I) We consider a system governed by a free boundary problem with Tresca condition on a part of the boundary of a material domain with a source term g through a parabolic variational inequality of the second kind. We prove the existence and uniqueness results to a family of distributed optimal control problems over g for each parameter h > 0, associated to the Newton law (Robin boundary conditio...

It is known that optimal stopping problems for controlled diffusion processes can be transformed into optimal control problems by using the method of randomized stopping (see [2] and [8]). Since only a few optimal stopping problems can be solved analytically (see [13]), one has to resort to numerical approximations of the solution. In such cases, one would like to know the rate of convergence o...

In this article, the fractional derivatives in the sense of Caputo, and the homotopy analysis method (HAM) are used to construct the approximate solutions for the nonlinear fractional variant Bussinesq equations with respect to time fractional derivative. The HAM contains a certain auxiliary h parameter which provides us a simple way to adjust and control the convergence region and rate of conv...

We present a novel finite-time average consensus protocol based on event-triggered control strategy for multiagent systems. The system stability is proved. The lower bound of the interevent time is obtained to guarantee that there is no Zeno behavior. Moreover, the upper bound of the convergence time is obtained. The relationship between the convergence time and protocol parameter with initial ...

The fractional derivatives in the sense of Caputo, and the homotopy analysis method (HAM) are used to construct the approximate solutions for nonlinear fractional dispersive long wave equation with reaspect to time fractional derivative. The HAM contains a certain auxiliary parameter which provides us with a simple way to adjust and control the convergence region and rate of convergence of the ...

We consider a class of hybrid nonlinear optimal control problems having a discontinuous dynamics ruled by a partition of the state space. For this class of problem, some hybrid versions of the usual Pontryagin Maximum Principle are known. We introduce general regularization procedures, parameterized by a small parameter, smoothing the previous hybrid problems to standard smooth optimal control ...

As we know, the homotopy analysis method (HAM) provides us with a convenient way to adjust and control the convergence region and rate of the obtained series solutions. This great advantage of method is possible by finding a proper value of the so-called control parameter 0 c . In this paper, an efficient way of obtaining 0 c is proposed. Such value of parameter can be determined at the any ord...

Based on the homotopy analysis method (HAM), we propose an analytical approach for solving the following type of nonlinear boundary value problems in finite domain. In framework of HAM a convenient way to adjust and control the convergence region and rate of convergence of the obtained series solutions, by defining the so-called control parameter , is provided. This paper aims to propose an eff...

Current engineering practice for adaptive control schemes is to base the design on globally convergent schemes for simple plant models, An important class of such schemes uses least squares estimation of assumed simple input–output models and constructs the controller using the parameter estimates. This paper studies the robustness of such schemes to the presence of unmodelled plant colourcd no...