP. In this paper, the resulting Kronecker structure that appears in the system matrices due to vectorization is exploited for developing a scalable subspace-like identification approach. This approach consists of first estimating the Markov parameters associated to the MSSM via the solution of a regularized bilinear least-squares problem that is solved in a globally convergent manner. Second, a bilinear low-rank minimization problem is tackled which allows to write a three-dimensional low-rank tensor and consequently to estimate the state sequence and the lower-dimensional matrices $\mathbf {A}_1,\mathbf {A}_2,\mathbf {B}_1,\mathbf {B}_2,\mathbf {C}_1,\mathbf {C}_2$. A numerical example on a large-scale adaptive optics system demonstrates the ability of the algorithm to handle the identification of state-space models within the class of Kronecker structured matrices in a scalable manner which results in more compact models. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new state observer design technique for nonlinear systems. It combines the well-known Kazantzis–Kravaris–Luenberger observer and the recently introduced parameter estimation-based observer, which become special cases of it—extending the realm of applicability of both methods. A second contribution of this paper is the proof that these designs can be recast as particular cases of immersion and invariance observers—providing in this way a unified framework for their analysis and design. Simulation results of a physical system that illustrates the superior performance of the proposed observer compared to other existing observers are presented. [ABSTRACT FROM AUTHOR]

In this paper, stability and stabilization of Boolean networks with stochastic delays are studied via semi-tensor product of matrices. The stochastic delays, randomly attaining finite values, are modeled by Markov chains. By utilizing an augmented method, the considered Boolean network is first converted into two coupled Markovian switching systems without delays. Then, some stochastic stability results are obtained based on stability results of positive systems. Subsequently, the stabilization of Boolean networks with stochastic delays is further investigated, and an equivalent condition for the existence of feedback controllers is provided in terms of a convex programming problem, which can be easily solved and also conveniently applied to design controller gains. Finally, numerical examples are given to illustrate feasibility of the obtained results. [ABSTRACT FROM AUTHOR]

This paper is concerned with the recursive filtering problem for a class of networked linear time-varying systems subject to the scheduling of the random access protocol (RAP). The communication between the sensor nodes and the remote filter is implemented via a shared network. For the purpose of preventing the data from collisions, only one sensor node is allowed to get access to the network at each time instant. The transmission order of sensor nodes is orchestrated by the RAP scheduling, under which the selected nodes obtaining access to the network could be characterized by a sequence of independent and identically-distributed variables. The aim of the addressed filtering problem is to design a recursive filter such that the filtering error covariance could be minimized by properly designing the filter gain at each time instant. The desired filter gain is calculated recursively by solving two Riccati-like difference equations. Furthermore, the boundedness issue of the corresponding filtering error covariance is investigated. Sufficient conditions are obtained to ensure the lower and upper bounds of the filtering error covariance. Two illustrative examples are given to demonstrate the correctness and effectiveness ofour developed recursive filtering approach. [ABSTRACT FROM AUTHOR]

In this paper, we present a generalization of a recent result on the almost sure consensus for networks affected by relative-state-dependent measurement noise. Specifically, we give two sufficient conditions for the synchronization of networks of diffusively coupled nonlinear nodes affected by certain state-dependent noise diffusion processes. We use this condition to study the onset of synchronization in a network of Lorenz systems and collective opinion dynamics. [ABSTRACT FROM AUTHOR]

The topic of this paper is model predictive control (MPC) for max-plus linear systems with stochastic uncertainties the distribution of which is supposed to be known. We consider linear constraints on the inputs and the outputs. Due to the uncertainties, these linear constraints are formulated as probabilistic or chance constraints, i.e., the constraints are required to be satisfied with a predefined probability level. The proposed chance constraints can be equivalently rewritten into a max-affine (i.e., the maximum of affine terms) form if the linear constraints are monotonically nondecreasing as a function of the outputs. Based on the resulting max-affine form, two methods are developed for solving the chance-constrained MPC problem for stochastic max-plus linear systems. Method 1 uses Boole's inequality to convert the multivariate chance constraint into univariate chance constraints for which the probability can be computed more efficiently. Method 2 employs Chebyshev's inequality and transforms the chance constraint into linear constraints on the inputs. The simulation results for a production system example show that the two proposed methods are faster than the Monte Carlo simulation method and yield lower closed-loop costs than the nominal MPC method. [ABSTRACT FROM AUTHOR]

