Showing papers in "International Journal of Applied Mathematics and Computer Science in 2009"
TL;DR: It is shown that practical stability of the system is equivalent to asymptotic instability of the corresponding standard positive discrete-time systems of the same order.
Abstract: In the paper the problem of practical stability of linear positive discrete-time systems of fractional order is addressed. New simple necessary and sufficient conditions for practical stability and for practical stability independent of the length of practical implementation are established. It is shown that practical stability of the system is equivalent to asymptotic stability of the corresponding standard positive discrete-time systems of the same order. The discussion is illustrated with numerical examples.
115 citations
TL;DR: An improved method for 1-24 hours load forecasting in the power system, integrating and combining different neural forecasting results by an ensemble system is presented.
Abstract: The paper presents an improved method for 1-24 hours load forecasting in the power system, integrating and combining different neural forecasting results by an ensemble system. We will integrate the results of partial predictions made by three solutions, out of which one relies on a multilayer perceptron and two others on self-organizing networks of the competitive type. As the expert system we will apply different integration methods: simple averaging, SVD based weighted averaging, principal component analysis and blind source separation. The results of numerical experiments, concerning forecasting the hourly load for the next 24 hours of the Polish power system, will be presented and discussed. We will compare the performance of different ensemble methods on the basis of the mean absolute percentage error, mean squared error and maximum percentage error. They show a significant improvement of the proposed ensemble method in comparison to the individual results of prediction. The comparison of our work with the results of other papers for the same data proves the superiority of our approach.
82 citations
TL;DR: An overview of centralized distance-based algorithms for estimating the positions of nodes in a sensor network and a hybrid scheme that uses a combination of trilateration, and stochastic optimization for performing sensor localization is proposed.
Abstract: Many applications of wireless sensor networks (WSN) require information about the geographical location of each sensor node. Self-organization and localization capabilities are one of the most important requirements in sensor networks. This paper provides an overview of centralized distance-based algorithms for estimating the positions of nodes in a sensor network. We discuss and compare three approaches: semidefinite programming, simulated annealing and two-phase stochastic optimization-a hybrid scheme that we have proposed. We analyze the properties of all listed methods and report the results of numerical tests. Particular attention is paid to our technique-the two-phase method-that uses a combination of trilateration, and stochastic optimization for performing sensor localization. We describe its performance in the case of centralized and distributed implementations.
65 citations
TL;DR: Various robotics problems that have been solved with interval analysis are emphasized, many of which are currently beyond the reach of other mathematical approaches.
Abstract: Interval analysis is a relatively new mathematical tool that allows one to deal with problems that may have to be solved numerically with a computer. Examples of such problems are system solving and global optimization, but numerous other problems may be addressed as well. This approach has the following general advantages: (a) it allows to find solutions of a problem only within some finite domain which make sense as soon as the unknowns in the problem are physical parameters; (b) numerical computer round-off errors are taken into account so that the solutions are guaranteed; (c) it allows one to take into account the uncertainties that are inherent to a physical system. Properties (a) and (c) are of special interest in robotics problems, in which many of the variables are parameters that are measured (i.e., known only up to some bounded errors) while the modeling of the robot is based on parameters that are submitted to uncertainties (e.g., because of manufacturing tolerances). Taking into account these uncertainties is essential for many robotics applications such as medical or space robotics for which safety is a crucial issue. A further inherent property of interval analysis that is of interest for robotics problems is that this approach allows one to deal with the uncertainties that are unavoidable in robotics. Although the basic principles of interval analysis are easy to understand and to implement, this approach will be efficient only if the right heuristics are used and if the problem at hand is formulated appropriately. In this paper we will emphasize various robotics problems that have been solved with interval analysis, many of which are currently beyond the reach of other mathematical approaches.
56 citations
TL;DR: The paper investigates the possibility of decomposing vibration signals into deterministic and nondeterministic parts, based on the Wold theorem, and proposes a self-adaptive filter that shows a very good ability to decompose the signal.
