Search

This paper is concerned with the analysis and synthesis of interconnected systems constructed from heterogeneous positive subsystems and a nonnegative interconnection matrix. We first show that admissibility, to be defined in this paper, is an essential requirement in constructing such interconnected systems. Then, we clarify that the interconnected system is admissible and stable if and only if a Metzler matrix, which is built from the coefficient matrices of positive subsystems and the nonnegative interconnection matrix, is Hurwitz stable. By means of this key result, we further provide several results that characterize the admissibility and stability of the interconnected system in terms of the Frobenius eigenvalue of the interconnection matrix and the weighted L1- induced norm of the positive subsystems again to be defined in this paper. Moreover, in the case where every subsystem is SISO, we provide explicit conditions under which the interconnected system has the property of persistence, i.e., its state converges to a unique strictly positive vector (that is known in advance up to a strictly positive constant multiplicative factor) for any nonnegative and nonzero initial state. As an important consequence of this property, we show that the output of the interconnected system converges to a scalar multiple of the right eigenvector of a nonnegative matrix associated with its Frobenius eigenvalue, where the nonnegative matrix is nothing but the interconnection matrix scaled by the steady-stage gains of the positive subsystems. This result is then naturally and effectively applied to formation control of multiagent systems with positive dynamics. This result can be seen as a generalization of a well-known consensus algorithm that has been basically applied to interconnected systems constructed from integrators. [ABSTRACT FROM PUBLISHER]

This paper considers the quadratic control problem of discrete-time Markov jump linear systems with constraints on the norm of the state and control variables. We assume that the Markov chain parameter is not available, and instead, there is a detector, which emits signals providing information on this parameter. It is desired to derive a feedback linear control using the information provided by this detector in order to stochastically stabilize the closed-loop system, satisfy the constraints whenever the initial conditions belong to an invariant set, and minimize an upper bound for the quadratic cost. We show that a linear matrix inequality (LMI) optimization problem can be formulated in order to obtain a solution for this problem. Two other related problems, one for minimizing the guaranteed quadratic cost considering fixed initial conditions and the other for maximizing an estimate of the domain of an invariant set, can also be formulated using our LMI approach. This paper is concluded with some numerical simulations. [ABSTRACT FROM AUTHOR]

This paper deals with optimal feedback selection problem in linear time-invariant (LTI) structured systems for arbitrary pole placement, an important open problem in structured systems. Specifically, we solve the sparsest feedback selection problem for LTI structured systems. In this paper, we consider structurally cyclic systems with dedicated inputs and outputs. For this class of systems, we prove that the sparsest feedback selection problem is equivalent to the strong connectivity augmentation problem in graph theory. We present an $O(n^2)$ algorithm to find a sparsest feedback matrix for structured systems when every state is actuated by a dedicated input and every state is sensed by a dedicated output, where $n$ denotes the number of states in the system. If the inputs and the outputs are such that not every state is actuated by a dedicated input and/or not every state is sensed by a dedicated output, then we provide an $O(n^3)$ algorithm for the sparsest feedback selection problem. These results show that sparsest feedback selection with dedicated i/o is a specific case of the optimal feedback selection problem that is solvable in polynomial time. We later analyze the sparsest feedback selection problem for structurally cyclic systems when both the input and the output are dedicated and the feedback pattern is constrained. When some of the feedback links are forbidden, we prove that the problem is NP-hard. The results in this paper along with the previously known results conclude that the optimal feedback selection problem is polynomial-time solvable only for the dedicated input–output case without forbidden feedback links and also without weights for the feedback links. [ABSTRACT FROM AUTHOR]

