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This paper investigates adaptive sampled-data control for strict-feedback nonlinear plants with unmatched uncertainties by means of radial basis function neural networks (RBFNNs). First, the continuous-time plant is locally discretized as a disturbed strict-feedback model by using the approximate Euler model approach. Then, as a basis of rigorous stability analysis, the concept of validity is proposed, which, considering the locality of the universal approximation capacity in RBFNNs, requires that the argument of each RBFNN be inside the corresponding compact set all the time. Meanwhile, to address the noncausality issue, delayed signals are utilized in the backstepping method for discrete-time plants. Subsequently, the validity and stability are proved rigorously; meanwhile, a practical output tracking problem is solved under a time-varying reference signal, the order of whose continuous derivatives is the same as the plants. This is the first time the interdependence on the design of sampling periods and RBFNNs in different design steps has been shown. Finally, simulation results are provided to illustrate the efficiency and feasibility of the obtained results. [ABSTRACT FROM AUTHOR]

A type of matrix decomposition called unilateral orthogonal nonnegative matrix factorization is proposed for decomposing real-valued matrices. The associated optimization problem is nonconvex and nonlinear. We design an iterative algorithm based on alternating minimization, where a data compensation mechanism is used to avoid ill-conditioned problems. We also show that there is an interesting connection between the iterative algorithm and switched nonlinear systems. By analyzing the switched systems, we prove that each iteration of the algorithm is rank-preserving and thus avoids ill-conditioned problems. The solution to the optimization problem is also strictly feasible without any approximations. The optimization variables are proved to be convergent, and the limit satisfies the Karush-Kuhn-Tucker conditions. Furthermore, it is proved that the limit is almost surely a local minimizer rather than a saddle point. For the equivalent switched systems, the states of all subsystems are convergent. [ABSTRACT FROM AUTHOR]

This study introduces a general event triggered framework of state estimation for discrete-time systems with parameter uncertainties residing in a polytope. A robust filter is designed to ensure the l2 stability from disturbance to the estimation error and to minimise the l2 gain subject to both packet rate and size constraints. The number of data transmission and the data size are reduced by the utilisation of an event detector and a logarithmic quantiser, respectively. The event detector compares the current output measurement with the last transmitted measurement: if the difference is beyond a prescribed percentage of the current measurement, then the current measurement is transmitted to the quantiser. The quantiser encodes the measurement before sending to the filter via a digital communication channel. Conditions for filter design are found using polynomially parameter-dependent Lyapunov functions, which generalise the results using quadratic and linearly parameter-dependent Lyapunov functions. The usefulness of the techniques is demonstrated with an illustrative example. [ABSTRACT FROM AUTHOR]

This article formulates a multi-rate linear minimum mean squared error (LMMSE) state estimation problem, which includes four rates as follows: the state updating rate in the model, the measurement sampling rate, the estimate updating rate and the estimate output rate. This formulation is unique in two ways. First, the rate ratio between state measurement and state estimate is more general (a rational number), instead of just an integer or its reciprocal as considered in the existing literature. Second, state estimates are produced in blocks, which have never been considered before in the multi-rate estimator design. The multi-rate LMMSE estimation problem is solved by examining several distinctive cases for single-rate state estimation, obtained through the lifting technique. Also, sufficient conditions are given for asymptotic stability of the proposed multi-rate LMMSE estimators. An example in tracking a manoeuvering target is given to illustrate the proposed multi-rate state estimators. [ABSTRACT FROM AUTHOR]

This paper investigates the problems of passivity analysis and passification for network-based linear control systems. A new sampled-data model is first formulated based on the updating instants of the ZOH (zeroth order hold), where the physical plant and the controller are, respectively, in continuous time and discrete time. In this model, network-induced delays, data packet dropouts, and signal measurement quantization have been taken into account. The measurement quantizer is assumed to be logarithmic, and the network-induced delays are assumed to have both a lower bound and an upper bound, which is more general than those assumptions used in the literature. The key idea is to transform the sampled-data model into a linear system with two successive delay components in the state. Then, by using a Lyapunov-Krasovskii approach plus the free weighting matrix technique, a passivity performance condition is formulated in the form of linear matrix inequalities (LMIs). Based on this condition, two procedures are proposed for designing passification controllers, which guarantee that the closed-loop networked control system (NCS) is passive. Finally, two illustrative examples are presented: one shows the advantage of introducing the lower bound of transmission delays and shows how much the quantization behavior affects the passivity performance; the other illustrates the applicability and effectiveness of the proposed passification results. [ABSTRACT FROM AUTHOR]

