The present work approaches the problem of achieving the approximate solution of the second order initial value problems (IVPs) via its conversion into a Volterra integral equation of the second kind (VIE2). Therefore, we initially solve the IVPs using Runge–Kutta of the forth–order method (RK), and then convert it into VIE2, and apply the εmodified block–pulse functions (εMBPFs) and their oper...

In order to find the optimal control of continuous state-space and time reinforcement learning (RL) problems, we approximate the value function (VF) with a particular class of functions called the barycentric interpolators. We establish sufficient conditions under which a RL algorithm converges to the optimal VF, even when we use approximate models of the state dynamics and the reinforcement fu...

We state an approximate policy iteration algorithm to find stochastic policies that optimize single-agent behavior for several environments and reinforcement functions simultaneously. After introducing a geometric interpretation of policy improvement for stochastic policies we discuss approximate policy iteration and evaluation. We present examples for two blockworld environments and reinforcem...

This paper addresses the problem of adaptive fuzzy tracking control for aclass of nonlinearly parameterized systems with unknown control directions.In this paper, the nonlinearly parameterized functions are lumped into the unknown continuous functionswhich can be approximated by using the fuzzy logic systems (FLS) in Mamdani type. Then, the Nussbaum-type function is used to de...

by replacing the discrete value f(k/n) by the integral (n−1)∫∞ 0 pn,k(t)f (t)dt in order to approximate Lebesgue integrable functions on the interval [0,∞). Some approximation properties of the operators (1.1) were discussed in [6, 7, 8]. In [2, 3], the author defined another modification of the Baskakov operators with the weight functions of Beta operators so as to approximate Lebesgue integra...

In this paper the approximation of the optimal compressor function using the first-degree spline functions and quadratic spline functions is done. Coefficients on which we form approximative spline functions are determined by solving equation systems that are formed from treshold conditions. For Gaussian source at the input of the quantizer, using the obtained approximate spline functions a com...

In order to nd the optimal control of continuous state-space and time reinforcement learning (RL) problems, we approximate the value function (VF) with a particular class of functions called the barycentric interpolators. We establish su cient conditions under which a RL algorithm converges to the optimal VF, even when we use approximate models of the state dynamics and the reinforcement functi...

*Correspondence: [email protected] School of Basic Science, Changchun University of Technology, Changchun, 130012, P.R. China Abstract In this paper, we investigate the approximate controllability of the coupled system with boundary degeneracy. The control functions act on the degenerate boundary. We prove the Carleman estimate and the unique continuation of the adjoint system. Then we get the ...

In this paper, the homotopy perturbation method (HPM) is considered for finding approximate solutions of two-dimensional viscous flow. This technique provides a sequence of functions which converges to the exact solution of the problem. The HPM does not need a small parameters in the equations, but; the perturbation method depends on small parameter assumption and the obtained results. In most ...