This paper establishes some new results on the Bott–Duffin procedure—a fundamental result in both passive network synthesis and linear systems theory. Since its appearance in 1949, this procedure has puzzled circuit and systems researchers as the networks produced contain an apparently extravagant number of elements. In this paper, we prove that the networks obtained by the Bott–Duffin procedure contain the least number of reactive elements (six) and the least number of resistors (two) among all series-parallel networks realizing a certain type of impedance function (a biquadratic minimum function). We further show that the Bott–Duffin procedure, in combination with some simple network transformations, can be used to produce all of the series-parallel networks containing exactly six reactive elements and two resistors which realize any specified biquadratic minimum function. In the course of the argument, we prove several additional interesting results pertaining to series-parallel realizations of minimum functions. The results are motivated by the application of the inerter device to passive mechanical control. [ABSTRACT FROM AUTHOR]

In this paper, we will study coupled dynamical systems and investigate dimension properties of the subspace spanned by solutions of each individual system. Relevant problems on collinear dynamical systems and their variations are discussed recently by Montenbruck et al. in , while in this paper we aim to provide a unified analysis to derive the dimensional-invariance principles for networked coupled systems, and to generalize the invariance principles for networked systems with more general forms of coupling terms. To be specific, we consider two types of coupled systems, one with scalar couplings and the other with matrix couplings. Via the rank-preserving flow theory, we show that any scalar-coupled dynamical system (with constant, time-varying, or state-dependent couplings) possesses the dimensional-invariance principles, in that the dimension of the subspace spanned by the individual systems’ solutions remains invariant. For coupled dynamical systems with matrix coefficients/couplings, necessary and sufficient conditions (for constant, time-varying, and state-dependent couplings) are given to characterize dimensional-invariance principles. The proofs via a rank-preserving matrix flow theory in this paper simplify the analysis in , and we also extend the invariance principles to the cases of time-varying couplings and state-dependent couplings. Furthermore, subspace-preserving property and signature-preserving flows are also developed for coupled networked systems with particular coupling terms. These invariance principles provide insightful characterizations to analyze transient behaviors and solution evolutions for a large family of coupled systems, such as multiagent consensus dynamics, distributed coordination systems, formation control systems, etc. [ABSTRACT FROM AUTHOR]

This paper introduces an explicit reference governor to supervise closed-loop linear time-delay systems. The proposed scheme enforces state and input constraints by modifying the reference of the supervised system so that the state vector always belongs to admissible sublevel sets of a suitably defined Lyapunov–Krasovskii functional. To accomplish this, this paper extends the existing definition of “dynamic safety margin” to a time-delay setting and illustrates how to employ classic Lyapunov–Krasovskii functionals even though the reference is time varying. Constraint enforcement for arbitrary reference signals and asymptotic convergence to any strictly steady-state admissible set point is rigorously proven. Experimental results are reported to demonstrate the simplicity, practicality, and robustness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we study the distributed fusion estimation problem for linear time-varying systems and nonlinear systems with bounded noises, where the addressed noises do not provide any statistical information, and are unknown but bounded. When considering linear time-varying fusion systems with bounded noises, a new local Kalman-like estimator is designed such that the square error of the estimator is bounded as time goes to $\infty$. A novel constructive method is proposed to find an upper bound of fusion estimation error, then a convex optimization problem on the design of an optimal weighting fusion criterion is established in terms of linear matrix inequalities, which can be solved by standard software packages. Furthermore, according to the design method of linear time-varying fusion systems, each local nonlinear estimator is derived for nonlinear systems with bounded noises by using Taylor series expansion, and a corresponding distributed fusion criterion is obtained by solving a convex optimization problem. Finally, target tracking system and localization of a mobile robot are given to show the advantages and effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

