Exact boundary controllability of vibrating non-classical Euler–Bernoulli micro-scale beams

This study investigates the exact controllability problem for a vibrating non-classical Euler–Bernoulli micro-beam whose governing partial differential equation (PDE) of motion is derived based on the non-classical continuum mechanics. In this paper, it is proved that via boundary controls, it is possible to obtain exact controllability which consists of driving the vibrating system to rest in finite time. This control objective is achieved based on the PDE model of the system which causes that spillover instabilities do not occur.     

Verification by Stochastic Perron's Method in stochastic exit time control problems

We apply the Stochastic Perron Method, created by Bayraktar and Sîrbu, to a stochastic exit time control problem. Our main assumption is the validity of the Strong Comparison Result for the related Hamilton–Jacobi–Bellman (HJB) equation. Without relying on Bellman's optimality principle we prove that inside the domain the value function is continuous and coincides with a viscosity solution of the Dirichlet boundary value problem for the HJB equation.     

Optimal control of semilinear parabolic systems with state constraint

The aim of this work is to obtain the existence of optimal solution and maximum principle for optimal control problem with pointwise type state constraint governed by semilinear parabolic systems with certain polynomial-like nonlinearity. Application to optimal control problems of the phase transition system is given.     

On optimal periodic dividend strategies in the dual model with diffusion

The dual model with diffusion is appropriate for companies with continuous expenses that are offset by stochastic and irregular gains. Examples include research-based or commission-based companies. In this context, Bayraktar et al. (2013a) show that a dividend barrier strategy is optimal when dividend decisions are made continuously. In practice, however, companies that are capable of issuing dividends make dividend decisions on a periodic (rather than continuous) basis.In this paper, we consider a periodic dividend strategy with exponential inter-dividend-decision times and continuous monitoring of solvency. Assuming hyperexponential gains, we show that a periodic barrier dividend strategy is the periodic strategy that maximizes the expected present value of dividends paid until ruin. Interestingly, a ‘liquidation-at-first-opportunity’ strategy is optimal in some cases where the surplus process has a positive drift. Results are illustrated.     

Optimal admission control for two station tandem queues with loss

We consider a two-station tandem queue with a buffer size of one at the first station and a finite buffer size at the second station. Silva et al. (2013) gave a criterion determining the optimal admission control policy for this model. In this paper, we improve the results of Silva et al. (2013) and also solve the problem conjectured by Silva et al. (2013).     

A new discrete mechanics approach to swing-up control of the cart-pendulum system

This paper develops a new swing-up control method for the cart-pendulum system via discrete mechanics. The swing-up control law consists of two parts: the swing-up stage and the stabilization one. In the swing-up stage, we use a controller based on a discrete Lyapunov function and it can swing up the pendulum. Then, in the stabilization stage, we utilize a stabilizing controller based on the linearized system and discrete-time optimal regulator theory. In addition, transformation methods from discrete control inputs into continuous zero-order hold inputs are introduced. From some simulation results, we can confirm that the cart-pendulum system is swung up and stabilized by our new method.     

An adaptive Newton-method based on a dynamical systems approach

The traditional Newton method for solving nonlinear operator equations in Banach spaces is discussed within the context of the continuous Newton method. This setting makes it possible to interpret the Newton method as a discrete dynamical system and thereby to cast it in the framework of an adaptive step size control procedure. In so doing, our goal is to reduce the chaotic behavior of the original method without losing its quadratic convergence property close to the roots. The performance of the modified scheme is illustrated with various examples from algebraic and differential equations.     

Attitude control of rigid spacecraft with disturbance generated by time varying exosystems

This paper is concerned with the problem of attitude control and disturbance rejection of rigid spacecraft in the presence of parameter uncertainty. It is assumed that the external disturbance is generated by some time varying exosystems. The unit quaternion is used as the kinematic variables since it is free of singularity. An internal model and an adaptive control law are proposed. The parameter uncertainty caused by the unknown inertia matrix is handled by combining the semi-tensor product and adaptive control method. The asymptotical stability of the closed-loop system is given via backstepping and Lyapunov analysis. Finally, an illustrative example is provided to show the effectiveness of the proposed approach.     

Robust decentralized adaptive synchronization of general complex networks with coupling delayed and uncertainties

The problem of robust decentralized adaptive synchronization of general complex networks with coupling delayed and uncertainties is investigated in this article. It is only assumed that the upper normal bound of uncertain inner and outer coupling matrices is positive but its concrete structure is not also required to be known. The time‐varying coupling delay is a any nonnegative continuous and bounded function and not require its derivative to be less than one, that is, general time‐varying coupling delays and uncertainties. For such a class of uncertain complex networks, a new synchronization scheme is presented by a class of continuous memoryless robust decentralized adaptive synchronization controllers. It is also shown that the synchronization error dynamics of uncertain complex networks can be guaranteed as uniformly exponentially convergent toward a ball that can be as small as desired. Finally, numerical simulations are provided to demonstrate the effectiveness and robustness of proposed complex networks synchronization schemes. © 2013 Wiley Periodicals, Inc. Complexity 19: 10–26, 2014