This paper is motivated by the practical control considerations that nonlinearity is abundant in industrial processes and output sampling rates are often limited due to hardware constraints. In particular, for a Hammerstein nonlinear sampled-data system in which the output sampling period is an integer multiple of the input updating period, we derive, by using a polynomial transformation technique, a mathematical model which is suitable for parameter estimation with dual-rate measurement data. Further, we present an adaptive control scheme for such a dual-rate nonlinear system; the parameter estimation-based adaptive algorithm can achieve virtually asymptotically optimal control and ensure that the closed-loop system is stable and globally convergent. The simulation results are included. [ABSTRACT FROM AUTHOR]

In this paper, the generalized bilinear transformation (GBT) is proposed. Compared with the traditional bilinear, zero-order hold (ZOH) and first-order hold transformations, one advantage of GBT is that it may convert unstable poles (zeros) to stable poles (zeros). It is proved that controllability and observability are invariant under GBT. After that, it is shown that the performance of a sampled-data system obtained via GBT approaches that of the analogue system as the underlying sampling period goes to zero. Performance studied here is characterized in terms of internal stability and lp induced norms for all 1 ≤ p ≤ ∞. This results extends the main results in [G. Zhang and T. Chen, Dyn. Contin. Discrete Impuls. Syst. Ser. B Appl. Algorithms, Suppl., 2003, pp. 28-33] and [G. Zhang and T. Chen, Automatica J. IFAC, 40 (2004), pp. 327-330] from SISO to MIMO and also removes the limitation on the ‘A’ matrix of the system. Finally, an example is employed to compare digital implementations via GBT and the ZOH transformation. [ABSTRACT FROM AUTHOR]

In this paper we study coupled matrix equations, which are encountered in many systems and control applications. First, we extend the well-known Jacobi and Gauss-Seidel iterations and present a large family of iterative methods, which are then applied to develop iterative solutions to coupled Sylvester matrix equations. The basic idea is to regard the unknown matrices to be solved as parameters of a system to be identified and to obtain the iterative solutions by applying a hierarchical identification principle. Next, we generalize the Sylvester equations to general coupled matrix equations, and propose a gradient-based iterative algorithm for the solutions, using a block-matrix inner product—the star (★) product; we prove that the iterative algorithm always converges to the (unique) solutions for any initial values. One advantage of the algorithms proposed is that they require less storage space in implementation than existing numerical methods. Finally, we test the algorithms and show their effectiveness using numerical examples. [ABSTRACT FROM AUTHOR]

This paper presents a new method, named as the variability method, to estimate the cyclo-period of a discrete-time cyclo-stationary signal. The method is essentially based on the time-varying correlation and/or the time-varying mean, whose estimators are associated with some statistics of blocked signals; a plot of variability of these statistics as a function of the blocking operator index visually reveals a periodic pattern, from which the cyclo-period is obtained. Properties of the variability method are analyzed and compared with three existing cyclo-period estimation methods via simulation and real-life examples. [ABSTRACT FROM AUTHOR]

This paper studies two problems in the spectral theory of discrete-time cyclostationary signals: the cyclospectrum representation and the cyclospectrum transformation by linear multi-rate systems. Four types of cyclospectra are presented, and their interrelationships are explored. In the literature, the problem of cyclospectrum transformation by linear systems was investigated only for some specific configurations and was usually developed with inordinate complexities due to lack of a systematic approach. A general multirate system that encompasses most common systems-linear time-invariant systems and linear periodically time-varying systems-is proposed as the unifying framework; more importantly, it also includes many configurations that have not been investigated before, e.g., fractional sample-rate changers with cyclostationary inputs. The blocking technique provides a systematic solution as it associates a multirate system with an equivalent linear time-invariant system and cyclostationary signals with stationary signals; thus, the original problem is elegantly converted into a relatively simple one, which is solved in the form of matrix multiplication. [ABSTRACT FROM AUTHOR]

Studies optimal design incorporating filter stopband energy and passband magnitude constraints for multichannel, uniform and nonuniform transmultiplexers. Multirate signal processing; Quadratic programming; Finite-impulse-response synthesis.