This paper addresses optimal feedback selection for arbitrary pole placement of structured systems when each feedback edge is associated with a cost. Given a structured system and a feedback cost matrix, our aim is to find a feasible feedback matrix of minimum cost that guarantees arbitrary pole placement of the closed-loop structured system. The same problem but with uniform costs has been considered recently, but the claim and the NP-hardness proof there has subtle flaws: we mention this briefly in our paper and then prove the NP-hardness of the feedback selection problem using a reduction from the weighted set cover problem. We next prove the polynomial time constant factor inapproximability of the problem by showing that a constant factor approximation for the problem does not exist, unless the weighted set cover problem can also be approximated within a constant factor. We study a subclass of systems whose directed acyclic graph constructed using the strongly connected components of the state digraph is a line graph and the state bipartite graph has a perfect matching. We propose a polynomial time algorithm based on dynamic programming principles for optimal feedback selection on this class of systems. Further, over the same class of systems we relax the perfect matching assumption, and provide a polynomial time 2-optimal solution using a minimum cost perfect matching algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we propose new algebraic Gramians for continuous-time switched linear systems, which satisfy generalized Lyapunov equations. The main contribution of this paper is twofold. First, we show that the ranges of those Gramians encode the reachability and observability spaces of a switched linear system. As a consequence, a simple Gramian-based criterion for reachability and observability is established. Second, a balancing-based model order reduction technique is proposed and, under some sufficient conditions, stability preservation and an error bound are shown. Finally, the efficiency of the proposed method is illustrated by means of numerical examples. [ABSTRACT FROM AUTHOR]

This paper focuses on the modeling of time-varying covariance matrices using the state covariance of linear systems. Following concepts from optimal mass transport, we investigate and compare three types of covariance paths, which are solutions to different optimal control problems. One of the covariance paths solves the Schrödinger bridge problem. The other two types of covariance paths are based on generalizations of the Fisher–Rao metric in information geometry, which are the major contributions of this paper. The general framework is an extension of the approach proposed in the paper “Smooth interpolation of covariance matrices and brain network estimation” (IEEE Trans. Autom. Control), which focuses on linear systems without stochastic input The performances of the three covariance paths are compared using synthetic data and a real-data example on the estimation of dynamic brain networks using functional magnetic resonance imaging. [ABSTRACT FROM AUTHOR]

This paper provides a new analytic test to check strong accessibility of nonlinear control systems. This test can be applied to nonlinear systems described by meromorphic vector fields (whose components are fractions of analytic functions). The test consists in checking the rank of a certain finite matrix (which extends to a nonlinear case the classical “controllability matrix” of linear systems theory) and, unlike the classical accessibility test, always terminates giving an exhaustive answer (yes/no) within a fixed number of steps. Further, a generic feature of accessibility is proven: the accessibility from a point $p$ of the system analyticity domain implies the accessibility from almost every point of the domain (generic strong accessibility). The paper provides two simple examples, which illustrate the proposed analytic test and its advantages with respect to the existing results. [ABSTRACT FROM AUTHOR]

One often wishes for the ability to formally analyze large-scale systems—typically, however, one can either formally analyze a rather small system or informally analyze a large-scale system. This paper tries to further close this performance gap for reachability analysis of linear systems. Reachability analysis can capture the whole set of possible solutions of a dynamic system and is thus used to prove that unsafe states are never reached; this requires full consideration of arbitrarily varying uncertain inputs, since sensor noise or disturbances usually do not follow any patterns. We use Krylov methods in this paper to compute reachable sets for large-scale linear systems. While Krylov methods have been used before in reachability analysis, we overcome the previous limitation that inputs must be (piecewise) constant. As a result, we can compute reachable sets of systems with several thousand state variables for bounded, but arbitrarily varying inputs. [ABSTRACT FROM AUTHOR]

Motivated by robotic surveillance applications, this paper studies the novel problem of maximizing the return time entropy of a Markov chain, subject to a graph topology with travel times and stationary distribution. The return time entropy is the weighted average, over all graph nodes, of the entropy of the first return times of the Markov chain; this objective function is a function series that does not admit, in general, a closed form. This paper features theoretical and computational contributions. First, we obtain a discrete-time delayed linear system for the return time probability distribution and establish its convergence properties. We show that the objective function is continuous over a compact set and therefore admits a global maximum. We then establish upper and lower bounds between the return time entropy and the well-known entropy rate of the Markov chain. To compute the optimal Markov chain numerically, we establish the asymptotic equality between entropy, conditional entropy, and truncated entropy, and propose an iteration to compute the gradient of the truncated entropy. Finally, we apply these results to the robotic surveillance problem. Our numerical results show that for a model of rational intruder over prototypical graph topologies and test cases, the maximum return time entropy Markov chain outperforms several pre-existing Markov chains. [ABSTRACT FROM AUTHOR]

