Abstract: Both the minimum energy consumption and
smoothness, which is quantified as a function of jerk, are generally
needed in many dynamic systems such as the automobile and the
pick-and-place robot manipulator that handles fragile equipments.
Nevertheless, many researchers come up with either solely
concerning on the minimum energy consumption or minimum jerk
trajectory. This research paper proposes a simple yet very interesting
relationship between the minimum direct and indirect jerks
approaches in designing the time-dependent system yielding an
alternative optimal solution. Extremal solutions for the cost functions
of direct and indirect jerks are found using the dynamic optimization
methods together with the numerical approximation. This is to allow
us to simulate and compare visually and statistically the time history
of control inputs employed by minimum direct and indirect jerk
designs. By considering minimum indirect jerk problem, the
numerical solution becomes much easier and yields to the similar
results as minimum direct jerk problem.
Abstract: In this paper, we consider nested sliding mode control of SISO nonlinear systems, perturbed by bounded matched and unmatched uncertainties. The systems are assumed to be in strict-feedback form. A step wise procedure is introduced to obtain the controller. In each step, a continuous sliding mode controller is designed as virtual control law. Then the next step sliding surface is defined by using this virtual controller. These sliding surfaces are selected as nonlinear static functions of the system states. Finally in the last step, smooth static state feedback control law is determined such that the output reaches the desired set-point while the system is forced arbitrary close to the intersection of sliding surfaces and the states remain bounded.
Abstract: In this paper, we present the preconditioned mixed-type
splitting iterative method for solving the linear systems, Ax = b,
where A is a Z-matrix. And we give some comparison theorems
to show that the convergence rate of the preconditioned mixed-type
splitting iterative method is faster than that of the mixed-type splitting
iterative method. Finally, we give a numerical example to illustrate
our results.
Abstract: A multi-rate discrete-time model, whose response
agrees exactly with that of a continuous-time original at all sampling
instants for any sampling periods, is developed for a linear system,
which is assumed to have multiple real eigenvalues. The sampling
rates can be chosen arbitrarily and individually, so that their ratios
can even be irrational. The state space model is obtained as a
combination of a linear diagonal state equation and a nonlinear output
equation. Unlike the usual lifted model, the order of the proposed
model is the same as the number of sampling rates, which is less than
or equal to the order of the original continuous-time system. The
method is based on a nonlinear variable transformation, which can be
considered as a generalization of linear similarity transformation,
which cannot be applied to systems with multiple eigenvalues in
general. An example and its simulation result show that the proposed
multi-rate model gives exact responses at all sampling instants.
Abstract: We present a new numerical method for the computation of the steady-state solution of Markov chains. Theoretical analyses show that the proposed method, with a contraction factor α, converges to the one-dimensional null space of singular linear systems of the form Ax = 0. Numerical experiments are used to illustrate the effectiveness of the proposed method, with applications to a class of interesting models in the domain of tandem queueing networks.
Abstract: This paper introduces a new method called ARPDC (Advanced Robust Parallel Distributed Compensation) for automatic control of nonlinear systems. This method improves a quality of robust control by interpolating of robust and optimal controller. The weight of each controller is determined by an original criteria function for model validity and disturbance appreciation. ARPDC method is based on nonlinear Takagi-Sugeno (T-S) fuzzy systems and Parallel Distributed Compensation (PDC) control scheme. The relaxed stability conditions of ARPDC control of nominal system have been derived. The advantages of presented method are demonstrated on the inverse pendulum benchmark problem. From comparison between three different controllers (robust, optimal and ARPDC) follows, that ARPDC control is almost optimal with the robustness close to the robust controller. The results indicate that ARPDC algorithm can be a good alternative not only for a robust control, but in some cases also to an adaptive control of nonlinear systems.
Abstract: The stability test problem for homogeneous large-scale perturbed bilinear time-delay systems subjected to constrained inputs is considered in this paper. Both nonlinear uncertainties and interval systems are discussed. By utilizing the Lyapunove equation approach associated with linear algebraic techniques, several delay-independent criteria are presented to guarantee the robust stability of the overall systems. The main feature of the presented results is that although the Lyapunov stability theorem is used, they do not involve any Lyapunov equation which may be unsolvable. Furthermore, it is seen the proposed schemes can be applied to solve the stability analysis problem of large-scale time-delay systems.
Abstract: Both the minimum energy consumption and
smoothness, which is quantified as a function of jerk, are generally
needed in many dynamic systems such as the automobile and the
pick-and-place robot manipulator that handles fragile equipments.
Nevertheless, many researchers come up with either solely
concerning on the minimum energy consumption or minimum jerk
trajectory. This research paper considers the indirect minimum Jerk
method for higher order differential equation in dynamics
optimization proposes a simple yet very interesting indirect jerks
approaches in designing the time-dependent system yielding an
alternative optimal solution. Extremal solutions for the cost functions
of indirect jerks are found using the dynamic optimization methods
together with the numerical approximation. This case considers the
linear equation of a simple system, for instance, mass, spring and
damping. The simple system uses two mass connected together by
springs. The boundary initial is defined the fix end time and end
point. The higher differential order is solved by Galerkin-s methods
weight residual. As the result, the 6th higher differential order shows
the faster solving time.
Abstract: This paper addresses the controller synthesis problem of discrete-time switched positive systems with bounded time-varying delays. Based on the switched copositive Lyapunov function approach, some necessary and sufficient conditions for the existence of state-feedback controller are presented as a set of linear programming and linear matrix inequality problems, hence easy to be verified. Another advantage is that the state-feedback law is independent on time-varying delays and initial conditions. A numerical example is provided to illustrate the effectiveness and feasibility of the developed controller.
