Contraction theory is a recently developed dynamic analysis and nonlinear control system design tool based on an exact differential analysis of convergence. This paper extends contraction theory to local and global stability analysis of important classes of nonlinear distributed dynamics, such as convection-diffusion-reaction processes, Lagrangian and Hamilton-Jacobi dynamics, and optimal contr...

Abstract In classical texts, equations for fields are proposed without derivation of right-hand sides. Below, the sides Maxwell and Einstein derived within framework Vlasov–Maxwell–Einstein from a classical, but slightly more general principle least action Hamilton–Jacobi used to obtain cosmological solutions.

In 1964, the great evolutionary biologist, William Hamilton proposed that evolutionary selection would result in a population of individuals in which each acts to maximize its inclusive tness, which Hamilton de ned as a weighted average of its own survival probability and the survival probabilities of its kin, with the weights applied to relatives being proportional to their degree of relations...

We review the development and practical uses of a generalized Maupertuis least action principle in classical mechanics, in which the action is varied under the constraint of fixed mean energy for the trial trajectory. The original Maupertuis (Euler-Lagrange) principle constrains the energy at every point along the trajectory. The generalized Maupertuis principle is equivalent to Hamilton's prin...

In this paper, we study one kind of stochastic recursive optimal control problem with Markovian Switching. problem, the cost functional is described by solution backward differential equations Markov chains. We prove dynamic programming principle for and show that value function unique viscosity corresponding Hamilton-Jacobi-Bellman equation.

This paper is a survey of the Hamilton-Jacobi partial differential equation. We begin with its origins in Hamilton’s formulation of classical mechanics. Next, we show how the equation can fail to have a proper solution. Setting this issue aside temporarily, we move to a problem of optimal control to show another area in which the equation arises naturally. In the final section, we present some ...

Using the Hamilton-Jacobi-Bellman equation, we derive both a Keynes-Ramsey rule and a closed form solution for an optimal consumption-investment problem with labor income. The utility function is unbounded and uncertainty stems from a Poisson process. Our results can be derived because of the proofs presented in the accompanying paper by Sennewald (2006). Additional examples are given which hig...

This paper proposes an adaptive control method for robotic manipulators with input toque uncertainties. For each link of manipulators, it is assumed that the input torque uncertainties can be divided into unknown parameters term and bounded disturbance term. In addition, all the parameters for input torque uncertainties and robot are unknown. The proposed method ensures that the unknown paramet...

This paper examines the problem of link position tracking control for robot manipulators with input toque uncertainty. It is assumed that the input torque uncertainty can be regarded as dead-zone phenomena at each link of manipulator and all the system parameters for robotic manipulator and dead-zone model are unknown. The proposed method ensures that the unknown parameters are estimated adapti...