This paper is concerned with stability analysis and synthesis for discrete-time linear systems with stochastic dynamics. Equivalence is first proved for three stability notions under some key assumptions on the randomness behind the systems. In particular, we use the assumption that the stochastic process determining the system dynamics is independent and identically distributed with respect to the discrete time. Then, a Lyapunov inequality condition is derived for stability in a necessary and sufficient sense. Although our Lyapunov inequality will involve decision variables contained in the expectation operation, an idea is provided to solve it as a standard linear matrix inequality; the idea also plays an important role in state feedback synthesis based on the Lyapunov inequality. Motivating numerical examples are further discussed as an application of our approach. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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]

In this paper, we consider the output synchronization problem for a network of heterogeneous diffusively-coupled nonlinear agents. Specifically, we show how the (heterogeneous) agents can be controlled in such a way that their outputs asymptotically track the output of a prescribed nonlinear exosystem. The problem is solved in two steps. In the first step, the problem of achieving consensus among (identical) nonlinear reference generators is addressed. In this respect, it is shown how the techniques recently developed to solve the consensus problem among linear agents can be extended to agents modeled by nonlinear $d$-dimensional differential equations, under the assumption that the communication graph is connected. In the second step, the theory of nonlinear output regulation is applied in a decentralized control mode, to force the output of each agent of the network to robustly track the (synchronized) output of a local reference model. Simulation results are presented to show the effectiveness of the design methodology. [ABSTRACT FROM PUBLISHER]

Recently, several convergence rate results for Douglas-Rachford splitting and the alternating direction method of multipliers (ADMM) have been presented in the literature. In this paper, we show global linear convergence rate bounds for Douglas-Rachford splitting and ADMM under strong convexity and smoothness assumptions. We further show that the rate bounds are tight for the class of problems under consideration for all feasible algorithm parameters. For problems that satisfy the assumptions, we show how to select step-size and metric for the algorithm that optimize the derived convergence rate bounds. For problems with a similar structure that do not satisfy the assumptions, we present heuristic step-size and metric selection methods. [ABSTRACT FROM PUBLISHER]

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 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 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]

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]

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 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]

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 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]

This paper addresses the problem of obtaining an estimate of a particular module of interest that is embedded in a dynamic network with known interconnection structure. In this paper it is shown that there is considerable freedom as to which variables can be included as inputs to the predictor, while still obtaining consistent estimates of the particular module of interest. This freedom is encoded into sufficient conditions on the set of predictor inputs that allow for consistent identification of the module. The conditions can be used to design a sensor placement scheme, or to determine whether it is possible to obtain consistent estimates while refraining from measuring particular variables in the network. As identification methods the Direct and Two Stage Prediction-Error methods are considered. Algorithms are presented for checking the conditions using tools from graph theory. [ABSTRACT FROM AUTHOR]

System identification is a key enabling component for the implementation of quantum technologies, including quantum control. In this paper, we consider the class of passive linear input-output systems, and investigate several basic questions: 1) which parameters can be identified? 2) Given sufficient input-output data, how do we reconstruct the system parameters? 3) How can we optimize the estimation precision by preparing appropriate input states and performing measurements on the output? We show that minimal systems can be identified up to a unitary transformation on the modes, and systems satisfying a Hamiltonian connectivity condition called “infecting” are completely identifiable. We propose a frequency domain design based on a Fisher information criterion, for optimizing the estimation precision for coherent input state. As a consequence of the unitarity of the transfer function, we show that the Heisenberg limit with respect to the input energy can be achieved using non-classical input states. [ABSTRACT FROM AUTHOR]