Abstract: The paper investigates the possibility of decomposing vibration signals into deterministic and nondeterministic parts, based on the Wold theorem. A short description of the theory of adaptive filters is presented. When an adaptive filter uses the delayed version of the input signal as the reference signal, it is possible to divide the signal into a deterministic (gear and shaft related) part and a nondeterministic (noise and rolling bearings) part. The idea of the self-adaptive filter (in the literature referred to as SANC or ALE) is presented and its most important features are discussed. The flowchart of the Matlab-based SANC algorithm is also presented. In practice, bearing fault signals are in fact nondeterministic components, due to a little jitter in their fundamental period. This phenomenon is illustrated using a simple example. The paper proposes a simulation of a signal containing deterministic and nondeterministic components. The self-adaptive filter is then applied-first to the simulated data. Next, the filter is applied to a real vibration signal from a wind turbine with an outer race fault. The necessity of resampling the real signal is discussed. The signal from an actual source has a more complex structure and contains a significant noise component, which requires additional demodulation of the decomposed signal. For both types of signals the proposed SANC filter shows a very good ability to decompose the signal.
55 citations
TL;DR: An introduction to Simultaneous Localization And Mapping (SLAM), with the focus on probabilistic SLAM utilizing a feature-based description of the environment, and a solution based on the Extended Kalman Filter.
Abstract: This article provides an introduction to Simultaneous Localization And Mapping (SLAM), with the focus on probabilistic SLAM utilizing a feature-based description of the environment. A probabilistic formulation of the SLAM problem is introduced, and a solution based on the Extended Kalman Filter (EKF-SLAM) is shown. Important issues of convergence, consistency, observability, data association and scaling in EKF-SLAM are discussed from both theoretical and practical points of view. Major extensions to the basic EKF-SLAM method and some recent advances in SLAM are also presented.
54 citations
TL;DR: The main idea of the new approach presented is to discover indirect associations existing between pages that rarely occur together but there are other, "third" pages, called transitive, with which they appear relatively frequently.
Abstract: Classical association rules, here called "direct", reflect relationships existing between items that relatively often co-occur in common transactions. In the web domain, items correspond to pages and transactions to user sessions. The main idea of the new approach presented is to discover indirect associations existing between pages that rarely occur together but there are other, "third" pages, called transitive, with which they appear relatively frequently. Two types of indirect associations rules are described in the paper: partial indirect associations and complete ones. The former respect single transitive pages, while the latter cover all existing transitive pages. The presented IDARM* Algorithm extracts complete indirect association rules with their important measure-confidence-using pre-calculated direct rules. Both direct and indirect rules are joined into one set of complex association rules, which may be used for the recommendation of web pages. Performed experiments revealed the usefulness of indirect rules for the extension of a typical recommendation list. They also deliver new knowledge not available to direct ones. The relation between ranking lists created on the basis of direct association rules as well as hyperlinks existing on web pages is also examined.
51 citations
TL;DR: The convergence of finite element approximation for the topological derivatives is shown and the error estimates in the L∞ norm are obtained.
Abstract: The form of topological derivatives for an integral shape functional is derived for a class of semilinear elliptic equations. The convergence of finite element approximation for the topological derivatives is shown and the error estimates in the L∞ norm are obtained. The results of numerical experiments which confirm the theoretical convergence rate are presented.
50 citations
TL;DR: It will be proved that, under suitable assumptions, relative controllability of an associated deterministic linear dynamic system is equivalent to stochastic relative exact controllable and sto chastic relative approximate controllabilities of the original linear stochastically dynamic system.
Abstract: Finite-dimensional stationary dynamic control systems described by linear stochastic ordinary differential state equations with multiple point delays in control are considered. Using the notation, theorems and methods used for deterministic controllability problems for linear dynamic systems with delays in control as well as necessary and sufficient conditions for various kinds of stochastic relative controllability in a given time interval are formulated and proved. It will be proved that, under suitable assumptions, relative controllability of an associated deterministic linear dynamic system is equivalent to stochastic relative exact controllability and stochastic relative approximate controllability of the original linear stochastic dynamic system. As a special case, relative stochastic controllability of dynamic systems with a single point delay is also considered. Some remarks and comments on the existing results for stochastic controllability of linear dynamic systems are also presented.
48 citations
TL;DR: The proposed control scheme is based on the Almost Strictly Positive Realness (ASPR) property of the plant, and it is shown that this condition implies also robust stability in the case of fractional order controllers.
