Related papers: A Remarkable Property of the Dynamic Optimization …
In this paper, we propose novel learning frameworks to tackle optimal control problems by applying the Pontryagin maximum principle and then solving for a Hamiltonian dynamical system. Applying the Pontryagin maximum principle to the…
A geometric approach to time-dependent optimal control problems is proposed. This formulation is based on the Skinner and Rusk formalism for Lagrangian and Hamiltonian systems. The corresponding unified formalism developed for optimal…
Consider, on the one part, a general nonlinear finite-dimensional optimal control problem and assume that it has a unique solution whose state is denoted by $x^*$. On the other part, consider the sampled-data control version of it. Under…
Necessary conditions for existence of normal extremals in optimal control of systems subject to nonholonomic constraints are derived as solutions of a constrained second order variational problems. In this work, a geometric interpretation…
We derive a Maximum Principle for optimal control problems with constraints given by the coupling of a system of ODEs and a PDE of Vlasov-type. Such problems arise naturally as ${\Gamma}$-limits of optimal control problems subject to ODE…
Pontrygin-type maximum principle is extended for the present value Hamiltonian systems and current value Hamiltonian systems of nonlinear difference equations for uniform time step $h$. A new method termed as a discrete time current value…
Optimal control problems with symmetries often admit a non stationary turnpike property called trim turnpike, which characterizes the convergence of optimal solutions to certain symmetry induced trajectories called trim primitives. In this…
In this paper, we discuss a new general formulation of fractional optimal control problems whose performance index is in the fractional integral form and the dynamics are given by a set of fractional differential equations in the Caputo…
Optimal Control Theory is a powerful mathematical tool, which has known a rapid development since the 1950s, mainly for engineering applications. More recently, it has become a widely used method to improve process performance in quantum…
We obtain a maximum principle for stochastic control problem of general controlled stochastic differential systems driven by fractional Brownian motions (of Hurst parameter $H>1/2$). This maximum principle specifies a system of equations…
A least action principle for damping motion has been previously proposed with a Hamiltonian and a Lagrangian containing the energy dissipated by friction. Due to the space-time nonlocality of the Lagrangian, mathematical uncertainties…
This paper provides necessary conditions of optimality for optimal control problems with time delays in both state and control variables. Different versions of the necessary conditions cover fixed end-time problems and, under additional…
We consider the optimal control problem of minimizing some quadratic functional over all possible solutions of an internally controlled multi-dimensional heat equation with a periodic terminal state constraint. This problem has a unique…
We consider nonsmooth optimal control problems subject to a linear elliptic partial differential equation with homogeneous Dirichlet boundary conditions. It is well-known that local solutions satisfy the celebrated Pontryagin maximum…
In this paper we consider the Hamiltonian formulation of the equations of incompressible ideal fluid flow from the point of view of optimal control theory. The equations are compared to the finite symmetric rigid body equations analyzed…
The key element of the approach to the theory of necessary conditions in optimal control discussed in the paper is reduction of the original constrained problem to unconstrained minimization with subsequent application of a suitable…
Numerical ``direct'' approaches to time-optimal control often fail to find solutions that are singular in the sense of the Pontryagin Maximum Principle, performing better when searching for saturated (bang-bang) solutions. In previous work…
A number of optimization algorithms have been inspired by the physics of Newtonian motion. Here, we ask the question: do algorithms themselves obey some ``natural laws of motion,'' and can they be derived by an application of these laws? We…
The paper concerns the study of the Pontryagin Maximum Principle for an infinite dimensional and infinite horizon boundary control problem for linear partial differential equations. The optimal control model has already been studied both in…
We obtain the dynamic programming equations and optimality conditions akin to Pontryagin's extremum principle for certain mathematical models of hybrid control systems.