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This paper presents a performance analysis of a system for electrochemical impedance spectroscopy (EIS). The system, composed by an analog front-end (AFE) and a custom microcontroller (MCU) board, performs the impulse response (IR) measurement of linear and time-invariant (LTI) systems with pseudo-random excitation signals. As a novelty, a specific AFE for the interfacing of two-terminal resistive and capacitive sensors is covered in detail. The paper proposes, for the first time, a mathematical model to predict the impact of the main noise sources in the measured IR. Thanks to the proposed approach, the AFE and the system’s parameters can be properly designed in order to reduce the error, thus, minimizing the energy-per-error figure of merit (FOM) as well. The AFE is realized as discrete-components circuit and it has been included in a custom MCU-based measurement system as an expansion module. The predicted results from the mathematical model, in terms of noise power, SNR, and measurement error are validated through system-level simulation and experimental measurements. The system performs the IR measurement with 1023 points, showing root-mean-square (RMS) measurement errors of 1% and 1.4% for the tested ADC sampling frequencies of 62.5 kHz and 125 kHz, respectively. These lead to excellent FOM values of 128.9 mJ $\cdot $ %2 and 252.6 mJ $\cdot $ %2 that outstand the state of the art. [ABSTRACT FROM AUTHOR]

We consider the problem of identifying a dissipative linear model of an unknown nonlinear system that is known to be dissipative, from time-domain input–output data. We first learn an approximate linear model of the nonlinear system using standard system identification techniques and then perturb the system matrices of the linear model to enforce dissipativity, while closely approximating the dynamical behavior of the nonlinear system. Further, we provide an analytical relationship between the size of the perturbation and the radius in which the dissipativity of the linear model guarantees local dissipativity of the unknown nonlinear system. We demonstrate the application of this identification technique through two examples. [ABSTRACT FROM AUTHOR]

In this article, the problem of distributed state estimation for a continuous-time linear system with a sensor network is investigated, where each sensor can only communicate with its neighbors and contains time-correlated measurement noise. To solve this problem, a novel augmented leader-following information fusion strategy is first proposed to collect measurements and system matrices. Then, a class of distributed state estimators is developed with bounded estimation error covariances. Further, a closed-form relation between the designed distributed estimator and the centralized estimator is established. It is found that the estimation performance of the former converges to that of the latter when the consensus gain tends to infinity. The proposed estimator is further extended to the fully distributed case by introducing an adaptive law for the consensus gain without using any global information. Moreover, it is shown that the designed estimator is applicable for systems with deterministic noise. Finally, several comparative numerical simulations are provided to demonstrate the effectiveness and superiority of the theoretical results. [ABSTRACT FROM AUTHOR]

This article provides an extension of the observability rank condition to time-varying nonlinear systems. Previous conditions to check the state observability only hold for nonlinear systems that do not explicitly depend on time, or, for time-varying systems, they only account for the linear case. In this article, a general analytic condition is provided. The new condition reduces to the well-known observability rank condition in the two simpler cases of time-varying linear systems and time-invariant nonlinear systems. The proposed condition is applied to aerospace robotics to study the observability of a lunar-module-type system equipped with monocular vision and inertial sensors. [ABSTRACT FROM AUTHOR]

This article is concerned with the distributed Kalman filtering problem for discrete-time linear systems whose measurement information comes from a set of sensor nodes that can communicate with their direct neighbors. Two algorithms for distributed Kalman filtering are proposed, where the first algorithm is based on single-node measurement and the second algorithm is based on neighboring-node measurements. In order to improve the performance, a novel criterion is introduced to the algorithm design, where in the criterion, the proximity of matrix’s trace is used to determine the proximity of positive semidefinite matrix. We prove that all the proposed algorithms for distributed Kalman filtering are unbiased. Numerical examples are provided to demonstrate the correctness of the proposed theoretical method and the performance of the proposed new design technique. [ABSTRACT FROM AUTHOR]

