Related papers: The Discrete-Time Geometric Maximum Principle
In this note our aim is to give a proof of the Pontryagin maximum principle for a general optimal control problem with running state constraints and smooth dynamics. Our proof is based on the classical Ekeland variational principle. The…
This paper is concerned with the partial information optimal control problem of mean-field type under partial observation, where the system is given by a controlled mean-field forward-backward stochastic differential equation with…
We prove a maximum principle of optimal control of stochastic delay equations on infinite horizon. We establish first and second sufficient stochastic maximum principles as well as necessary conditions for that problem. We illustrate our…
We consider a continuous time stochastic optimal control problem under both equality and inequality constraints on the expectation of some functionals of the controlled process. Under a qualification condition, we show that the problem is…
Stochastic maximum principle of nonlinear controlled forward-backward systems, where the set of strict (classical) controls need not be convex and the diffusion coefficient depends explicitly on the variable control, is an open problem…
Optimal control remains as one of the most versatile frameworks in systems theory, enabling applications ranging from classical robust control to real-time safe operation of fleets of vehicles. While some optimal control problems can be…
We prove necessary optimality conditions of Euler-Lagrange type for a problem of the calculus of variations with time delays, where the delay in the unknown function is different from the delay in its derivative. Then, a more general…
In this paper, we consider a class of time-optimal control problems governed by linear parabolic equations with mixed control-state constraints and end-point constraints, and without Tikhonov regularization term in the objective function.…
The purpose of this work is the development of space-time discretization schemes for phase-field optimal control problems. Specifically in the optimal control minimization problem, a tracking-type cost functional is minimized to steer the…
A continuous optimal control problem governed by an elliptic variational inequality was considered in Boukrouche-Tarzia, Comput. Optim. Appl., 53 (2012), 375-392 where the control variable is the internal energy $g$. It was proved the…
This paper presents a new and straightforward procedure for solving bilinear quadratic optimal control problem. In this method, first the original optimal control problem is transformed into a nonlinear twopoint boundary value problem…
We consider general shape optimization problems governed by Dirichlet boundary value problems. The proposed approach may be extended to other boundary conditions as well. It is based on a recent representation result for implicitly defined…
In this paper we study a discrete variational optimal control problem for the rigid body. The cost to be minimized is the external torque applied to move the rigid body from an initial condition to a pre-specified terminal condition.…
We consider the Lagrange problem of optimal control with unrestricted controls and address the question: under what conditions we can assure optimal controls are bounded? This question is related to the one of Lipschitzian regularity of…
This article develops variational integrators for a class of underactuated mechanical systems using the theory of discrete mechanics. Further, a discrete optimal control problem is formulated for the considered class of systems and…
This paper is concerned with the maximum principle of stochastic optimal control problems, where the coefficients of the state equation and the cost functional are uncertain, and the system is generally under Markovian regime switching.…
In this paper, we consider a state constrained optimal control problem governed by the transient Stokes equations. The state constraint is given by an L2 functional in space, which is required to fulfill a pointwise bound in time. The…
We investigate the time-optimal solution of the selective control of two uncoupled spin 1/2 particles. Using the Pontryagin Maximum Principle, we derive the global time-optimal pulses for two spins with different offsets. We show that the…
This work discusses the finite element discretization of an optimal control problem for the linear wave equation with time-dependent controls of bounded variation. The main focus lies on the convergence analysis of the discretization…
We study a class of optimal control problems governed by nonlinear stochastic equations of monotone type under certain coercivity and linear growth conditions. We give first order necessary conditions of optimality. A stochastic Pontryagin…