Related papers: The Discrete-Time Geometric Maximum Principle
In this paper, we consider optimal control problems derived by stochastic systems with delay, where control domains are non-convex and the diffusion coefficients depend on control variables. By an estimate of the integral of…
We investigate symmetry reduction of optimal control problems for left-invariant control systems on Lie groups, with partial symmetry breaking cost functions. Our approach emphasizes the role of variational principles and considers a…
This article provides quasi-optimal a priori error estimates for an optimal control problem constrained by an elliptic obstacle problem where the finite element discretization is carried out using the symmetric interior penalty…
We present a novel framework for optimal control in both classical and quantum systems. Our approach leverages the Dirac--Bergmann algorithm: a systematic method for formulating and solving constrained dynamical systems. In contrast to the…
We extend the Pontryagin Maximum Principle (PMP) to the geometric setting of almost-Lie (AL) algebroids -- objects which generalize Lie algebroids. The result may be understood as a very general reduction scheme for optimal control problems…
In this paper, we consider a varying terminal time structure for the stochastic optimal control problem under state constraints, in which the terminal time varies with the mean value of the state. In this new stochastic optimal control…
In this work, we investigate the optimal control problem for continuous-time Markov decision processes with the random impact of the environment. We provide conditions to show the existence of optimal controls under finite-horizon criteria.…
In this paper, we propose an efficient implementation of deep policy gradient method (PGM) for optimal control problems in continuous time. The proposed method has the ability to manage the allocation of computational resources, number of…
In this study, we consider an optimal control problem driven by a stochastic differential system with a stopping time terminal cost functional. We establish the stochastic maximum principle for this new kind of an optimal control problem by…
In this paper, we study a discrete-time stochastic optimal control problem under distribution uncertainty with convex control domain. By weak convergence method and Sion's minimax theorem, we obtain the variational inequality for cost…
Since the second half of the 20th century, Pontryagin's Maximum Principle has been widely discussed and used as a method to solve optimal control problems in medicine, robotics, finance, engineering, astronomy. Here, we focus on the proof…
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…
We present a new geometric unfolding of a prototype problem of optimal control theory, the Mayer problem. This approach is crucially based on the Stokes Theorem and yields to a necessary and sufficient condition that characterizes the…
We study the reduction of degrees of freedom for the equations that determine necessary optimality conditions for extrema in an optimal control problem for a multiagent system by exploiting the physical symmetries of agents, where the…
On the ground of origins of the theory of Lie groups and Lie algebras, their (co)adjoint representations, and the Pontryagin maximum principle for the time-optimal problem are given an independent foundation for methods of geodesic vector…
Direct methods for the simulation of optimal control problems apply a specific discretization to the dynamics of the problem, and the discrete adjoint method is suitable to calculate corresponding conditions to approximate an optimal…
In many problems in optimal control, one seeks to minimise an objective function subject to constraints on the velocity of the system. Imposing these constraints directly -- the ``hard-constrained'' approach -- is often analytically and…
At the core of optimal control theory is the Pontryagin maximum principle - the celebrated first order necessary optimality condition - whose solutions are called extremals and which are obtained through a function called Hamiltonian, akin…
This article treats optimal sparse control problems with multiple constraints defined at intermediate points of the time domain. For such problems with intermediate constraints, we first establish a new Pontryagin maximum principle that…
Discrete control systems, as considered here, refer to the control theory of discrete-time Lagrangian or Hamiltonian systems. These discrete-time models are based on a discrete variational principle, and are part of the broader field of…