In this article, we present a novel data-driven model predictive control (MPC) approach to control unknown nonlinear systems using only measured input–output data with closed-loop stability guarantees. Our scheme relies on the data-driven system parameterization provided by the fundamental lemma of Willems et al. We use new input–output measurements online to update the data, exploiting local linear approximations of the underlying system. We prove that our MPC scheme, which only requires solving strictly convex quadratic programs online, ensures that the closed loop (practically) converges to the (unknown) optimal reachable equilibrium that tracks a desired output reference while satisfying polytopic input constraints. As intermediate results of independent interest, we extend the fundamental lemma to affine systems and we derive novel robustness bounds w.r.t. noisy data for the open-loop optimal control problem, which are directly transferable to other data-driven MPC schemes in the literature. The applicability of our approach is illustrated with a numerical application to a continuous stirred tank reactor. [ABSTRACT FROM AUTHOR]

This article investigates the transformation of Hamiltonian structures under sampling. It is shown that the exact sampled equivalent model associated to a given port-Hamiltonian continuous-time dynamics exhibits a discrete-time representation in terms of the discrete gradient, with the same energy function but modified damping and interconnection matrices. By construction, the proposed sampled-data dynamics guarantees exact matching of both the state evolutions and the energy-balance at all sampling instants. Its generalization to port-controlled Hamiltonian dynamics leads to characterize a new power conjugate output so recovering the concept of average passivation. On these bases, energy-management control strategies can be proposed. An energetic interpretation of the approach is confirmed by its formulation in the Dirac formalism. Two classical examples are worked out to validate the proposed sampled-data modeling in a comparative way with the literature. [ABSTRACT FROM AUTHOR]

Considering a discrete-time linear parameter-varying systems with input constraints, this article deals with the codesign of a parameter-dependent state-feedback controller and a new parameter-dependent event-triggering mechanism. Two independent event-triggering policies are introduced at the sensor node to economize the limited network resources. They indicate whether the current state or the current scheduling parameters should be transmitted to the controller or not. In this sense, the controller scheduling parameters can differ from those of the system, yielding a certain degree of robustness concerning parameter deviations. Sufficient conditions, given in terms of linear matrix inequalities, ensure the regional asymptotic stability of the closed loop. To formulated them, we use the Lyapunov theory along with the generalized sector condition. Moreover, we formulate a convex optimization procedure indirectly reducing the transmission activity over the network. The proposed methodology effectiveness is attested through numerical examples and comparisons with related works from the literature. [ABSTRACT FROM AUTHOR]

Critical systems must be designed resilient to malfunctions and especially to a loss of control authority over actuators. This malfunction considers actuators producing uncontrolled and possibly undesirable outputs. We investigate the design of resilient linear systems capable of reaching their target even after such a malfunction. In contrast with the settings considered by robust control and fault-tolerant control, we consider undesirable but observable inputs of the same magnitude as controls since they are produced by a faulty actuator belonging to the system. The control inputs can then depend on these undesirable inputs. Building on our previous work, we focus on designing resilient systems able to withstand the loss of one or multiple actuators. Since resilience refers to the existence of a control law driving the state to the target, we naturally continue with the synthesis of such a control law. We conclude with the application of our theory to the ADMIRE-fighter-jet model. [ABSTRACT FROM AUTHOR]

This article investigates the stealthy false data injection attack design problem for a class of cyber physical systems equipped with state estimators and attack detectors. The objective is to worsen the estimation performance without triggering any alarm. First, a necessary and sufficient condition for the existence of perfect attacks, which alter the state estimate without affecting residual signals, is provided. It is shown that the estimation error can be arbitrarily large under the well-designed perfect attacks. Second, if the perfect attacks do not exist, the existence of nonperfect attacks, which worsen the estimation performance with a degree influence on residual signals, is analyzed. It is shown that the desired nonperfect attack sequence can be designed by analyzing the maximum eigenvalue and the corresponding eigenvector of an auxiliary matrix. Compared with the existing methods, in this article, attacks are designed without knowledge of estimators and can be injected from any time point. Finally, a numerical simulation is provided to illustrate the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

This article deals with the input–output finite-time stability (IO-FTS) of linear discrete-time systems. In current control science, discrete-time systems play a very important role in many engineering contexts. Moreover, many discrete-time control problems are defined over a finite-interval of time; therefore, the development and application of finite-time control methodologies is of particular relevance. The first contribution of this article is a pair of necessary and sufficient conditions for IO-FTS. The former involves the solution of a set of generalized difference Lyapunov equations; the latter allows one to establish the feasibility of an optimization problem by solving a set of difference linear matrix inequalities (DLMIs). The second contribution of this article is a theorem for IO finite-time stabilization via state feedback, followed by a more general one for stabilization via output feedback. Both conditions are necessary and sufficient, and lead to optimization problems cast in the form of DLMIs. The applicability of the devised results is illustrated through a numerical example. [ABSTRACT FROM AUTHOR]