This paper deals with the reduced-order H[sub infin;] filtering problem for stochastic systems. Necessary and sufficient conditions are obtained for the existence of solutions to the continuous-time and discrete-time problems in terms of certain linear matrix inequalities (LMIs) and a coupling nonconvex rank constraint condition. Furthermore, when these conditions are feasible, an explicit parametrization of all desired reduced-order filters corresponding to a feasible solution is given. In particular, when the reduced-order filter is restricted to be a static one, then simple conditions expressed by LMIs only without any rank constraints are derived, and a parametrization of all solutions is also given. Finally, an illustrative example is provided to show the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

Studies a general multirate filter-bank system with multiple channels and nonuniform bands. The blocking technique used to transform linear periodic systems into equivalent linear time-invariant (LTI); Blocking fractionally decimated filter banks; Analysis results for the multirate system; Design; Conclusions of the study.

Discusses about Hybrid multiareolate filter banks which consist of analog analysis filters, slow A/D converters, digital expanders, and digital synthesis filters. Conversion to a problem of H infinity optimization; Examples that bring some points on the reconstruction performance of the FIR truncation to the optimal synthesis filters; Performance limitation; Conclusion of the study.

An affine formation tracking problem of multiple mobile agents is studied in this work. Each agent in the system is modeled as an underactuated kinematic rigid body with nonholonomic constraints, maneuvering on the special Euclidean group (SE(3)). A controller is designed for each agent directly on the corresponding Lie algebra of SE(3). Moreover, only local information accessible to each agent in its body-fixed frame is involved. The proposed control protocol can be implemented under both directed and undirected topologies. In addition, for directed graphs, an algorithm is proposed to realize the formation under switching topologies. Finally, numerical simulations are given to illustrate the efficiency and feasibility of the proposed results. [ABSTRACT FROM AUTHOR]

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

Time synchronisation is required for a variety of distributed control applications in wireless sensor networks (WSNs). In this study, a consensus-based time synchronisation protocol is presented. The proposed protocol considers asynchronous framework where the sensor nodes can have different time-periods, starting times and input update times. The communication links are assumed to be unreliable. The clocks in a WSN are modelled by a time-varying system with timedelay terms. The objective is to design local control inputs to achieve time synchronisation by processing the information received from available neighbour nodes. By employing tools from non-negative matrix and graph theories, the convergence analysis is presented. Numerical examples are given to demonstrate the effectiveness of the proposed protocol. [ABSTRACT FROM AUTHOR]

Alarm flooding is one of the main problems in alarm management. Alarm flood pattern analysis is helpful for root cause analysis of historical floods and for incoming flood prediction. This paper deals with a data driven method for alarm flood pattern matching. An alarm flood is represented by a time-stamped alarm sequence. A modified Smith-Waterman algorithm considering the time stamp information is proposed to calculate a similarity index of alarm floods. The effectiveness of the algorithm is validated by a case study on actual chemical process alarm data. [ABSTRACT FROM AUTHOR]

In this article, an iterative learning control approach is proposed for a class of sampled-data non-linear systems over network communication channels. The effects of constant time delays and stochastic packet loss are discussed and demonstrated by simulation results. The focus of this article is to study the remote control problems when the environment is periodic or repeatable over iterations in a fixed finite interval. Because of the existence of time delays and packet loss in input and output signal transmissions, it is not trivial to accomplish the remote stabilisation task of any system. Moreover, to track a desired trajectory through a remote controller is even more difficult. Previous cycle-based learning method is incorporated into the network-based control for a class of non-linear systems which satisfies a global Lipschitz condition. The convergence property of this approach is proven. Furthermore, the convergence in the iteration domain is also discussed when there exists packet loss in both transmission channels of the system. Finally, one single-link rigid robot is given as an example to show the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