This paper addresses problems on the structural design of large-scale control systems. An efficient and unified framework is proposed to select the minimum number of manipulated/measured variables to achieve structural controllability/observability of the system, and to select the minimum number of feedback interconnections between measured and manipulated variables such that the closed-loop system has no structural fixed modes. Global solutions are computed using polynomial complexity algorithms in the number of the state variables of the system. Finally, graph-theoretic characterizations are proposed, which allow a characterization of all possible solutions. [ABSTRACT FROM PUBLISHER]

In this paper, a novel framework to address the problem of parametric estimation for continuous-time linear time-invariant dynamic systems is dealt with. The proposed methodology entails the design of suitable kernels of non-anticipative linear integral operators thus obtaining estimators showing, in the ideal case, “non-asymptotic” (i.e., “finite-time”) convergence. The analysis of the properties of the kernels guaranteeing such a convergence behaviour is addressed and a novel class of admissible kernel functions is introduced. The operators induced by the proposed kernels admit implementable (i.e., finite-dimensional and internally stable) state-space realizations. Extensive numerical results are reported to show the effectiveness of the proposed methodology. Comparisons with some existing continuous-time estimators are addressed as well and insights on the possible bias affecting the estimates are provided. [ABSTRACT FROM PUBLISHER]

This note points out certain limitations of our results from the paper mentioned in the title, and provides a modified approach to overcome these limitations. Specifically, the observer design addressed in the aforementioned paper is, in general, only applicable to switched linear systems with invertible state reset maps and this note presents a modified algorithm for state estimation that can also handle non-invertible state reset maps. In the process, we also identify some equalities from that paper which may not hold in general for arbitrary state reset maps. [ABSTRACT FROM PUBLISHER]

This paper describes an approach to the control of continuous systems through the use of symbolic models describing the system behavior only at a finite number of points in the state space. These symbolic models can be seen as abstract representations of the continuous dynamics enabling the use of algorithmic controller design methods. We identify a class of linear control systems for which the loss of information incurred by working with symbolic subsystems can be compensated by feedback. We also show how to transform symbolic controllers designed for a symbolic subsystem mb controllers for the original system. The resulting controllers combine symbolic controller dynamics with continuous feedback control laws and can thus be seen as hybrid systems. Furthermore, if the symbolic controller already accounts for software/hardware requirements, the hybrid controller is guaranteed to enforce the desired specifications by construction thereby reducing the need for formal verification. [ABSTRACT FROM AUTHOR]

This paper addresses the problems of determining the \mathcal H_2 norm and the root mean square (RMS) gain of continuous-time switched linear systems. A novel class of Lyapunov functions is proposed for reaching this goal, called homogeneous rational Lyapunov functions (HRLFs). It is shown that sufficient conditions for establishing upper bounds of the sought performance indexes in the case of arbitrary switching can be given in terms of linear matrix inequality (LMI) feasibility tests by searching for an HRLF of chosen degree. Moreover, it is shown that these conditions are also necessary by searching for an HRLF of degree sufficiently large. It is worth mentioning that necessary and sufficient LMI conditions have not been proposed yet in the literature for the considered problems. Hence, the paper continues by considering the case of switching with dwell time constraints, showing that analogous LMI conditions can be obtained for this case by searching for a family of HRLFs mutually constrained by the dwell time specification. Some numerical examples illustrate the proposed methodology and highlight the advantages with respect to the existing works. [ABSTRACT FROM AUTHOR]

This paper presents a new approach to event-triggered control for nonlinear uncertain systems by using the notion of input-to-state stability (ISS) and the nonlinear small-gain theorem. The contribution of this paper is threefold. First, it is proved that infinitely fast sampling can be avoided if the system is input-to-state stabilizable with the sampling error as the external input and the corresponding ISS gain is locally Lipschitz. No assumption on the existence of known ISS-Lyapunov functions is made in the discussions. Moreover, the forward completeness problem with event-triggered control is studied systematically by using ISS small-gain arguments. Second, the proposed approach gives rise to a new self-triggered sampling strategy for a class of nonlinear systems subject to external disturbances. If an upper bound of the external disturbance is known, then the closed-loop system can be designed to be robust to the external disturbance, and moreover, the system state globally asymptotically converges to the origin if the external disturbance decays to zero. Third, a new design method is developed for event-triggered control of nonlinear uncertain systems in the strict-feedback form. It is particularly shown that the ISS gain with the sampling error as the input can be designed to satisfy the proposed condition for event-triggered control and self-triggered control. [ABSTRACT FROM PUBLISHER]

