A deterministic optimal control problem is solved for a control-affine nonlin-ear system with a nonquadratic cost function. We algebraically solve the Hamilton-Jacobi equation for the gradient of the value function. This eliminates the need to explicitly solve the solution of a Hamilton-Jacobi partial differential equation. We interpret the value function in terms of the control Lyapunov functi...

A novel approach to solving the optimal nonlin-ear control problem is presented. Instead of seeking a global approximation to the Hamilton-Jacobi-Bellman equation, a local approximation is obtained by successively solving the Generalized Hamilton-Jacobi-Bellman (GHJB) equation on a local region of the state space. The optimal control is generated by solving the GHJB equation algebraically at se...

Larson, B.A., 1992. Principles of stochastic dynamic optimization in resource management: the continuous-time case. Agric. Econ., 7: 91-107. A wide range of problems in economics, agriculture, and natural resource management have been analyzed using continuous-time optimal control models, where the state variables change over time in a stochastic manner. Using a firm-level investment model and ...

We study a second-order stationary Hamilton-Jacobi equation in innnite dimension. This equation is nonlinear and convex with respect to the rst-order term. We use properties of a the transition semigroup associated to the linear equation to write the Hamilton-Jacobi equation in integral form and we prove that this solution is the pointwise limit of a uniformly bounded sequence of classical solu...

The paper is devoted to singular perturbation problems with a finite number of scales where both the dynamics and the costs may oscillate. Under some coercivity assumptions on the Hamiltonian, we prove that the value functions converge locally uniformly to the solution of an effective Cauchy problem for a limit Hamilton-Jacobi equation and that the effective operators preserve several propertie...