Identification of nonlinear systems using hybrid functions

Most real systems have nonlinear behavior and thus model linearization may not produce an accurate representation of them. This paper presents a method based on hybrid functions to identify the parameters of nonlinear real systems. A hybrid function is a combination of two groups of orthogonal functions: piecewise orthogonal functions (e.g. Block-Pulse) and continuous orthogonal functions (e.g. Legendre polynomials). These functions are completed with an operational matrix of integration and a product matrix. Therefore, it is possible to convert nonlinear differential and integration equations into algebraic equations. After mathematical manipulation, the unknown linear and nonlinear parameters are identified. As an example, a mechanical system with single degree of freedom is simulated using the proposed method and the results are compared against those of an existing approach.

Robust multi-sensor data fusion

This research obtains the optimal estimation and data fusion for linear and nonlinear systems suffering from uncertain observations (missing measurements). The noise from the different data sources are considered to correlated. The derivation of the robust Kalman filter for systems subject to aditional uncertainties in the modelling parameters is presented.

Partial-state observers for nonlinear systems

This note deals with the design of reduced-order observers for a class of nonlinear systems. The order reduction of the observer is achieved by only estimating a required partial set of the state vector. Necessary and sufficient conditions are derived for the existence of reduced-order observers. An observer design procedure based on linear matrix inequalities is given. A numerical example is given to illustrate the design method.

Nonlinear identification of pneumatic servo-drive

Three nonlinear approaches to model the nonlinear pneumatic servo- drive are presented. The three nonlinear approaches are: (1) the multi input-single output (MISO) approach, which describes the single input-single output (SISO) nonlinear plant using a MISO linear representation which allows replacement of the nonlinear analysis by a linear one without approximation, and is studied in both time and frequency domains; (2) piecewise linearization, which systematically replaces, using artificial neural network, the nonlinear surface representing the plant in the hyper input-output space by a number of linear planes that are continuous over the boundaries between them; and (3) Adaptive Neuro-Fuzzy Inference System (ANFIS), in which the fuzzy rules are placed in a neural network structure, and which consequently utilizes neural networks learning rules to systematically tune the nonlinear fuzzy model. The superiority of these nonlinear models over the best model that can be developed using linear identification techniques is shown.

State and input simultaneous estimation for a class of nonlinear systems

This paper addresses the problem of estimating simultaneously the state and input of a class of nonlinear systems. Here, the systems nonlinear part comprises a Lipschitz nonlinear function with respect to the state and input, and a state-dependent unknown function including additive disturbance as well as uncertain/nonlinear/time-varying terms. Upon satisfying some conditions, the observer design problem can be solved via a Riccati inequality or a LMI-based technique with asymptotic estimation guaranteed. A numerical example is included for illustration.

An algebraic approach for delay-independent and delay-dependent stability of linear time-delay systems

This paper addresses the problem of asymptotic stability of a linear system with many delay units. A novel algebraic test is proposed for the delay-independent stability of the system, based on the root distribution of the system's characteristic equation. If the system is only stable dependent of delay, the whole stable regions of the system can be perfectly obtained. Two algorithms are derived to examine the delay-independent stability, and to compute the whole stable regions if the system is of delay-dependent stability. These algorithms are computationally efficient and applicable to both certain and uncertain systems. Some illustrative examples demonstrate the validity of the approach.

A family of simple and robust finite elements for linear and geometrically nonlinear analysis of laminated composite plates

A family of simple, displacement-based and shear-flexible triangular and quadrilateral flat plate/shell elements for linear and geometrically nonlinear analysis of thin to moderately thick laminate composite plates are introduced and summarized in this paper.

The developed elements are based on the first-order shear deformation theory (FSDT) and von-Karman’s large deflection theory, and total Lagrangian approach is employed to formulate the element for geometrically nonlinear analysis. The deflection and rotation functions of the element boundary are obtained from Timoshenko’s laminated composite beam functions, thus convergence can be ensured theoretically for very thin laminates and shear-locking problem is avoided naturally.

The flat triangular plate/shell element is of 3-node, 18-degree-of-freedom, and the plane displacement interpolation functions of the Allman’s triangular membrane element with drilling degrees of freedom are taken as the in-plane displacements of the element. The flat quadrilateral plate/shell element is of 4-node, 24-degree-of-freedom, and the linear displacement interpolation functions of a quadrilateral plane element with drilling degrees of freedom are taken as the in-plane displacements.

The developed elements are simple in formulation, free from shear-locking, and include conventional engineering degrees of freedom. Numerical examples demonstrate that the elements are convergent, not sensitive to mesh distortion, accurate and efficient for linear and geometric nonlinear analysis of thin to moderately thick laminates.

Optimal actuator fault tolerance for static nonlinear systems based on minimum output velocity jump

Fault tolerance for a class of non linear systems is addressed based on the velocity of their output variables. This paper presents a mapping to minimize the possible jump of the velocity of the output, due to the actuator failure. The failure of the actuator is assumed as actuator lock. The mapping is derived and it provides the proper input commands for the healthy actuators of the system to tolerate the effect of the faulty actuator on the output of the system. The introduced mapping works as an optimal input reconfiguration for fault recovery, which provides a minimum velocity jump suitable for static nonlinear systems. The proposed mapping is validated through different case studies and a complementary simulation. In the case studies and the simulation, the mapping provides the commands to compensate the effect of different faults within the joints of a robotic manipulator. The new commands and the compare between the velocity of the output variables for the health and faulty system are presented.

Performance of first and second-order sliding mode observers for nonlinear systems

This paper presents a brief study on the design and performance comparison of conventional first-order and super-twisting second-order sliding mode observers for some nonlinear control systems. Estimation accuracy, fast response, chattering effect, peaking phenomenon and robustness are considered for nonlinear ystems under observer-based output feedback control and state feedback control.

A finite-time stability theorem of stochastic nonlinear systems and stabilization designs

This paper focuses on the finite-time stability and stabilization designs of stochastic nonlinear systems. We first present and discuss a definition on the finite-time stability in probability of stochastic nonlinear systems, then we introduce a stochastic Lyapunov theorem on the finite-time stability, which has been established by Yin et al. We also employ this theorem to design a continuous state feedback controller that makes a class of stochastic nonlinear systems to be stable in finite time. An example and a simulation are given to illustrate the theoretical analysis.

Multiple actuator fault tolerance for static nonlinear systems based on minimum velocity jump

Static nonlinear systems are common when the model of the kinematics of mechanical or civil structures is analyzed for instance kinematics of robotic manipulators. This paper addresses the maximum effort toward fault tolerance for any number of the locked actuators failures in static nonlinear systems. It optimally reconfigures the inputs via a mapping that maximally accommodates the failures. The mapping maps the failures to an extra action of healthy actuators that results to a minimum jump for the velocity of the output variables. Then from this mapping, the minimum jump of the velocity of the output is calculated. The conditions for a zero velocity jump of the output variables are discussed. This shows that, when the conditions of fault tolerance are maintained, the proposed framework is capable of fault recovery not only at fault instances but also at the whole output trajectory. The proposed mapping is validated by three case studies.

Adaptive fast finite time control of a class of uncertain nonlinear systems

This paper concerns the adaptive fast finite time control of a class of nonlinear uncertain systems of which the upper bounds of the system uncertainties are unknown. By using the fast non-smooth control Lyapunov function and the method of so-called adding a power integrator merging with adaptive technique, a recursive design procedure is provided, which guarantees the fast finite time stability of the closed-loop system. It is proved that the control input is bounded, and a simulation example is given to illustrate the effectiveness of the theoretical results.