In this paper, we introduce and study the notion of norm-controllability for nonlinear systems. This property captures the responsiveness of a system with respect to applied inputs, which is quantified via the norm of an output. As a main contribution, we obtain several Lyapunov-like sufficient conditions for norm-controllability, some of which are based on higher-order derivatives of a Lyapunov-like function. Various aspects of the proposed concept and the sufficient conditions are illustrated by several examples, including a chemical reactor application. Furthermore, for the special case of linear systems, we establish connections between norm-controllability and standard controllability. [ABSTRACT FROM AUTHOR]

The paper presents a system theoretic analysis framework for a network-of-networks, formed from smaller factor networks via graph Cartesian products. We provide a compositional framework for extending the controllability and observability of the factor networks to that of the composite network-of-networks. We then delve into the effectiveness of designing control and estimation algorithms for the composite network via its symmetry and gramian structure. An example demonstrating the usefulness of our results in the context of social networks with a Cartesian product structure is then presented. [ABSTRACT FROM PUBLISHER]

This paper is about the state feedback regulator problem for infinite-dimensional linear systems. The plant, assumed to be an exponentially stable regular linear system, is driven by a linear (possibly infinite-dimensional) exosystem via a disturbance signal. The exosystem has its spectrum in the closed right half-plane and also generates the reference signal for the plant output. The regulator problem is to design a controller that, while guaranteeing the stability of the closed-loop system without the exosystem, drives the tracking error to zero. A particular version of this problem is the state feedback regulator problem in which the states of the exosystem and the plant are known to the controller. Under suitable assumptions, we show that the latter problem is solvable if and only if a pair of algebraic equations, called the regulator equations, is solvable. We derive conditions, in terms of the transfer function of the plant and eigenvalues of the exosystem, for the solvability of the regulator equations. Three examples illustrating the theory are presented. [ABSTRACT FROM PUBLISHER]

In this paper, we propose an event-based sampling policy to implement a constraint-tightening, robust MPC method. The proposed policy enjoys a computationally tractable design and is applicable to perturbed, linear time-invariant systems with polytopic constraints. In particular, the triggering mechanism is suitable for plants with no centralized sensory node as the triggering mechanism can be evaluated locally at each individual sensor. From a geometrical viewpoint, the mechanism is a sequence of hyperrectangles surrounding the optimal state trajectory such that robust recursive feasibility and robust stability are guaranteed. The design of the triggering mechanism is cast as a constrained parametric-in-set optimization problem with the volume of the set as the objective function. Reparameterized in terms of the set vertices, we show that the problem admits a finite tractable convex program reformulation and a linear program relaxation. Several numerical examples are presented to demonstrate the effectiveness and limitations of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper addresses the event-triggered dynamic output feedback control for switched linear systems with frequent asynchronism. Different from existing work, which limits at most once switching during an interevent interval, we adopt the average dwell time approach without limiting the minimum dwell time of each subsystem, and thus frequent switching is allowed to happen in an interevent interval. Since the difficulty in acquiring the full information of system states, the dynamic output feedback controller is taken into account to stabilize the switched system. By employing a controller-mode-dependent Lyapunov functional, stability criterion is proposed for the resulting closed-loop system, based on which the dynamic output feedback controller together with the mode-dependent event-triggered mechanism is codesigned. Besides, the existence of the lower bound on interevent intervals is attentively discussed, which gets rid of the Zeno behavior. Finally, the effectiveness of the proposed method is illustrated by numerical simulations. [ABSTRACT FROM AUTHOR]