This article proposes a new approach to identification of Hammerstein systems, where a non-linearity precedes a linear dynamic system, driven by piece-wise constant inputs. The proposed approach does not require an explicit parameterisation of the non-linearity. Moreover, the non-linearity does not have to be static, but could be the one with finite memories like backlash. By exploiting input's piecewise constant property, the denominator of the linear system described by an ARX model is consistently identified from the information of the output only; next, a subspace direct equalisation method estimates the unmeasurable inner signal based on the resulted denominator estimate and output measurements. Contrary to the existing blind approaches, the numerator of the linear system is not required, which leads to a significant improvement of removing an error propagation. On the basis of the estimated inner signal, the measured input and output, the non-linearity and linear system are obtained separately. The proposed approach is validated and compared with two existing blind approaches through numerical and experimental examples. [ABSTRACT FROM AUTHOR]

Crosstalk between multiple services transmitting through the same telephone cable is the primary limitation to digital subscriber line (DSL) services. From a spectrum management point of view, it is important to have an accurate map of all the services that generate crosstalk into a given pair. This paper on crosstalk identification is motivated by an important practical consideration: the signals constituting the crosstalk are transmitted at different rates in xDSL systems. Therefore, we here propose to use the ‘blocking technique,’ we derive blocked state-space models for multirate xDSL networks, and we set up the mapping relationship between available input and output data. Further, we use the least-squares principle to identify the crosstalk functions, and study the convergence rate and upper bound of the parameter-estimation error. Finally, we illustrate and verify the theoretical findings with simulation examples. [ABSTRACT FROM AUTHOR]

The correlation analysis based methods are not suitable for identifying parameters of nonstationary autoregressive (AR), moving average (MA), and ARMA systems. By using estimation residuals in place of unmeasurable noise terms in information vector or matrix, we develop a least squares based and gradient based algorithms and establish the consistency of the proposed algorithms without assuming noise stationarity, ergodicity, or existence of higher order moments. Furthermore, we derive the conditions for convergence of the parameter estimation. The simulation results validate the convergence theorems proposed. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problem of robust H∞ filtering for linear systems with both discrete and distributed delays, which are subject to norm-bounded time-varying parameter uncertainties. Both the state and measurement equations are assumed to have discrete and distributed delays. A delay-dependent condition for the existence of H∞, filters is proposed, which is less conservative than existing ones in the literature. Via solutions to certain linear matrix inequalities, general full-order filters are designed that ensure asymptotic stability and a prescribed H∞ performance level, irrespective of the parameter uncertainties. An illustrative example is provided to demonstrate the effectiveness and the reduced conservatism of the proposed method. [ABSTRACT FROM AUTHOR]

In this correspondence, we add a condition in Theorem 1 and some explanations in the proof of Theorem 2 in IEEE TRANSACTIONS ON SIGNAL PROCESSING, vol. 54, no. 3, pp. 1041-1053, March 2006. [ABSTRACT FROM AUTHOR]

In this work, a parameter tuning problem of two-degrees-of-freedom model predictive control of industrial paper-making processes is explored to achieve satisfactory time-domain robust closed-loop performance in terms of worst-case overshoots and worst-case settling times, under user-specified parametric uncertainties. An efficient visualization method is first developed to characterize the set of time-domain closed-loop responses in the presence of parametric model-plant mismatch. On the basis of the visualization technique and the unmodality/monotonicity properties of the performance indices with respect to the tuning parameters, the feasibility of the tuning problem can be analyzed, and a three-step iterative line-search based automatic tuning algorithm is proposed to determine the controller parameters that meet the time-domain performance requirements robustly for the given parametric uncertainty specifications. The effectiveness of the algorithm is illustrated by applying the results to a process from stock to conditioned weight in an industrial paper machine and by comparing the performance of the algorithm with that of brutal search. [ABSTRACT FROM AUTHOR]