Abstract: This paper presents a new approach to robust adaptive control, using fractional order systems as parallel feedforward in the adaptation loop. The problem is that adaptive control systems may diverge when confronted with finite sensor and actuator dynamics, or with parasitic disturbances. One of the classical robust adaptive control solutions to these problems makes use of parallel feedforward and simplified adaptive controllers based on the concept of positive realness. The proposed control scheme is based on the Almost Strictly Positive Realness (ASPR) property of the plant. We show that this condition implies also robust stability in the case of fractional order controllers. An application to Model Reference Adaptive Control (MRAC) with a fractional order adaptation rule is provided with an implementable algorithm. A simulation example of a SISO robust adaptive control system illustrates the advantages of the proposed method in the presence of disturbances and noise.
46 citations
TL;DR: This paper introduces a technique for handling input constraints within a real time MPC/FL scheme, where the plant model employed is a class of dynamic neural networks, based on a simple affine transformation of the feasible area.
Abstract: The combination of model predictive control based on linear models (MPC) with feedback linearization (FL) has attracted interest for a number of years, giving rise to MPC+FL control schemes. An important advantage of such schemes is that feedback linearizable plants can be controlled with a linear predictive controller with a fixed model. Handling input constraints within such schemes is difficult since simple bound contraints on the input become state dependent because of the nonlinear transformation introduced by feedback linearization. This paper introduces a technique for handling input constraints within a real time MPC/FL scheme, where the plant model employed is a class of dynamic neural networks. The technique is based on a simple affine transformation of the feasible area. A simulated case study is presented to illustrate the use and benefits of the technique.
TL;DR: Simulation results demonstrating the potential of ValEncIA-IVP for solving DAEs in technical applications and relations to other existing verified simulation techniques for dynamical systems are demonstrated.
Abstract: A Novel Interval Arithmetic Approach for Solving Differential-Algebraic Equations with ValEncIA-IVPThe theoretical background and the implementation of a new interval arithmetic approach for solving sets of differential-algebraic equations DAEs are presented. The proposed approach computes guaranteed enclosures of all reachable states of dynamical systems described by sets of DAEs with uncertainties in both initial conditions and system parameters. The algorithm is based on ValEncIA-IVP, which has been developed recently for the computation of verified enclosures of the solution sets of initial value problems for ordinary differential equations. For the application to DAEs, ValEncIA-IVP has been extended by an interval Newton technique to solve nonlinear algebraic equations in a guaranteed way. In addition to verified simulation of initial value problems for DAE systems, the developed approach is applicable to the verified solution of the so-called inverse control problems. In this case, guaranteed enclosures for valid input signals of dynamical systems are determined such that their corresponding outputs are consistent with prescribed time-dependent functions. Simulation results demonstrating the potential of ValEncIA-IVP for solving DAEs in technical applications conclude this paper. The selected application scenarios point out relations to other existing verified simulation techniques for dynamical systems as well as directions for future research.
TL;DR: A novel description of the nonlinear part of the system, i.e., backlash, is developed and a modified recursive general identification algorithm (MRGIA) is employed to estimate the parameters of the proposed model.
Abstract: This paper proposes a recursive identification method for systems with output backlash that can be described by a pseudo-Wiener model. In this method, a novel description of the nonlinear part of the system, i.e., backlash, is developed. In this case, the nonlinear system is decomposed into a piecewise linearized model. Then, a modified recursive general identification algorithm (MRGIA) is employed to estimate the parameters of the proposed model. Furthermore, the convergence of the MRGIA for the pseudo-Wiener system with backlash is analysed. Finally, a numerical example is presented.
TL;DR: In this paper, an interval arithmetic approach for verified simulation of continuoustime dynamical system models is extended to include the synthesis, sensitivity analysis, and optimization of open-loop and closed-loop controllers, in addition to the calculation of guaranteed enclosures of the sets of all reachable states.