A time delay present in the observation represents a mathematical challenge in an output feedback stabilization for linear infinite-dimensional systems. It is well known that for a linear hyperbolic system, a stabilizing output feedback control may become unstable when the observation has a time delay. For the fixed time delay in observation, the problem for one-dimensional partial differential equations (PDEs) has been solved by the observer-based feedback in the time interval where the observation is available and the predictor where the observation is not available. However, the generalization to multidimensional PDE systems has been a long-standing unsolved problem. In this paper, we investigate the problem from operator point of view for abstract first-order equation setting of infinite-dimensional systems. We formulate the problem in the framework of the well-posed and regular linear systems and solve it in the operator form. The result is then applied to the stabilization of a multidimensional Schrödinger equation. [ABSTRACT FROM AUTHOR]

This paper considers the problem of designing adaptive feedforward control (AFC) systems for uncertain single-input single-output linear systems perturbed by multisinusoidal disturbances of known frequencies. The proposed approach removes the longstanding assumption that either the sign of the real part or the imaginary part of the transfer function of a stable plant at the frequency of excitation is known for AFC to be applicable, which is referred to in this paper as a strictly positive real (SPR)-like condition. Notable features of the solution are that persistence of excitation is not required, and stability analysis tools based on averaging are avoided; hence, the requirement of an exponentially stable equilibrium for the closed-loop system is circumvented. [ABSTRACT FROM AUTHOR]

In this paper, we propose a state-dependent switching controller for multiple-input multiple-output (MIMO) bilinear systems with constant delays in both the state and the input. The control input is assumed to be restricted to take only a finite number of values. The stability analysis of the closed loop is based on a Lyapunov–Krasovskii functional, and the design is reduced to solve a system of linear matrix inequalities. The controller can be designed by considering (state) delay-dependent or delay-independent conditions. [ABSTRACT FROM AUTHOR]

In this paper, we provide a general strategy based on Lyapunov functionals to analyze global asymptotic stability of linear infinite-dimensional systems subject to nonlinear dampings under the assumption that the origin of the system is globally asymptotically stable with a linear damping. To do so, we use the fact that for any linear infinite-dimensional system that is globally exponentially stable, there exists a Lyapunov functional. Then, we derive a Lyapunov functional for the nonlinear system, which is the sum of a Lyapunov functional coming from the linear system and another term that compensates the nonlinearity. Our results are then applied to the linearized Korteweg–de Vries equation and some wave equations. [ABSTRACT FROM AUTHOR]

In this paper, we study the problem of remote state estimation, in the presence of a passive eavesdropper. An authorized user estimates the state of an unstable linear plant, based on the packets received from a sensor, while the packets may also be intercepted by the eavesdropper. Our goal is to design a coding scheme at the sensor, which encodes the state information, in order to impair the eavesdropper's estimation performance while enabling the user to successfully decode the sent messages. We introduce a novel class of codes, termed State-Secrecy Codes, which use acknowledgment signals from the user and apply linear time-varying transformations to the current and previously received states. By exploiting the properties of the system's process noise, the channel physical model, and the dynamics, these codes manage to be fast, efficient, and suitable for real-time dynamical systems. We prove that under minimal conditions, State-Secrecy Codes achieve perfect secrecy, namely the eavesdropper's minimum mean square error (mmse) grows unbounded almost surely, whereas the user's estimation performance is optimal. These conditions only require that at least once, the user receives the corresponding packet while the eavesdropper fails to intercept it. Even one occurrence of this event renders the eavesdropper's mmse unbounded with asymptotically optimal rate of increase. State-Secrecy Codes are provided and studied for two cases, first, when direct state measurements are available and second, when we only have output measurements. The theoretical results are illustrated in simulations. [ABSTRACT FROM AUTHOR]