This paper is concerned with the optimal static distributed control problem for linear discrete-time deterministic and stochastic systems. The objective is to design a stabilizing static distributed controller whose performance is close to that of the optimal centralized controller. To this end, we first consider deterministic systems, where the initial state is either given or belongs to a known bounded region. Given an arbitrary centralized controller, we derive a condition under which there exists a distributed controller that generates input and state trajectories close to their counterparts in the centralized closed-loop system. This condition for the design of a distributed controller is translated into an optimization problem, where the optimal objective value of this problem quantifies the closeness of the designed distributed and given centralized control systems. The results are then extended to stochastic systems that are subject to input disturbance and measurement noise. The proposed optimization problem has a closed-form solution (explicit formula) and can be efficiently solved for large-scale systems. The mathematical framework developed in this paper is utilized to design a near-globally optimal distributed controller based on the optimal centralized controller, and strong theoretical lower bounds on the global optimality guarantee of the obtained distributed controller are derived. We show that if the optimal objective value of the proposed convex program is sufficiently small, the designed controller is stabilizing and nearly globally optimal. To illustrate the results, case studies on aircraft formation and frequency control of power systems are offered. [ABSTRACT FROM AUTHOR]

This paper investigates the remote state estimation problem over a bandwidth-limited channel. To improve the estimation quality, an event-based schedule is proposed to determine whether to transmit the current measurement to the remote estimator or not. We first show that it is erroneous to apply the widely used Gaussian-approximation assumption in the event-based scheduling. As a replacement, the generalized closed skew normal (GCSN) distribution is introduced to accurately portray the system state distribution in the event-based scheduling. Furthermore, we present the probability density functions of the minimum mean-squared error estimation algorithm exactly without approximation for the first time. The closed-form expressions for the mean and covariance of the GCSN distribution are derived as well. Numerical examples validate the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

An observer for simultaneous localization and mapping is considered in this paper. The proposed observer is based on recent theoretical foundations in a gradient-based observer design on Lie groups. As such, the form of the observer is similar to recently developed nonlinear attitude and pose observers. Translational and angular velocity measurements, as well as relative position measurements of nearby landmarks, are used directly within the observer structure. The case of biased translational and angular velocity measurements is also considered. Stability results are presented that demonstrate an asymptotic convergence of the pose and map estimates. The proposed algorithm is implemented successfully in experiment. [ABSTRACT FROM AUTHOR]

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, which 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. [ABSTRACT FROM AUTHOR]

We establish a new condition for global consensus of continuous-time multiagent systems with undirected switching interaction graphs. The condition is strictly weaker than the persistency of excitation, one recently shown in , to be necessary and sufficient for global exponential consensus. The price paid for the relaxation of the excitation requirement is twofold; on one hand, we establish only global asymptotic consensus without the “exponential” qualifier. On the other hand, we prove that our condition is not necessary. We also prove in this paper that an additional assumption is needed in to extend the consensus result to the case of negatively weighted edges. [ABSTRACT FROM AUTHOR]

Linear parameter varying (LPV) subspace identification methods suffer from an exponential growth in number of parameters to estimate. This results in problems with ill-conditioning. In literature, attempts have been made to address the ill-conditioning by using regularization. Its effectiveness hinges on suitable a priori knowledge. In this paper, we propose using a novel, alternative regularization. That is, we first show that the LPV sub-Markov parameters can be organized into several tensors that are multilinear low rank by construction. Namely, their matricization along any mode is a low-rank matrix. Then, we propose a novel convex method with tensor nuclear norm regularization, which exploits this low-rank property. Simulation results show that the novel method can have higher performance than the regularized LPV-PBSID $_{\text{opt}}$ technique in terms of variance accounted for. [ABSTRACT FROM AUTHOR]

