Classic, and Explicit Turnpikes Paolo Guasoni · Constantinos Kardaras · Scott Robertson · Hao Xing Received: date / Accepted: date Abstract Portfolio turnpikes state that, as the investment horizon increases, optimal portfolios for generic utilities converge to those of isoelastic utilities. This paper proves three kinds of turnpikes. In a general semimartingale setting, the abstract turnpike s...

In this paper, a new analytical method to find a near-optimal high gain controller for the non-minimum phase affine nonlinear systems is introduced. This controller is derived based on the closed form solution of the Hamilton-Jacobi-Bellman (HJB) equation associated with the cheap control problem. This methodology employs an algebraic equation with parametric coefficients for the systems with s...

Optimal control is the policy of getting the optimized control value for minimizing a predefined cost function. Recently, several optimization methods have been introduced for achieving this purpose.1–4 Among these methods, Pontryagins maximum principle5 and the Hamilton Jacobi Bellman equation6 are the most popular. In Pontryagins maximum principle, the optimal control problem will be converte...

The usual framework of control is the one given in probably the most studied control problem, stochastic regulator control problem, which deals with minimizing a performance index of a system governed by a set of differential equations. The stochastic linear regulator problem has been studied by many authors including Bensoussan [4], Fleming and Soner [9] for nondegenerate diffusions. Da Prato ...

In this paper, an event-triggered Reinforcement Learning (RL) method is proposed for the optimal attitude consensus of multiple rigid body networks with unknown dynamics. Firstly, error constructed through According to Bellman optimality principle, implicit form controller and corresponding Hamilton-Jacobi-Bellman (HJB) equations are obtained. Because augmented system, can be obtained directly ...

For nonlinear Itô-type stochastic systems, the problem of event-triggered optimal control (ETOC) is studied in this paper, and adaptive dynamic programming (ADP) approach explored to implement it. The value function Hamilton–Jacobi–Bellman(HJB) equation approximated by applying critical neural network (CNN). Moreover, a new event-triggering scheme proposed, which can be used design ETOC directl...

This research focuses on designing a min–max robust control based neural dynamic programming approach using class of continuous differential networks (DNNs). The proposed controller solves the optimization cost function that depends trajectories system with an uncertain mathematical model satisfying non-linear perturbed systems. formulation enables concerning bounded modelling uncertainties and...

In this paper we investigate the optimal risk control and dividend distribution problem for a diffusion model with a terminal value. Usually the insurer cedes risk by means of a reinsurance contract, and pays dividends out dynamically from the surplus. Consider that the insurer is trying to balance risk control and dividend payout in terms of reinsurance and dividend distribution policies. Then...