Related papers: On the Hybrid Minimum Principle
This paper concerns state constrained optimal control problems, in which the dynamic constraint takes the form of a differential inclusion. If the differential inclusion does not depend on time, then the Hamiltonian, evaluated along the…
This work proposes a control law for a manipulator with the aim of realizing desired time-varying motion-force profiles in the presence of a stiff environment. In many cases, the interaction with the environment affects only one degree of…
In recent years, much effort in designing numerical methods for the simulation and optimization of mechanical systems has been put into schemes which are structure preserving. One particular class are variational integrators which are…
A Hamiltonian algorithm, both theoretical and numerical, to obtain the reduced equations implementing Pontryagine's Maximum Principle for singular linear-quadratic optimal control problems is presented. This algorithm is inspired on the…
In recent years, the embedding approach for solving switched optimal control problems has been developed in a series of papers. However, the embedding approach, which advantageously converts the hybrid optimal control problem to a classical…
State-space models (SSMs) are effective architectures for sequential modeling, but a rigorous theoretical understanding of their training dynamics is still lacking. In this work, we formulate the training of SSMs as an ensemble optimal…
Max-pressure (MP) is a decentralized adaptive traffic signal control approach that has been shown to maximize throughput for private vehicles. However, MP-based signal control algorithms do not differentiate the movement of transit vehicles…
The hybrid optimal control problem with reach time to a target set is addressed and the continuity and uniqueness of the associated value function is proved. Hybrid systems involves interaction of different types of dynamics: continuous and…
We consider a continuous-time positive bilinear control system (PBCS), i.e. a bilinear control system with Metzler matrices. The positive orthant is an invariant set of such a system, and the corresponding transition matrix C(t) is…
In this paper, we develop a rigorous optimal control-theoretic approach to Transformer training that respects key structural constraints such as (i) realized-input-independence during execution, (ii) the ensemble control nature of the…
We derive sufficient and necessary optimality conditions in terms of a stochastic maximum principle (SMP) for controls associated with cost functionals of mean-field type, under dynamics driven by a class of Markov chains of mean-field type…
Safety filters provide a practical approach for enforcing safety constraints in autonomous systems. While learning-based tools scale to high-dimensional systems, their performance depends on informative data that includes states likely to…
We consider a type of optimal switching problems with non-uniform execution delays and ramping. Such problems frequently occur in the operation of economical and engineering systems. We first provide a solution to the problem by applying a…
The fundamental theorem of the theory of optimal control, the Pontryagin maximum principle (PMP), is extended to the setting of almost Lie (AL) algebroids, geometrical objects generalizing Lie algebroids. This formulation of the PMP yields,…
This paper proposes a novel hybrid control framework for switched linear parameter-varying (LPV) systems under hysteresis switching logic. By introducing a controller state-reset mechanism, the hybrid LPV synthesis problem is reformulated…
Optimal pulse patterns (OPPs) are a modulation method in which the switching angles and levels of a switching signal are computed via an offline optimization procedure to minimize a performance metric, typically the harmonic distortions of…
For a wide class of Hamiltonians, a novel method to obtain lower and upper bounds for the lowest energy is presented. Unlike perturbative or variational techniques, this method does not involve the computation of any integral (a…
The aim of this paper is to investigate from the numerical point of view the possibility of coupling the Hamilton-Jacobi-Bellman (HJB) equation and Pontryagin's Minimum Principle (PMP) to solve some control problems. A rough approximation…
We study the problem of state transition on a finite time interval with minimal energy supply for linear port-Hamiltonian systems. While the cost functional of minimal energy supply is intrinsic to the port-Hamiltonian structure, the…
The noncanonical Hamiltonian formulation of magnetohydrodynamics (MHD) is used to construct variational principles for symmetric equilibrium configurations of magnetized plasma including flow. In particular, helical symmetry is considered…