In this paper, we consider a discrete-time consensus network, and assume that one of the agents acts as a leader and injects an input signal to improve the overall system performance, in particular to increase the speed of convergence to consensus or to achieve finite-time consensus. Two possible control protocols are proposed, and the characteristic polynomials of the resulting closed-loop systems are determined. These results allow us to investigate the consensus and finite-time consensus of the overall systems. Open problems and future research directions conclude this paper. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to provide a generalization of the so-called Simultaneous Long–Short (SLS) stock-trading result in the feedback control literature. The significance of the SLS strategy is that it guarantees a “win” in expected value of profits. Whereas previous work involves use of static linear feedback to establish this robust positive expectation property of the gain–loss function, here we obtain the same result for the more general case of PI control. In this SLS setting, robustness is assured with respect to stock prices governed by a Geometric Brownian Motion whose drift and volatility parameters are unknown to the trader. This technical note also includes numerical simulations. [ABSTRACT FROM AUTHOR]

The finite-time attitude synchronization problem is considered in this paper, where the rotation of each rigid body is expressed using the axis-angle representation. Two discontinuous and distributed controllers using the vectorized signum function are proposed, which guarantee almost global and local convergence, respectively. Filippov solutions and nonsmooth analysis techniques are adopted to handle the discontinuities. Sufficient conditions are provided to guarantee finite-time convergence and boundedness of the solutions. Simulation examples are provided to verify the performances of the control protocols designed in this paper. [ABSTRACT FROM AUTHOR]

In this paper, we provide a detailed analysis of the global convergence properties of an extensively studied and extremely effective fixed-point algorithm for the Kullback–Leibler approximation of spectral densities, proposed by Pavon and Ferrante in their paper “On the Georgiou–Lindquist approach to constrained Kullback–Leibler approximation of spectral densities.” Our main result states that the algorithm globally converges to one of its fixed points. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This paper addresses the actuator fault estimation sliding-mode observer (SMO) design problem of linear continuous-time systems over digital communication channels. This problem frequently occurred in a network environment where data has to be quantized before being transmitted via digital communication channels. Traditional observers (linear Luenberger observer, Walcott–ZaK SMO) are not effective to solve this design issue since the effects of signal quantization will degrade estimation performances evidently. In this paper, a new descriptor SMO method is presented to overcome this difficult problem. It is shown that, if the quantizer density is larger than $\sqrt{2}-1$ , the designed observer can compensate quantization errors completely, and the fault vector can be reconstructed despite of signal quantization. Finally, a simulation example with the F-404 aircraft engine model is proposed to demonstrate the effectiveness of the proposed robust digital observer design approach. [ABSTRACT FROM AUTHOR]

In this paper, we consider robust stability analysis of large-scale sparsely interconnected uncertain systems. By modeling the interconnections among the subsystems with integral quadratic constraints, we show that robust stability analysis of such systems can be performed by solving a set of sparse linear matrix inequalities. We also show that a sparse formulation of the analysis problem is equivalent to the classical formulation of the robustness analysis problem and hence does not introduce any additional conservativeness. The sparse formulation of the analysis problem allows us to apply methods that rely on efficient sparse factorization techniques, and our numerical results illustrate the effectiveness of this approach compared to methods that are based on the standard formulation of the analysis problem. [ABSTRACT FROM AUTHOR]

