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# IMA Journal of Mathematical Control and Information Current Issue

Published: Tue, 28 Jun 2016 00:00:00 GMT

Last Build Date: Tue, 03 Oct 2017 12:54:26 GMT

Controllability for retarded semilinear integrodifferential control systems with unbounded operators

2016-06-28

Abstract
In this article we establish sufficient conditions for the approximate controllability of retarded semilinear integrodifferential control systems with unbounded operators under simple conditions on the controller and a weak backward uniqueness property for the adjoint system of the corresponding linear system. A simple example to which our main result can be applied is given.

Projective lag synchronization of second-order chaotic systems via modified terminal sliding mode control

2016-06-28

Abstract
This article addresses the projective lag synchronization for a class of second-order chaotic systems via a modified terminal sliding mode control (TSMC). The terminal sliding surface is constructed with a differential odd function, which is a superset of the conventional terminal sliding surfaces. Based on the TSMC technique, the sufficient conditions are given to assure the valid projective lag synchronization of second-order chaotic systems occurs. The corresponding numerical simulation is provided to illustrate the effectiveness of the developed theoretical results.

Zero-error convergence of iterative learning control using quantized error information

2016-06-28

Abstract
An iterative learning control algorithm using quantized error information is proposed in this article for both linear and nonlinear systems. The actual output is first compared with the reference signal and then the corresponding error is quantized and transmitted. A logarithmic quantizer is used to guarantee an adaptive improvement for tracking performance. The tracking error under this scheme is proved to converge to zero asymptotically. Illustrative examples verify the theoretical results.

Tracking control for uncertain fractional-order chaotic systems based on disturbance observer and neural network

2016-06-27

Abstract
This article proposes an adaptive neural tracking control scheme for uncertain fractional-order chaotic systems (FOCSs) subject to unknown disturbance and input saturation. To tackle the system uncertainty in the FOCS, the radial basis function neural network (RBFNN) is employed. Furthermore, the sliding mode fractional-order disturbance observer (SMFODO) is designed to estimate the unknown disturbance. Using the backstepping technique, an adaptive neural control is proposed for uncertain FOCSs by employing the RBFNN and the developed SMFODO. To avoid the tedious analytic computation in the backstepping method, a fractional-order differentiator is introduced. The stability is proved via fractional-order analysis method for the whole closed-loop system in the presence of the system uncertainty, the input saturation and the unknown external disturbance. Simulation results of the fractional-order chaotic electronic oscillator model are presented to illustrate the effectiveness of the proposed adaptive neural tracking control scheme.

The null controllability of nonlinear discrete control systems with degeneracy

2016-06-27

Abstract
This article mainly concerns the null controllability of autonomous and non-autonomous nonlinear discrete control systems. By using Cayley–Hamilton theorem and Brouwer's fixed point theorem under a condition on the nonlinearity, sufficient and necessary conditions of null controllability for nonlinear discrete control systems are presented. In our approach, the linear part of systems under consideration might admit some degeneracy. In addition, applications are given to illustrate the obtained results.

Lower bounds on eigenvalue summation for the solution of the Lyapunov matrix differential equation

2016-04-04

Abstract
The Lyapunov matrix differential equation has widely applications in control theory and linear system. In this paper, applying the properties of exponential matrices and integrable functions, we obtain lower bounds on eigenvalue summation for the solution of this equation using eigenvalue inequalities and majorization inequalities. Finally, we give a corresponding numerical example to show the effectiveness of the derived bounds.

Optimal control problem for a class of bilinear systems via block pulse functions

2016-03-25

Abstract
This paper deals with an optimal control problem with quadratic cost for a class of bilinear systems using the orthogonal functions technique. The main idea of this technique is that it reduces the problem to solving a system of algebraic equations, thus simplifying the problem. The control variable and the state variables are approximated by block pulse functions series. Then the system dynamics is transformed into systems of algebraic equations. Finally, numerical results are given to illustrate the proposed method.

Regional stabilization of semi-linear parabolic systems

2016-03-17

Abstract
In this paper, we study the regional stability and stabilization of semi-linear systems defined on a Hilbert state space. We prove that the system is stable once the strong controllability assumption is fulfilled together with a Lipschitz property of the non-linear operator. Furthermore, we propose a design of a class of non-linear controls that guaranteed regional exponential stabilization.

Viscosity solutions for a system of PDEs and optimal switching

2016-03-15

Abstract
In this paper, we study the existence and uniqueness of viscosity solutions for a system of $m$ variational partial differential inequalities with interconnected obstacles. A particular case of this system is the deterministic version of the Verification Theorem of the Markovian optimal $m$-states optimal switching problem in finite horizon. The switching cost functions are arbitrary and can be positive or negative. This has an economic incentive in terms of central valuation in cases where such organizations or states give grants or financial assistance to power plants that promote green energy in their production activity or that uses less polluting modes in their production. Our main tools is an approximation scheme and the notion of systems of reflected backward stochastic differential equations.

Non-linear observer design for a class of singular time-delay systems with Lipschitz non-linearities

2016-03-11

Abstract
In this paper, we consider a class of time-delay singular systems with Lipschitz non-linearities. A method of designing full-order observers for the systems is presented which can handle non-linearities with large-Lipschitz constants. The Lipschitz conditions are reformulated into linear parameter varying systems, then the Lyapunov–Krasovskii approach and the convexity principle are applied to study stability of the new systems. Furthermore, the observers design does not require the assumption of regularity for singular systems. In case the systems are non-singular, a reduced-order observers design is proposed instead. In both cases, synthesis conditions for the observers designs are derived in terms of linear matrix inequalities which can be solved efficiently by numerical methods. The efficiency of the obtained results is illustrated by two numerical examples.

