In this work, we introduce Pontryagin Neural Networks (PoNNs) and employ them to learn the optimal control actions for unconstrained constrained intercept problems. PoNNs represent a particular family of Physics-Informed (PINNs) specifically designed tackling problems via Minimum Principle (PMP) application (e.g., indirect method). The PMP provides first-order necessary optimality conditions, w...

The target of this paper is to draw attention to some important relations between different procedures of state space synthesis of discrete linear systems optimizing the quadratic cost function. Common form of the synthesis concerns one-dimensional and multi-dimensional control problems solved by Second Method of Lyapunov, Maximum Principle of Pontryagin and by Bellamn's Dynamic Programming. Em...

We study optimal control problems for general unstructured nonlinear differential-algebraic equations of arbitrary index. In particular, we derive necessary conditions in the case of linear-quadratic control problems and extend them to the general nonlinear case. We also present a Pontryagin maximum principle for general unstructured nonlinear DAEs in the case of restricted controls. Moreover, ...

Reach set computation is a basic component of many veri cation and control synthesis procedures. E ective computation schemes are available for discrete systems described by nite state machines and continuous-variable systems described by linear di erential inequalities. This paper suggests an approach based on the Pontryagin maximum principle of optimal control theory. The approach is elaborat...

Abstract In this paper, we combine two main topics in mechanics and optimal control theory: contact Hamiltonian systems Pontryagin maximum principle. As an important result, among others, develop a principle that permits to deal with problems dissipation. We also consider the Herglotz problem, which is simultaneously generalization of variational problem. An application study thermodynamic syst...

We study a trajectory-planning problem whose solution path evolves by means of a Lie group action and passes near a designated set of target positions at particular times. This is a higher-order variational problem in optimal control, motivated by potential applications in computational anatomy and quantum control. Reduction by symmetry in such problems naturally summons methods from Lie group ...

Abstract. We study a class of mean-field stochastic differential equations driven by a fractional Brownian motion with Hurst parameter H ∈ (1/2, 1) and a related stochastic control problem. We derive a Pontryagin type maximum principle and the associated adjoint mean-field backward stochastic differential equation driven by a classical Brownian motion, and we prove that under certain assumption...