Abstract A critic-observer decentralized force/position approximate optimal control method is presented to address the joint trajectory and contacted force tracking problem of modular reconfigurable manipulators (MRMs) with uncertain environmental constraints. The dynamic model MRM systems formulated as an integration subsystems via extensive state observer (ESO) associated effect interconnecte...

<p style='text-indent:20px;'>In this paper, we present a mean field game to model the impact of coexistence mechanism carbon tax and trading (we call it compound abatement mechanism) on production behaviors for large number producers. The game's equilibrium can be presented by system which is composed forward Kolmogorov equation backward Hamilton-Jacobi-Bellman (HJB) partial differential ...

This paper is concerned with optimization of uncertain stochastic systems, in which uncertainty is described by a total variation distance constraint between the measures induced by the uncertain systems and the measure induced by the nominal system, while the pay-off is a linear functional of the uncertain measure. Robustness at the abstract setting is formulated as a minimax game, in which th...

Many problems in finance can be posed in terms of an optimal stochastic control. Some well-known examples include transaction cost/uncertain volatility models [17, 2, 25], passport options [1, 26], unequal borrowing/lending costs in option pricing [9], risk control in reinsurance [23], optimal withdrawals in variable annuities[13], optimal execution of trades [20, 19], and asset allocation [28,...

This paper concerns the continuous time mean-variance portfolio selection problem with a special nonlinear wealth equation. This nonlinear wealth equation has a nonsmooth coefficient and the dual method developed in [6] does not work. We invoke the HJB equation of this problem and give an explicit viscosity solution of the HJB equation. Furthermore, via this explicit viscosity solution, we obta...

The optimal trade execution problem is formulated in terms of a mean-variance tradeoff, as seen at the initial time. The mean-variance problem can be embedded in a Linear-Quadratic (LQ) optimal stochastic control problem, A semi-Lagrangian scheme is used to solve the resulting non-linear Hamilton Jacobi Bellman (HJB) PDE. This method is essentially independent of the form for the price impact f...

We solve the optimal asset allocation problem using a mean variance approach. The original mean variance optimization problem can be embedded into a class of auxiliary stochastic LinearQuadratic (LQ) problems using the method in (Zhou and Li, 2000; Li and Ng, 2000). We use a finite difference method with fully implicit timestepping to solve the resulting non-linear Hamilton-Jacobi-Bellman (HJB)...

The design of control laws for systems subject to complex state constraints still presents a significant challenge. This paper explores a dynamic programming approach to a specific class of such problems, that of reachability under state constraints. The problems are formulated in terms of nonstandard minmax and maxmin cost functionals, and the corresponding value functions are given in terms o...

In this paper, a type of fuzzy system structure is applied to heuristic dynamic programming (HDP) algorithm to solve nonlinear discrete-time Hamilton–Jacobi–Bellman (DT-HJB) problems. The fuzzy system here is adopted as a 0-order T–S fuzzy system using triangle membership functions (MFs). The convergence of HDP and approximability of the multivariate 0-order T–S fuzzy system is analyzed in this...

To sidestep the curse of dimensionality when computing solutions to Hamilton-Jacobi-Bellman partial differential equations (HJB PDE), we propose an algorithm that leverages a neural network to approximate the value function. We show that our final approximation of the value function generates near optimal controls which are guaranteed to successfully drive the system to a target state. Our fram...