The discrete distributed observer is developed recently to solve the cooperative output regulation problem. The validation of the existing discrete distributed observer depends on the establishment of the communication network. In some practical applications, only the sensor network can be established among all agents. To handle such cases, we propose a sensory feedback-based discrete distributed observer, which depends on the relative output of neighboring agents. In contrast to existing results, the design of the discrete distributed observer and cooperative output regulation analysis should be conducted simultaneously. Resorting to the small-gain theorem, we develop a small-gain condition-based approach and a low-gain-based approach, respectively. By these two approaches, we demonstrate that the discrete distributed observer holds and the cooperative output regulation problem of heterogeneous discrete-time linear multiagent systems can be solved. [ABSTRACT FROM AUTHOR]

This article derives a solution to the appointed-time and attack-free bipartite synchronization problem for generic linear multiagent systems over directed switching networks accommodating cooperative and antagonistic interactions. Herein, appointed-time means that the settling time is independent of any parameters and is preappointed in advance. Attack-free requires that the communication channel is protected, which means that no state and observer information exchange is allowed, and only measured relative output information is available when designing protocols. Firstly, by virtue of Pontryagin’s maximum principle, a distributed appointed-time state-feedback protocol is developed for directed switching networks, which tackles the appointed-time bipartite synchronization problem from a motion-planning approach based on sampling measurements, but takes the risk of facing cyber attacks on information exchange channels. Then, to be free of network attacks, a sampling-based attack-free observer using relative output information is designed to observe bipartite synchronization errors at an appointed time. By combining the appointed-time state-feedback protocol with the sampling-based attack-free observer, an attack-free output-feedback protocol is developed without requiring the state or control input information. The attack-free appointed-time bipartite synchronization problem is thus resolved. Both the state-feedback and attack-free protocols show the ability of disturbance rejection to the nonidentical bounded disturbances. To our knowledge, it is the first time to solve the appointed-time and attack-free bipartite synchronization problem for generic linear multiagents based on state- and output-feedback information, respectively. Finally, simulations verify the effectiveness of the two protocols. [ABSTRACT FROM AUTHOR]

This study investigates the bipartite fixed-time time-varying output formation-containment tracking issue for heterogeneous linear multiagent systems with multiple leaders. Both cooperative communication and antagonistic communication between neighbor agents are taken into account. First, the bipartite fixed-time compensator is put forward to estimate the convex hull of leaders’ states. Different from the existing techniques, the proposed compensator has the following three highlights: 1) it is continuous without involving the sign function, and thus, the chattering phenomenon can be avoided; 2) its estimation can be achieved within a fixed time; and 3) the communication between neighbors can not only be cooperative but also be antagonistic. Note that the proposed compensator is dependent on the global information of network topology. To deal with this issue, the fully distributed adaptive bipartite fixed-time compensator is further proposed. It can estimate not only the convex hull of leaders’ states but also the leaders’ system matrices. Based on the proposed compensators, the distributed controllers are then developed such that the bipartite time-varying output formation-containment tracking can be achieved within a fixed time. Finally, two examples are given to illustrate the feasibility of the main theoretical findings. [ABSTRACT FROM AUTHOR]