Abstract: Design of an observer based controller for a class of
fractional order systems has been done. Fractional order mathematics
is used to express the system and the proposed observer. Fractional
order Lyapunov theorem is used to derive the closed-loop asymptotic
stability. The gains of the observer and observer based controller are
derived systematically using the linear matrix inequality approach.
Finally, the simulation results demonstrate validity and effectiveness
of the proposed observer based controller.
Abstract: We present new finite element methods for Helmholtz and Maxwell equations on general three-dimensional polyhedral meshes, based on domain decomposition with boundary elements on the surfaces of the polyhedral volume elements. The methods use the lowest-order polynomial spaces and produce sparse, symmetric linear systems despite the use of boundary elements. Moreover, piecewise constant coefficients are admissible. The resulting approximation on the element surfaces can be extended throughout the domain via representation formulas. Numerical experiments confirm that the convergence behavior on tetrahedral meshes is comparable to that of standard finite element methods, and equally good performance is attained on more general meshes.
Abstract: In automotive systems almost all steps concerning the
calibration of several control systems, e.g., low idle governor or
boost pressure governor, are made with the vehicle because the timeto-
production and cost requirements on the projects do not allow for
the vehicle analysis necessary to build reliable models. Here is
presented a procedure using parametric and NN (neural network)
models that enables the generation of vehicle system models based
on normal ECU engine control unit) vehicle measurements. These
models are locally valid and permit pre and follow-up calibrations so
that, only the final calibrations have to be done with the vehicle.
Abstract: This paper shows a new method for design of fuzzy observers for Takagi-Sugeno systems. The method is based on Linear matrix inequalities (LMIs) and it allows to insert H constraint into the design procedure. The speed of estimation can tuned be specification of a decay rate of the observer closed loop system. We discuss here also the influence of parametric uncertainties at the output control system stability.
Abstract: The System Identification problem looks for a
suitably parameterized model, representing a given process. The
parameters of the model are adjusted to optimize a performance
function based on error between the given process output and
identified process output. The linear system identification field is
well established with many classical approaches whereas most of
those methods cannot be applied for nonlinear systems. The problem
becomes tougher if the system is completely unknown with only the
output time series is available. It has been reported that the
capability of Artificial Neural Network to approximate all linear and
nonlinear input-output maps makes it predominantly suitable for the
identification of nonlinear systems, where only the output time series
is available. [1][2][4][5]. The work reported here is an attempt to
implement few of the well known algorithms in the context of
modeling of nonlinear systems, and to make a performance
comparison to establish the relative merits and demerits.
Abstract: In this paper, a wavelet based method is proposed to
identify the constant coefficients of a second order linear system and
is compared with the least squares method. The proposed method
shows improved accuracy of parameter estimation as compared to the
least squares method. Additionally, it has the advantage of smaller
data requirement and storage requirement as compared to the least
squares method.
Abstract: This paper presents the application of discrete-time
variable structure control with sliding mode based on the 'reaching
law' method for robust control of a 'simple inverted pendulum on
moving cart' - a standard nonlinear benchmark system. The
controllers designed using the above techniques are completely
insensitive to parametric uncertainty and external disturbance. The
controller design is carried out using pole placement technique to find
state feedback gain matrix , which decides the dynamic behavior
of the system during sliding mode. This is followed by feedback gain
realization using the control law which is synthesized from 'Gao-s
reaching law'. The model of a single inverted pendulum and the
discrete variable structure control controller are developed, simulated
in MATLAB-SIMULINK and results are presented. The response of
this simulation is compared with that of the discrete linear quadratic
regulator (DLQR) and the advantages of sliding mode controller over
DLQR are also presented
Abstract: Nonlinear system identification is becoming an important tool which can be used to improve control performance. This paper describes the application of adaptive neuro-fuzzy inference system (ANFIS) model for controlling a car. The vehicle must follow a predefined path by supervised learning. Backpropagation gradient descent method was performed to train the ANFIS system. The performance of the ANFIS model was evaluated in terms of training performance and classification accuracies and the results confirmed that the proposed ANFIS model has potential in controlling the non linear system.
Abstract: Reduction of Single Input Single Output (SISO) continuous systems into Reduced Order Model (ROM), using a conventional and an evolutionary technique is presented in this paper. In the conventional technique, the mixed advantages of Mihailov stability criterion and continued fraction expansions (CFE) technique is employed where the reduced denominator polynomial is derived using Mihailov stability criterion and the numerator is obtained by matching the quotients of the Cauer second form of Continued fraction expansions. In the evolutionary technique method Particle Swarm Optimization (PSO) is employed to reduce the higher order model. PSO method is based on the minimization of the Integral Squared Error (ISE) between the transient responses of original higher order model and the reduced order model pertaining to a unit step input. Both the methods are illustrated through numerical example.
Abstract: In this paper, we present parallel alternating two-stage
methods for solving linear system Ax=b, where A is a symmetric
positive definite matrix. And we give some convergence results of
these methods for nonsingular linear system.
Abstract: In this paper, the performance of two adaptive
observers applied to interconnected systems is studied. The
nonlinearity of systems can be written in a fractional form. The first
adaptive observer is an adaptive sliding mode observer for a Lipchitz
nonlinear system and the second one is an adaptive sliding mode
observer having a filtered error as a sliding surface. After comparing
their performances throughout the inverted pendulum mounted on a
car system, it was shown that the second one is more robust to
estimate the state.