In this paper we study the convergence of the Galerkin approximation method applied to the Generalized Hamilton-Jacobi-Bellman (GHJB) equation over a compact set containing the origin. The GHJB equation gives the cost of an arbitrary control law and can be used to improve the performance of this control. The GHJB equation can also be used to successively approximate the Hamilton-Jacobi-Bellman ...

The torque ripples in a switched reluctance motor (SRM) are minimized via an optimal adaptive dynamic regulator that is presented this research. A novel reinforcement neural network learning approach based on machine adopted to find the best solution for tracking problem of SRM drive real time. reference signal model which minimizes pulsations combined with error construct augmented structure d...

Path integral control solves a class of stochastic optimal control problems with a Monte Carlo (MC) method for an associated Hamilton-Jacobi-Bellman (HJB) equation. The MC approach avoids the need for a global grid of the domain of the HJB equation and, therefore, path integral control is in principle applicable to control problems of moderate to large dimension. The class of problems path inte...

In this paper we investigate the optimal investment strategy for a defined contribution (DC) pension plan during the decumulation phrase which is risk-averse and pays close attention to inflation risk. The plan aims to maximize the expected constant relative risk aversion (CRRA) utility from the terminal wealth by investing the wealth in a financial market consisting of an inflation-indexed bon...

The paper deals with connections between optimality and passivity-like properties in discrete time. The problem is set in the framework of differential/difference representations of discrete-time dynamics. The Hamilton–Jacobi–Bellman equality associated with a given cost and the corresponding optimal control solution are characterized. On these bases the connection with u-average passivity is c...

We study nonzero-sum stochastic differential games with risk-sensitive ergodic cost criterion. Under certain conditions, using multi parameter eigenvalue approach, we establish the existence of a Nash equilibrium in space stationary Markov strategies. achieve our results by studying relevant systems coupled Hamilton–Jacobi–Bellman (HJB) equations. Exploiting representation principal eigenfuncti...

In defined contribution (DC) pension schemes, the financial risk borne by the member occurs during the accumulation phase. To build up sufficient funds for retirement, scheme members invest their wealth in a portfolio of assets. This paper considers an optimal investment problem of a scheme member facing stochastic inflation under the Markowitz mean–variance criterion. Besides, we consider a mo...

Adaptive dynamic programming (ADP) is a novel approximate optimal control scheme, which has recently become a hot topic in the field of optimal control. As a standard approach in the field of ADP, a function approximation structure is used to approximate the solution of Hamilton-Jacobi-Bellman (HJB) equation. The approximate optimal control policy is obtained by using the offline iteration algo...

We show that the value function of a stochastic control problem is the unique solution of the associated Hamilton-Jacobi-Bellman (HJB) equation, completely avoiding the proof of the so-called dynamic programming principle (DPP). Using Stochastic Perron's method we construct a super-solution lying below the value function and a sub-solution dominating it. A comparison argument easily closes the ...

This paper studies the time-consistent investment strategy for a defined contribution (DC) pension plan under the mean–variance criterion. Since the time horizon of a pension fund management problem is relatively long, two background risks are taken into account: the inflation risk and the salary risk. Meanwhile, there are a risk-free asset, a stock and an inflation-indexed bond available in th...