Related papers: On the Hybrid Minimum Principle
In this study, we address a control-constrained optimal control problem pertaining to the transformation of quantum states. Our objective is to navigate a quantum system from an initial state to a desired target state while adhering to the…
In this paper we combine two main topics in mechanics and optimal control theory: contact Hamiltonian systems and Pontryagin Maximum Principle. As an important result, among others, we develop a contact Pontryagin Maximum Principle that…
Exploiting our previous results on higher order controlled Lagrangians in [Nonlinear Anal. {\bf 207} (2021), 112263], we derive here an analogue of the classical first order Pontryagin Maximum Principle (PMP) for cost minimising problems…
Optimal control theory is developed for the task of obtaining a primary objective in a subspace of the Hilbert space while avoiding other subspaces of the Hilbert space. The primary objective can be a state-to-state transition or a unitary…
A controlled quantum system possesses a search landscape defined by the target physical objective as a function of the controls. This paper focuses on the landscape for the transition probability Pif between the states of a finite level…
We consider an optimal control problem for a system of local continuity equations on a space of probability measures. Such systems can be viewed as macroscopic models of ensembles of non-interacting particles or homotypic individuals,…
We study the design problems of state observers and tracking controllers for a class of hybrid systems whose state jumps. The idea is to utilize the well-known method of gluing the jump set (a part of domain where the jumps take place) onto…
IIn this paper, we study a partially observed progressive optimal control problem of forward-backward stochastic differential equations with random jumps, where the control domain is not necessarily convex, and the control variable enter…
Hybrid dynamical systems are systems which undergo both continuous and discrete transitions. The Bolza problem from optimal control theory was applied to these systems and a hybrid version of Pontryagin's maximum principle was presented.…
Hybrid systems are dynamical systems with continuous-time and discrete-time components in their dynamics. When hybrid systems are defined on a principal bundle we are able to define two classes of impacts for the discrete-time transition of…
This paper presents a nonlinear-model based hybrid optimal control technique to compute a suboptimal power-split strategy for power/energy management in a parallel hybrid electric vehicle (PHEV). The power-split strategy is obtained as…
In this paper, we prove the necessary and sufficient maximum principles (NSMPs in short) for the optimal control of systems described by a quasilinear stochastic heat equation within convex control domains, which all the coefficients…
Hybrid systems are characterized by having an interaction between continuous dynamics and discrete events. The contribution of this paper is to provide hybrid systems with a novel geometric formulation so that controls can be added. Using…
In this paper we provide a thorough, rigorous theoretical framework to assess optimality guarantees of sampling-based algorithms for drift control systems: systems that, loosely speaking, can not stop instantaneously due to momentum. We…
We describe a generalization of the Hierarchical Dirichlet Process Hidden Markov Model (HDP-HMM) which is able to encode prior information that state transitions are more likely between "nearby" states. This is accomplished by defining a…
In this paper we propose an Alternating Direction Method of Multipliers (ADMM) algorithm for solving a Model Predictive Control (MPC) optimization problem, in which the system has state and input constraints and a nonlinear input map. The…
We study a control problem where the state equation is a nonlinear partial differential equation of the calculus of variation in a bounded domain, perturbed by noise. We allow the control to act on the boundary and set stochastic boundary…
In mechanics, common energy principles are based on fixed boundary conditions. However, in bridge engineering structures, it is usually necessary to adjust the boundary conditions to make the structure's internal force reasonable and save…
Without exact knowledge of the true system dynamics, optimal control of non-linear continuous-time systems requires careful treatment under epistemic uncertainty. In this work, we translate a probabilistic interpretation of the Pontryagin…
In most sampling algorithms, including Hamiltonian Monte Carlo, transition rates between states correspond to the probability of making a transition in a single time step, and are constrained to be less than or equal to 1. We derive a…