This paper presents a human-inspired control approach to bipedal robotic walking: utilizing human data and output functions that appear to be intrinsic to human walking in order to formally design controllers that provably result in stable robotic walking. Beginning with human walking data, outputs—or functions of the kinematics—are determined that result in a low-dimensional representation of human locomotion. These same outputs can be considered on a robot, and human-inspired control is used to drive the outputs of the robot to the outputs of the human. The main results of this paper are that, in the case of both under and full actuation, the parameters of this controller can be determined through a human-inspired optimization problem that provides the best fit of the human data while simultaneously provably guaranteeing stable robotic walking for which the initial condition can be computed in closed form. These formal results are demonstrated in simulation by considering two bipedal robots—an underactuated 2-D bipedal robot, AMBER, and fully actuated 3-D bipedal robot, NAO—for which stable robotic walking is automatically obtained using only human data. Moreover, in both cases, these simulated walking gaits are realized experimentally to obtain human-inspired bipedal walking on the actual robots. [ABSTRACT FROM PUBLISHER]

Lyapunov's second theorem is an essential tool for stability analysis of differential equations. The paper provides an analog theorem for incremental stability analysis by lifting the Lyapunov function to the tangent bundle. The Lyapunov function endows the state-space with a Finsler structure. Incremental stability is inferred from infinitesimal contraction of the Finsler metrics through integration along solutions curves. [ABSTRACT FROM AUTHOR]

This article is concerned with the development and use of duality theory for a nonlinear filtering model with white noise observations. The main contribution of this article is to introduce a stochastic optimal control problem as a dual to the nonlinear filtering problem. The mathematical statement of the dual relationship between the two problems is given in the form of a duality principle. The constraint for the optimal control problem is the backward stochastic differential equation introduced in the companion paper. The optimal control solution is obtained from an application of the maximum principle, and subsequently used to derive the equation of the nonlinear filter. The proposed duality is shown to be an exact extension of the classical Kalman–Bucy duality, and different from other types of optimal control and variational formulations given in literature.

This technical note addresses the problem of transforming a single-input–single-output discrete-time system into the extended observer form, which comprise a linear time-invariant observable component, and a nonlinear injection term, which depends on the input, output, and their forward shifts up to a finite order. Intrinsic necessary and sufficient conditions are provided for obtaining the extended observer form via a parametrized state transformation. The conditions are formulated directly in terms of the state equations and do not rely on input–output equations as in the earlier papers. Further, an algorithm for obtaining the required transformation is presented. Unlike the existing results on observer forms, the results are not restricted to reversible systems but to more general submersive systems, i.e., to systems, which are reversible via static state feedback.

Kernel-based methods have been successfully introduced in system identification to estimate the impulse response of a linear system. Adopting the Bayesian viewpoint, the impulse response is modeled as a zero mean Gaussian process whose covariance function (kernel) is estimated from the data. The most popular kernels used in system identification are the tuned-correlated (TC), the diagonal-correlated (DC) and the stable spline (SS) kernel. TC and DC kernels admit a closed-form factorization of the inverse. The SS kernel induces more smoothness than TC and DC on the estimated impulse response, however, the aforementioned property does not hold in this case. In this paper we propose a second-order extension of the TC and DC kernel, which induces more smoothness than TC and DC, respectively, on the impulse response and a generalized-correlated kernel, which incorporates the TC and DC kernels and their second order extensions. Moreover, these generalizations admit a closed-form factorization of the inverse and thus they allow to design efficient algorithms for the search of the optimal kernel hyperparameters. We also show how to use this idea to develop higher oder extensions. Interestingly, these new kernels belong to the family of the so called exponentially convex local stationary kernels: such a property allows to immediately analyze the frequency properties induced on the estimated impulse response by these kernels.

Reliable quasi-static object manipulation and robotic locomotion require the verification of the stability of equilibria under unilateral contacts and friction. In a recent paper, Posa et al. (2016) demonstrated that sums-of-squares (SOS) programming can be used to verify the Lyapunov stability of planar systems via Lyapunov’s direct method if impacts are inelastic. However, this method appears to be too conservative to verify the stability of some remarkably simple examples. In this article, an extension of Lyapunov’s direct method is proposed, which makes use of a piecewise smooth Lyapunov function and allows a temporary increase of the Lyapunov function along a motion trajectory. In addition, a modified SOS formulation enables the investigation of planar systems with partially elastic contacts. The proposed method remains compatible with SOS programming techniques. The improved stability test is successfully applied to a point mass on a slope and to a rigid body with two contact points. For the latter, several mechanisms of instability have been demonstrated experimentally, but the exact conditions of Lyapunov stability are unknown.

