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...

We investigate in this work a fully-discrete semi-Lagrangian approximation of second order possibly degenerate Hamilton–Jacobi–Bellman (HJB) equations on bounded domain $${\mathcal {O}}\subset {\mathbb {R}}^N$$ ( $$N=1,2,3$$ ) with oblique derivatives boundary conditions. These appear naturally the study optimal control diffusion processes reflection at domain. The proposed scheme is shown to s...

This paper studies the infinite-horizon optimal consumption problem with a path-dependent reference under exponential utility. The performance is measured by difference between nonnegative rate and fraction of historical maximum. running maximum process chosen as an auxiliary state process, hence value function depends on two variables. Hamilton–Jacobi–Bellman (HJB) equation can be heuristicall...

The optimization of boiler soot blowing strategy and repair plan is investigated based on Hamilton–Jacobi–Bellman (HJB) equation in this paper. From the perspective soot, we build a Markov process with three modes to describe running process. For sake applying HJB equation, cost function constructed according built model, derived by using optimality principle. optimal can be obtained solving eq...

We develop a computationally efficient learning-based forward–backward stochastic differential equations (FBSDE) controller for both continuous and hybrid dynamical (HD) systems subject to noise state constraints. Solutions optimal control (SOC) problems satisfy the Hamilton–Jacobi–Bellman (HJB) equation. Using current FBSDE-based solutions, can be obtained from HJB using deep neural networks (...

The level of phosphodiesterase (PDE) activity is lower in collagenase-isolated human fat cells than in adipose tissue fragments. The inhibition is not species-specific since collagenase also inhibits PDE in rat adipose tissue and bovine heart. In subcellular fractions from isolated fat cells, the PDE activities were lowest in the plasma membrane-enriched fractions and highest in the cytosolic f...

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...

We consider a class of diffusions controlled through the drift and jump size, driven by Lévy process nondegenerate Wiener process, we study infinite horizon (ergodic) risk-sensitive control problems for this model. start with Dirichlet eigenvalue problem in smooth bounded domains, which also allows us to generalize current results literature on exit rate problems. Then average minimization maxi...