In this paper, an adaptive admittance control scheme is developed for robots to interact with time-varying environments. Admittance control is adopted to achieve a compliant physical robot–environment interaction, and the uncertain environment with time-varying dynamics is defined as a linear system. A critic learning method is used to obtain the desired admittance parameters based on the cost function composed of interaction force and trajectory tracking without the knowledge of the environmental dynamics. To deal with dynamic uncertainties in the control system, a neural-network (NN)-based adaptive controller with a dynamic learning framework is developed to guarantee the trajectory tracking performance. Experiments are conducted and the results have verified the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This article studied the stability and convergence of a robust iterative learning control (ILC) design for a class of nonlinear systems with unknown control input delay. First, the iterative integral sliding mode (IISM) design was proposed, which comprised iterative actions. The iterative action made the convergence of the tracking error under the ideal sliding mode. Then, a suitable iterative update law was provided for the IISM-based robust ILC controller. The controller had the capability of both minimizing the steady tracking error and suppressing the unrepeatable disturbance. Using the controller, the closed-loop system stability was analyzed, and the stability conditions were given. Consequently, the sliding mode convergence in the iteration domain was proved by a composite energy function (CEF). In addition, by analyzing the influence of affection on the tracking error, several measures were taken to solve the chattering problem of the sliding mode control. Finally, a one-link robotic manipulator and a vertical three-tank system were used to verify the control design. The application simulations validated the performance of the proposed sliding mode iterative learning control (SMILC) design, which achieved the stability of the nonlinear system and overcame the control input time delay. [ABSTRACT FROM AUTHOR]

This article aims to improve the stochastic filtering algorithm with bounded disturbances, proposed in 1. This filter is efficient for max-plus linear systems in explicit form, i.e., the timed event graph (TEG) described by this system is initially with one token on each place. Nevertheless, it needs strong assumptions in order to be accurate for systems in implicit form, i.e., the corresponding TEG is initially with some token-free places which implies that some entries of the system state vector are dependent on each other. In this article, we consider a more general method without these assumptions. It is based on an iterative procedure that widely increases the accuracy of the estimation. [ABSTRACT FROM AUTHOR]

This article focuses on the design of online optimal input sequence for robust active fault diagnosis of discrete-time linear parameter-varying systems using set-theoretic methods. Instead of the traditional set-separation constraint conditions leading to the design of offline input sequence, the proposed approach focuses on online (re)shaping of the input sequence based on the real-time information of the output to discriminate system modes at each time instant such that the diagnosability of system has potential to be further improved. The criterion on the design of optimal input is characterized based on a nonconvex fractional programming problem at each time instant, which is shown to be efficiently solved within a convex optimization framework. In addition to this main contribution, by exploiting Lagrange duality, the optimal input is explicitly obtained by solving a characteristic equation. At the end, a physical circuit model is provided to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

We investigate state estimation of linear systems over channels having a finite state not known by the transmitter or receiver. We show that similar to memoryless channels, zero-error capacity is the right figure of merit for achieving bounded estimation errors. We then consider finite-state, worst-case versions of the common erasure, and additive noise channels models, in which the noise is governed by a finite-state machine without any statistical structure. Upper and lower bounds on their zero-error capacities are derived, revealing a connection with the topological entropy of the channel dynamics. Separate necessary and sufficient conditions for bounded linear state estimation errors via such channels are obtained. These estimation conditions bring together the topological entropies of the linear system and the discrete channel. [ABSTRACT FROM AUTHOR]

Dissipativity properties have proven to be very valuable for systems analysis and controller design. With the rising amount of available data, there has, therefore, been an increasing interest in determining dissipativity properties from (measured) trajectories directly, while an explicit model of the system remains undisclosed. Most existing approaches for data-driven dissipativity, however, guarantee the dissipativity condition only over a finite-time horizon and provide weak or no guarantees on robustness in the presence of noise. In this article, we present a framework for verifying dissipativity properties from measured data with desirable guarantees. We first consider the case of input-state measurements, where we provide computationally attractive conditions in the presence of process noise. We extend this approach to input–output data, where similar results hold in the noise-free case, and finally provide results for the case of noisy input–output trajectories. [ABSTRACT FROM AUTHOR]

In a recent article, we have shown how to learn controllers for unknown linear systems using finite-length noisy data by solving linear matrix inequalities. In this article, we extend this approach to deal with unknown nonlinear polynomial systems by formulating stability certificates in the form of data-dependent sum of squares programs, whose solution directly provides a stabilizing controller and a Lyapunov function. We then derive variations of this result that lead to more advantageous controller designs. The results also reveal connections to the problem of designing a controller starting from a least-square estimate of the polynomial system. [ABSTRACT FROM AUTHOR]