Abstract: Control strategies for nonlinear dynamical systems often make use of special system properties, which are, for example, differential flatness or exact input-output as well as input-to-state linearizability. However, approaches using these properties are unavoidably limited to specific classes of mathematical models. To generalize design procedures and to account for parameter uncertainties as well as modeling errors, an interval arithmetic approach for verified simulation of continuoustime dynamical system models is extended. These extensions are the synthesis, sensitivity analysis, and optimization of open-loop and closed-loop controllers. In addition to the calculation of guaranteed enclosures of the sets of all reachable states, interval arithmetic routines have been developed which verify the controllability and observability of the states of uncertain dynamic systems. Furthermore, they assure asymptotic stability of controlled systems for all possible operating conditions. Based on these results, techniques for trajectory planning can be developed which determine reference signals for linear and nonlinear controllers. For that purpose, limitations of the control variables are taken into account as further constraints. Due to the use of interval techniques, issues of the functionality, robustness, and safety of dynamic systems can be treated in a unified design approach. The presented algorithms are demonstrated for a nonlinear uncertain model of biological wastewater treatment plants.
TL;DR: It is shown that the asymptotic stability of positive 2D linear systems with delays is independent of the number and values of the delays and it depends only on the sum of the system matrices.
Abstract: It is shown that the asymptotic stability of positive 2D linear systems with delays is independent of the number and values of the delays and it depends only on the sum of the system matrices, and that the checking of the asymptotic stability of positive 2D linear systems with delays can be reduced to testing that of the corresponding positive 1D systems without delays. The effectiveness of the proposed approaches is demonstrated on numerical examples.
TL;DR: The problem of designing control laws for path following robots, including two types of nonholonomic mobile manipulators, is described and a kinematic control algorithm is designed, a modification of a passivity-based controller.
Abstract: This paper describes the problem of designing control laws for path following robots, including two types of nonholonomic mobile manipulators. Due to a cascade structure of the motion equation, a backstepping procedure is used to achieve motion along a desired path. The control algorithm consists of two simultaneously working controllers: the kinematic controller, solving motion constraints, and the dynamic controller, preserving an appropriate coordination between both subsystems of a mobile manipulator, i.e. the mobile platform and the manipulating arm. A description of the nonholonomic subsystem relative to the desired path using the Frenet parametrization is the basis for formulating the path following problem and designing a kinematic control algorithm. In turn, the dynamic control algorithm is a modification of a passivity-based controller. Theoretical deliberations are illustrated with simulations.
TL;DR: An idealized algorithm is presented first, before a description of one of its possible implementations, where compact sets are wrapped into boxes, and the resulting path planner is then used for nonholonomic path planning in robotics.
Abstract: This paper is devoted to path planning when the safety of the system considered has to be guaranteed in the presence of bounded uncertainty affecting its model. A new path planner addresses this problem by combining Rapidly-exploring Random Trees (RRT) and a set representation of uncertain states. An idealized algorithm is presented first, before a description of one of its possible implementations, where compact sets are wrapped into boxes. The resulting path planner is then used for nonholonomic path planning in robotics.
TL;DR: The paper includes a control law design description, stability and convergence analysis of a closed-loop system, and practical verification of the proposed control concept, which guarantees asymptotic convergence of the position tracking error to zero in spite of the disturbing influence of skid-slip phenomena.
Abstract: The article is devoted to a motion control problem for a differentially driven mobile robot in the task of trajectory tracking in the presence of skid-slip effects. The kinematic control concept presented in the paper is the Vector Field Orientation (VFO) feedback approach with a nonlinear feed-forward skid-slip influence compensation scheme. The VFO control law guarantees asymptotic convergence of the position tracking error to zero in spite of the disturbing influence of skid-slip phenomena. The paper includes a control law design description, stability and convergence analysis of a closed-loop system, and practical verification of the proposed control concept. The experimental results illustrate control quality obtained on a laboratory setup equipped with vision feedback, where the Kalman filter algorithm was used in order to practically estimate skid-slip components.
TL;DR: Reachability of Cone Fractional Continuous-Time Linear Systems A new class of cone fractional continuous-time linear systems is introduced and necessary and sufficient conditions for a fractional linear system to be acone fractional one are established.
Abstract: A new class of cone fractional continuous-time linear systems is introduced. Necessary and sufficient conditions for a fractional linear system to be a cone fractional one are established. Sufficient conditions for the reachability of cone fractional systems are given. The discussion is illustrated with an example of linear cone fractional systems.