Stability of periodic solutions of nonlinear time-delay systems

2016-02-26

Abstract
General non-linear differential systems with time-varying delays are considered. Explicit criteria for existence, uniqueness and global exponential stability of periodic solutions are given. Then the obtained result is used to investigate exponential stability of periodic solutions of delayed neural networks.

Numerical solution of optimal control problem of the non-linear Volterra integral equations via generalized hat functions

2016-02-03

Abstract
This paper presents a numerical method for solving optimal control problems including non-linear Volterra integral equations. The method is based upon generalized hat functions (HFs). Using the properties of HFs and associated operational matrices, optimal control problem is converted to an optimization problem. Furthermore, error analysis of the proposed method is studied. Illustrative examples are included to demonstrate the validity and applicability of the approach.

Regional boundary controllability of time fractional diffusion processes

2016-01-28

Abstract
In this paper, we are concerned with the regional boundary controllability of the Riemann–Liouville time fractional diffusion systems of order $\alpha \in (0,1]$. The characterizations of strategic actuators are established when the systems studied are regionally boundary controllable. The determination of control to achieve regional boundary controllability with minimum energy is explored. We also show a connection between the regional internal controllability and regional boundary controllability. Several useful results for the optimal control from an implementation point of view are presented in the end.

Approximate controllability of impulsive fractional stochastic partial neutral integrodifferential inclusions with infinite delay

2016-01-20

Abstract
In this article, the problem of approximate controllability for impulsive fractional stochastic partial neutral integrodifferential inclusions with infinite delay in a Hilbert space is investigated. By using the Hölder inequality, the analytic $\alpha$-resolvent operator and fixed point strategy with stochastic analysis theory, we derive a new set of sufficient conditions for the approximate controllability of an impulsive fractional stochastic system under the assumption that the corresponding linear system is approximately controllable. Finally, an illustrative example is given to show the effectiveness of the obtained results.

Iterative learning control for quasi-one-sided Lipschitz non-linear systems

2016-01-20

Abstract
This paper addresses the problem of iterative learning control for non-linear systems in the presence of initial state errors. Here, the non-linear functions in the considered systems satisfy quasi-one-sided Lipschitz condition, which is an assumption weaker than the classical Lipschitz condition. And the P-type learning scheme is proposed for the corresponding quasi-one-sided Lipschitz non-linear systems. When the learning scheme is applied to the systems, the output tracking errors are bounded, and furthermore, the tracking errors can tend to zero along the iteration axis in the absence of initial state errors. The simulation result verifies the effectiveness of the proposed algorithm.

Distributed tracking control of the Schrödinger equation with internal disturbance

2016-01-20

Abstract
This paper concerns the existence of a solution and the stabilization of a one-dimensional Schrödinger equation with internal disturbance. Here, a non-linear controller is designed to stabilize the system. The existence of the solution for the system is verified by variation method, which can be regarded as an extended version of the Lions–Lax–Milgram theorem. The finite-time stability of the system under this control law is proved by Lyapunov analysis. Finally, some numerical simulations are presented for validating the effectiveness of the method.

The improved eigenvalue bounds for the solution of the discrete algebraic Riccati equation

2016-01-20

Abstract
In this paper, by using matrix eigenvalue inequalities and the properties of the positive definite solution for the discrete algebraic Riccati equation (DARE), we present upper and lower eigenvalue bounds for the solution of this equation. Moreover, applying majorization inequalities and eigenvalue summation (product) inequalities of special matrices, based on the derived results, we propose upper and lower bounds on eigenvalue summation and product for the solution of the DARE, which improve some of the recent results. The numerical examples show the effectiveness of the derived results.

Finite-time control of linear systems subject to time-varying disturbances

2016-01-12

Abstract
This paper considers finite-time control of linear systems subject to time-varying disturbances. The concepts of quasi finite-time stability and quasi finite-time boundedness are defined and a sufficient condition for a linear system with disturbances to be quasi finite-time bounded is derived. It is shown that the notions are more general and the condition is less conservative than the existing ones. A state feedback controller design method is given to solve the finite-time control problem. All the conditions are then reduced to feasibility problems involving linear matrix inequalities and numerical examples are given to illustrate the obtained results.

Iterative estimation for a non-linear IIR filter with moving average noise by means of the data filtering technique

2015-12-24

Abstract
This paper considers the parameter estimation issues of a non-linear infinite impulse response (IIR) filter with moving average noise. The main objective is to present novel iterative estimation methods of a non-linear IIR filter by using the data filtering technique. Firstly, the gradient-based iterative (GI) algorithm is given for a non-linear IIR filter with moving average noise as a comparison. Secondly, a data filtering-based GI algorithm is presented for improving the parameter estimation accuracy. Thirdly, a data filtering-based least squares iterative algorithm is derived for improving the computation efficiency and boosting up the convergence rate. Finally, the simulation results are given to illustrate the performances of the proposed algorithms.

The solution of some discretionary stopping problems

2015-12-17

Abstract
We present a methodology for obtaining explicit solutions to infinite time horizon optimal stopping problems involving general, one-dimensional, Itô diffusions, payoff functions that need not be smooth and state-dependent discounting. This is done within a framework based on dynamic programming techniques employing variational inequalities. The aim of this paper is to facilitate the solution of a wide variety of problems, particularly in finance or economics.