A linear dynamical system is called $k$ -positive if its dynamics maps the set of vectors with up to $k-1$ sign variations to itself. For $k=1$ , this reduces to the important class of positive linear systems. Since stable positive linear time-invariant systems always admit a diagonal quadratic Lyapunov function, i.e., they are diagonally stable, we may expect that this holds also for stable $k$ -positive systems. We show that, in general, this is not the case both in the continuous-time and discrete-time (DT) case. We then focus on DT $k$ -positive linear systems and introduce the new notion of the DT $k$ -diagonal stability. It is shown that this is a necessary condition for the standard DT diagonal stability. We demonstrate an application of this new notion to the analysis of a class of DT nonlinear systems. [ABSTRACT FROM AUTHOR]

In this article,we study the linear time-invariant state-feedback controller design problem for distributed systems. We follow the recently developed system level synthesis (SLS) approach and impose locality structure on the resulting closed-loop mappings; the corresponding controller implementation inherits this prescribed structure. In contrast to existing SLS results, we derive an explicit (rather than implicit) parameterization of all achievable stabilized closed-loops. This admits more efficient IIR representations of the temporal part of the closed-loop dynamics, and it allows for the $\mathcal {H}_2$ design problem with closed-loop spatial sparsity constraints to be converted to a standard model matching problem, with the number of transfer function parameters scaling linearly with the closed-loop spatial extent constraint. We illustrate our results with two applications: consensus of first-order subsystems and the vehicular platoons problem. In the case of first-order consensus, we provide analytic solutions and further analyze the architecture of the resulting controller implementation. Results for infinite extent spatially invariant systems are presented to provide insight to the case of a large but finite number of subsystems. [ABSTRACT FROM AUTHOR]

The Battistelli–Hespanha–Mosca–Tesi (BHMT) adaptive reset switching algorithm is enhanced to admit bumpless transfer and to control a nonlinear time-varying plant using the broad class of two-degree-of-freedom nonlinear time-varying controllers. Performance, including stability and exponential stability, is proved given only that the adaptive stabilization problem is $\lambda$ -feasible, which means at every time, there exists at least one exponentially stabilizing controller. We relax two restrictive BHMT assumptions: i) the plant is linear time-invariant (LTI) over most intervals and has finite order and ii) each controller is LTI. And, we expand the scope to include a broad class of bumpless switching algorithms. An example is provided to support the improved results. [ABSTRACT FROM AUTHOR]

In this article, a noisy-output-based direct learning tracking control is proposed for stochastic linear systems with nonuniform trial lengths. The iteration-varying trial length is modeled using a Markov chain for demonstration of the iteration dependence. The effect of the noisy output is asymptotically eliminated using a prior given decreasing gain sequence in the learning algorithm. Two alternative adaptive gains are presented for improving the tracking performance and the convergence speed. Both the mean-square and almost-sure convergence are provided. Numerical simulations on a four-degree-of-freedom robot arm are presented to illustrate the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

A structured preconditioned conjugate gradient (PCG) based solver is developed for implementing the Newton updates in second-order methods for a class of constrained network optimal control problems. Of specific interest are problems with discrete-time dynamics arising from the path-graph interconnection of $N$ heterogeneous subsystems. The arithmetic complexity of each PCG step is $O(NT)$ , where $T$ is the length of the time horizon. The proposed preconditioning involves a fixed number of block Jacobi iterations per PCG step. A decreasing analytic bound on the effective conditioning is given in terms of this number. The associated computations are decomposable across the spatial and temporal dimensions of the optimal control problem, into subproblems of size independent of $N$ and $T$. Numerical results are provided for two example systems. [ABSTRACT FROM AUTHOR]

The problem of solving linear equations is considered as one of the fundamental problems commonly encountered in science and engineering. In this article, the complex-valued time-varying linear matrix equation (CVTV-LME) problem is investigated. Then, by employing a complex-valued, time-varying QR (CVTVQR) decomposition, the zeroing neural network (ZNN) method, equivalent transformations, Kronecker product, and vectorization techniques, we propose and study a CVTVQR decomposition-based linear matrix equation (CVTVQR-LME) model. In addition to the usage of the QR decomposition, the further advantage of the CVTVQR-LME model is reflected in the fact that it can handle a linear system with square or rectangular coefficient matrix in both the matrix and vector cases. Its efficacy in solving the CVTV-LME problems have been tested in a variety of numerical simulations as well as in two applications, one in robotic motion tracking and the other in angle-of-arrival localization. [ABSTRACT FROM AUTHOR]