TL;DR: The notion of extended sensors is introduced and it is shown that the observation error decreases when the support of a sensor is widened and when the number of sensors increases.
Abstract: The purpose of this short paper is to provide original results related to the choice of the number of sensors and their supports for general distributed parameter systems. We introduce the notion of extended sensors and we show that the observation error decreases when the support of a sensor is widened. We also show that the observation error decreases when the number of sensors increases.
TL;DR: This paper considers a nonlinear model of a biological wastewater treatment process, based on two microbial populations and two substrates, and proposes a feedback control law for asymptotic stabilization of the closed-loop system towards a previously chosen operating point.
Abstract: In this paper we consider a nonlinear model of a biological wastewater treatment process, based on two microbial populations and two substrates. The model, described by a four-dimensional dynamic system, is known to be practically verified and reliable. First we study the equilibrium points of the open-loop system, their stability and local bifurcations with respect to the control variable. Further we propose a feedback control law for asymptotic stabilization of the closed-loop system towards a previously chosen operating point. A numerical extremum seeking algorithm is designed to stabilize the dynamics towards the maximum methane output flow rate in the presence of coefficient uncertainties. Computer simulations in Maple are reported to illustrate the theoretical results.
TL;DR: This paper proposes to reduce the consensus problem at hand to the solving of a strict matrix inequality with respect to a Lyapunov matrix and a controller gain matrix, and proposes two algorithms for solving the matrix inequality.
Abstract: In this paper, we study a consensus problem in multi-agent systems, where the entire system is decentralized in the sense that each agent can only obtain information (states or outputs) from its neighbor agents. The existing design methods found in the literature are mostly based on a graph Laplacian of the graph which describes the interconnection structure among the agents, and such methods cannot deal with complicated control specification. For this purpose, we propose to reduce the consensus problem at hand to the solving of a strict matrix inequality with respect to a Lyapunov matrix and a controller gain matrix, and we propose two algorithms for solving the matrix inequality. It turns out that this method includes the existing Laplacian based method as a special case and can deal with various additional control requirements such as the convergence rate and actuator constraints.
TL;DR: The motion planning as well as the motion realization stage are based on the Vector-Field-Orientation (VFO) approach applied here to a new task and the unique features of the resultant VFO control system may prove to be useful in practically motivated motion tasks.
Abstract: This paper is devoted to the way point following motion task of a unicycle where the motion planning and the closed-loop motion realization stage are considered. The way point following task is determined by the user-defined sequence of way-points which have to be passed by the unicycle with the assumed finite precision. This sequence will take the vehicle from the initial state to the target state in finite time. The motion planning strategy proposed in the paper does not involve any interpolation of way-points leading to simplified task description and its subsequent realization. The motion planning as well as the motion realization stage are based on the Vector-Field-Orientation (VFO) approach applied here to a new task. The unique features of the resultant VFO control system, namely, predictable vehicle transients, fast error convergence, vehicle directing effect together with very simple controller parametric synthesis, may prove to be useful in practically motivated motion tasks.
TL;DR: This paper addresses the synthesis problem of Jacobian inverse kinematics algorithms for stationary manipulators and mobile robots and develops two approaches to the approximation problem: one relies on variational calculus, the other is differential geometric.
Abstract: This paper addresses the synthesis problem of Jacobian inverse kinematics algorithms for stationary manipulators and mobile robots. Special attention is paid to the design of extended Jacobian algorithms that approximate the Jacobian pseudoinverse algorithm. Two approaches to the approximation problem are developed: one relies on variational calculus, the other is differential geometric. Example designs of the extended Jacobian inverse kinematics algorithm for 3DOF manipulators as well as for the unicycle mobile robot illustrate the theoretical concepts.
TL;DR: The crucial elements of the presented approach are the formalisation of human knowledge about the class of images that are to be automatically interpreted, a linguistic description and the realization of cognitive resonance.
Abstract: The main paradigm of image understanding and a concept for its practical machine realisation are presented. The crucial elements of the presented approach are the formalisation of human knowledge about the class of images that are to be automatically interpreted, a linguistic description and the realization of cognitive resonance.
TL;DR: It is proven that global stability of theclosed-loop system is guaranteed in the sense that all the closed-loop signals are bounded and simulation examples demonstrate the effectiveness of the proposed control scheme.