The overall dynamics of linear systems under pulsewidth modulated actuators is nonlinear, an inevitable fact that must be considered in designing feedback control for these systems. For small sampling periods, however, this nonlinearity is not severe, so that controller design can rely on the same techniques conventionally adopted for the linear systems. When a linear controller designed by these techniques is applied to the originally nonlinear system, it may not perform adequately at higher sampling periods. In particular, it may fail to stabilize the closed-loop system as predicted for a linear approximation of the original system. This paper introduces a class of nonlinear feedback laws outperforming their existing linear counterparts in terms of stability and transient response. The control laws in this class are nonlinearly modified forms of the linear quadratic (LQ) regulators and yield a closed-loop behavior similar to that of a linear system under a LQ regulator. As a result, the closed-loop dynamics is locally stable in essence, and will be globally stable under additional assumptions. As a case study, an inverted pendulum on a cart is stabilized using the proposed nonlinear control law. The superior performance of this control law over its linear counterparts is shown by numerical simulations. [ABSTRACT FROM AUTHOR]

This paper proposes an approach for assessing the stability of feedback interconnections where one element is a static slope-restricted nonlinearity and the other element is a linear system. The approach is based on the use of Zames–Falb multipliers where the dynamic portion of the multiplier is chosen as an externally positive noncausal transfer function. By restricting attention to a subset of these multipliers, a set of pure linear matrix inequality conditions is obtained which requires no initial parameterization by the user. A useful byproduct of using externally positive systems is that the results are applicable to nonodd slope restricted nonlinearities, which is not the case for all classes of Zames–Falb multipliers. [ABSTRACT FROM AUTHOR]

This paper considers a scalar continuous-time linear time-invariant system, whose feedback signal is transmitted through a communication network. Such a network has only finite bit rate and suffers from transmission delay which is characterized by both lower and upper delay bounds. The concerned system implements event-triggering strategies, i.e., only when certain events are triggered, the system samples and transmits feedback signals. This paper first derives some lower bounds on the feedback bit rate required to achieve the input-to-state stability under arbitrary event-triggering strategies. Then this paper proposes some constructive methods to design the event-triggering strategy and the controller, and can achieve the input-to-state stability at a bit rate being arbitrarily close to these obtained lower bit rate bounds. Moreover, this paper proves that the stabilizing bit rates under the proposed event-triggering strategies can be strictly lower than the stabilizing bit rate required by any time-triggering strategy. This bit rate superiority comes from the fact that under event triggering, the state information can be freely extracted from the receive time instants of feedback packets without consuming any bit rate. Simulations are done to demonstrate the bit rate superiority of the proposed event-triggering strategies. [ABSTRACT FROM AUTHOR]

In this paper, a numerically robust solver for least-square problems with bounded variables (BVLS) is presented for applications including, but not limited to, model predictive control (MPC). The proposed BVLS algorithm solves the problem efficiently by employing a recursive QR factorization method based on Gram–Schmidt orthogonalization. A reorthogonalization procedure that iteratively refines the QR factors provides numerical robustness for the described primal active-set method, which solves a system of linear equations in each of its iterations via recursive updates. The performance of the proposed BVLS solver, which is implemented in C without external software libraries, is compared in terms of computational efficiency against state-of-the-art quadratic programming solvers for small- to medium-sized random BVLS problems and a typical example of embedded linear MPC application. The numerical tests demonstrate that the solver performs very well even when solving ill-conditioned problems in single-precision floating-point arithmetic. [ABSTRACT FROM AUTHOR]

In this paper, we study connections between structured storage or Lyapunov functions of a class of interconnected systems (dynamical networks) and dissipativity properties of the individual systems. We prove that if a dynamical network, composed as a set of linear time invariant systems interconnected over an acyclic graph, admits an additive quadratic Lyapunov function, then the individual systems in the network are dissipative with respect to a (nonempty) set of interconnection neutral supply functions. Each supply function from this set is defined on a single interconnection link in the network. Specific characterizations of neutral supply functions are presented, which imply robustness of network stability/dissipativity to removal of interconnection links. [ABSTRACT FROM AUTHOR]