In this article, stabilization of systems by delayed noisy states is investigated. The time delays in the stabilizing noisy states are extended into the general form. To support this novelty, the familiar Doob martingale inequality in the continuous version is improved; the equivalence principle, which says that the exponential stability in moment of an anhysteretic stochastic system infers the same property of the corresponding hysteretic system, is extended to the cases with the newly proposed semi-Lipschitz condition; the implication theorem, which indicates that the exponential stability in moment implies almost sure exponential stability, is generalized to the stochastic systems with time delays of general forms only under the linear growth condition. Technically, variable substitution is applied to time to map the function spaces for the functional differential equation models with unbounded time delays into those with bounded ones. Unified framework for the stability analysis for both bounded and unbounded time delays is built with the mapping, the decay rates, including those for polynomial stability, for estimates of the solutions with time delays of general form are formulated. At the end of the article, typical strategies, including the divided state feedback with unbounded time delays, for the stabilizing noise are presented, a numerical example is proposed to illustrate the method and to show the efficiency of the results of the paper.

The paper proposes an identification procedure for autoregressive Gaussian stationary stochastic processes under the assumption that the manifest (or observed) variables are nearly independent when conditioned on a limited number of latent (or hidden) variables. The method exploits the sparse plus low-rank decomposition of the inverse of the manifest spectral density and the efficient convex relaxations recently proposed for such decompositions. [ABSTRACT FROM PUBLISHER]

Consensus in heterogeneous networks containing both linear and linear impulsive dynamics is considered in this paper. The model applies for networks of interconnected dynamical systems, called agents, that are partitioned into several clusters. Most of the agents can only update their state in a continuous way using only inner-cluster agent states. On top of this, few agents also have the peculiarity to update their states in a discrete way by reseting it using states from agents outside their clusters. Our main result gives sufficient conditions for consensus in these networks. We firstly analyze the case when the reset sequence verifies some explicit time conditions. Secondly we consider the case when the reset instants are event-triggered, i.e., defined by the occurrence of specific events. Finally, we treat the case when the reset instants arrive stochastically following a Poisson renewal process. [ABSTRACT FROM AUTHOR]

In this paper, we consider the l\infty gain characterizations of linear switched systems (LSS) and present various relevant results on their exact computation and optimization. Depending on the role of the switching sequence, we study two broad cases: first, when the switching sequence attempts to maximize, and second, when it attempts to minimize the l\infty gain. The first, named as worst-case throughout the paper, can be related to robustness of the system to uncontrolled switching; the second relates to situations when the switching can be part to the overall decision making. Although, in general, the exact computation of l\infty gains is difficult, we provide specific classes, the input-output switching systems, for which it is shown that linear programming can be used to obtain the worst-case l\infty gain. This is a sufficiently rich class of systems as any stable LSS can be approximated by one. Certain applications to robust control design are provided where we show that a switched compensation independently of the plant has no advantage over a linear time invariant (LTI) compensation, and further, if the plant is strictly causal, even a switched compensation which has a matched switching with the plant does not provide a better performance over an LTI compensation. Also, we present a new necessary and sufficient condition to check the stability of LSS in form of a model matching problem. On the other hand, if one is interested in minimizing the l\infty gain over the switching sequences, we show that, for finite impulse response (FIR) switching systems the minimizing switching sequence can be chosen to be periodic. For input-only or output-only switching an exact, readily computable, characterization of the minimal l\infty gain is provided, and it is shown that the minimizing switching sequence is constant, which, as also shown, is not true for input-output switching. [ABSTRACT FROM AUTHOR]