Abstract: In this paper, a unified nonlinear modeling and control scheme is presented. A self-structuring Takagi-Sugeno (T-S) fuzzy model is used to approximate the unknown nonlinear plant based on I/O data collected on-line. Both the structure and the parameters of the T-S fuzzy model are updated by an on-line clustering method and a recursive least squares estimation (RLSE) algorithm. The rules of the fuzzy model can be added, replaced or deleted on-line to allow a more flexible and compact model structure. The overall controller consists of an indirect adaptive controller and a supervisory controller. The former is the dominant controller, which maintains the closed-loop stability when the fuzzy system is a good approximation of the nonlinear plant. The latter is an auxiliary controller, which is activated when the tracking error reaches the boundary of a predefined constraint set. It is proven that global stability of the closed-loop system is guaranteed in the sense that all the closed-loop signals are bounded and simulation examples demonstrate the effectiveness of the proposed control scheme.
TL;DR: The purpose of this paper is to improve controller robustness by applying a neural network technique in order to compensate the effect of uncertainties in the robot model and show that this control strategy is robust with respect to payload uncertainties, position and environment stiffness, and dry and viscous friction.
Abstract: Force/position control strategies provide an effective framework to deal with tasks involving interaction with the environment One of these strategies proposed in the literature is external force feedback loop control It fully employs the available sensor measurements by operating the control action in a full dimensional space without using selection matrices The performance of this control strategy is affected by uncertainties in both the robot dynamic model and environment stiffness The purpose of this paper is to improve controller robustness by applying a neural network technique in order to compensate the effect of uncertainties in the robot model We show that this control strategy is robust with respect to payload uncertainties, position and environment stiffness, and dry and viscous friction Simulation results for a three degrees-of-freedom manipulator and various types of environments and trajectories show the effectiveness of the suggested approach compared with classical external force feedback loop structures
TL;DR: This paper considers the time-optimal control problem for infinite order hyperbolic systems in which time delays appear in the integral form both in state equations and in boundary conditions and characterized in terms of an adjoint system.
Abstract: In this paper, the time-optimal control problem for infinite order hyperbolic systems in which time delays appear in the integral form both in state equations and in boundary conditions is considered. Optimal controls are characterized in terms of an adjoint system and shown to be unique and bang-bang. These results extend to certain cases of nonlinear control problems. The particular properties of optimal control are discussed.
TL;DR: A general framework for the use of constraints based on physically motivated conservation properties in verified simulations of dynamical systems provides a computationally efficient procedure which restricts the state enclosures to regions that are physically meaningful.
Abstract: Interval arithmetic techniques such as ValEncIA-IVP allow calculating guaranteed enclosures of all reachable states of continuous-time dynamical systems with bounded uncertainties of both initial conditions and system parameters. Considering the fact that, in naive implementations of interval algorithms, overestimation might lead to unnecessarily conservative results, suitable consistency tests are essential to obtain the tightest possible enclosures. In this contribution, a general framework for the use of constraints based on physically motivated conservation properties is presented. The use of these constraints in verified simulations of dynamical systems provides a computationally efficient procedure which restricts the state enclosures to regions that are physically meaningful. A branch and prune algorithm is modified to a consistency test, which is based on these constraints. Two application scenarios are studied in detail. First, the total energy is employed as a conservation property for the analysis of mechanical systems. It is shown that conservation properties, such as the energy, are applicable to any Hamiltonian system. The second scenario is based on constraints that are derived from decoupling properties, which are considered for a high-dimensional compartment model of granulopoiesis in human blood cell dynamics.
TL;DR: A new two-step approach to FSM synthesis for PAL-based CPLDs that strives to find an optimum fit of an FSM to the structure of the CPLD.
Abstract: The paper presents a new two-step approach to FSM synthesis for PAL-based CPLDs that strives to find an optimum fit of an FSM to the structure of the CPLD. The first step, the original state assignment method, includes techniques of two-level minimization and aims at area minimization. The second step, PAL-oriented multi-level optimization, is a search for implicants that can be shared by several functions. It is based on the graph of outputs. Results of experiments prove that the presented approach is especially effective for PAL-based CPLD structures containing a low number of product terms.