Many of the physical phenomena, like friction, backlash, drag, and etc., which appear in mechanical systems are inherently nonlinear and have destructive effects on the control systems behavior. Generally, they are modeled by hard nonlinearities. In this paper, two different methods are proposed to cope with the effects of hard nonlinearities which exist in friction various models. Simple inver...

In this paper, the portfolio management problem with stochastic wage income and inflation risk for CRRA investors is solved. real life, experience risk. This could be due to events such as COVID-19, fiscal policy, financial policy adjustments, climate change. We consider an agent who invests in market one risk-free security (e.g. a money account or bond) risky stock index). Our goal choose opti...

In previous work of the author and others, max-plus methods have been explored for solution of first-order, nonlinear Hamilton-Jacobi-Bellman partial differential equations (HJB PDEs) and corresponding nonlinear control problems. These methods exploit the max-plus linearity of the associated semigroups. In particular, although the problems are nonlinear, the semigroups are linear in the max-plu...

In previous work of the first author and others, max-plus methods have been explored for solution of first-order, nonlinear Hamilton–Jacobi–Bellman partial differential equations (HJB PDEs) and corresponding nonlinear control problems. Although max-plus basis expansion and max-plus finite-element methods can provide substantial computational-speed advantages, they still generally suffer from th...

Control of vehicle formations has emerged as a topic of significant interest to the controls community. In applications such as microsatellites and underwater vehicles, formations have the potential for greater functionality and versatility than individual vehicles. In this thesis, we investigate two topics relevant to control of vehicle formations: optimal vehicle control and cooperative contr...

We treat infinite horizon optimal control problems by solving the associated stationary Hamilton-Jacobi-Bellman (HJB) equation numerically to compute value function and an feedback law. The dynamical systems under consideration are spatial discretizations of non linear parabolic partial differential equations (PDE), which means that HJB is suffers from curse dimensionality. Its linearity handle...

In previous work of the author and others, max-plus methods have been explored for solution of first-order, nonlinear Hamilton-Jacobi-Bellman partial differential equations (HJB PDEs) and corresponding nonlinear control problems. Although max-plus basis expansion and max-plus finite-element methods provide computational-speed advantages, they still generally suffer from the curse-of-dimensional...

We present a new method for the numerical solution of the Hamilton Jacobi Bellman PDE that arises in an infinite time optimal control problem. The method can be of higher order to reduce ”the curse of dimensionality”. It proceeds in two stages. First the HJB PDE is solved in a neighborhod of the origin using the power series method of Al’brecht. From a boundary point of this neighborhood, an ex...

5 We determine the optimal dynamic investment policy for a mean quadratic variation ob6 jective function by numerical solution of a nonlinear Hamilton-Jacobi-Bellman (HJB) partial 7 differential equation (PDE). We compare the efficient frontiers and optimal investment poli8 cies for three mean variance like strategies: pre-commitment mean variance, time-consistent 9 mean variance, and mean quad...

We study an optimal investment and risk control problem for an insurer under stochastic factor. The insurer allocates his wealth across a riskless bond and a risky asset whose drift and volatility depend on a factor process. The risk process is modeled by a jump-diffusion with state-dependent jump measure. By maximizing the expected power utility of the terminal wealth, we characterize the opti...