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High fidelity quantum state transfer is an essential part of quantum information processing. In this regard, we address the problem of maximizing the fidelity in a quantum state transformation process satisfying the Liouville-von Neumann equation. By introducing fidelity as the performance index, we aim at maximizing the similarity of the final state density operator with the one of the desired target state. Optimality conditions in the form of a Maximum Principle of Pontryagin are given for the matrix-valued dynamic control systems propagating the probability density function. These provide a complete set of relations enabling the computation of the optimal control strategy., 6 pages

This work aims to investigate conditions for normality and non-degeneracy of the maximum principle for general state-constrained optimal control problems in which the state constraints are given by equalities and inequalities. Non-degeneracy is proved under a regularity condition formulated in terms of the limiting normal cone to the feasible control set. The same regularity condition implies normality of the maximum principle if one of the end-points is free.

This article concerns a simple instance of an optimal control problem paradigm combining bi-level optimization with sweeping processes, initially investigated in Khalil and Lobo Pereira (2019). This class of problems arises, for instance, in structured crowd motion control problems in a confined space. We propose a specific class of time-optimal bi-level problem with sweeping process dynamics represented in terms of a truncated normal cone at the lower level. We establish the necessary optimality conditions of the Maximum Principle of Pontryagin type in the Gamkrelidze’s form. Two techniques are at the core of the analysis: a) the smooth approximation of the low level sweeping control system, thereby avoiding the absence of Lipschitzianity inherent to the sweeping process, and, b) the flattening of the bi-level structure to a single level problem by using a exact penalization technique involving the value function of the low level problem to incorporate its inherent constraint in the bi-level structure. Necessary optimality conditions are applied to the resulting approximate flattened problem, and the main result of this article is obtained by passing to the limit.

This paper proposes a two-layer hierarchical control scheme for trajectory tracking of a multicopter system using attitude quaternion. We first present the differential flatness properties of the system and then, exploit them to design the feedback linearization laws for the position controller at the high control level. Next, the computed-torque control method is employed for stabilizing the attitude quaternion. The whole control scheme is illustrated through simulations while the position controller is further tested under experiments over a nano-drone quadcopter platform.

In this article, a Model Predictive Control (MPC) scheme that, by taking advantage of the control problem time invariant ingredients, replaces as much as possible the on-line computational burden of the conventional schemes, by off-line computation, is presented and its asymptotic stability shown. The generated data is stored onboard in look-up tables and recruited and adapted on-line with small computation effort according to the real-time context specified by communicated or sensed data. This scheme is particularly important to the increasing range of applications exhibiting severe real-time constraints. The approach presented here provides a better re-conciliation of onboard resources optimization with state feedback control - to deal with the typical a priori high uncertainty - while managing the formation with a low computational budget which otherwise might have a significant impact in power consumption.

A new method to prove non-degenerate optimality conditions in optimal control problems with state constraints of inequality type is proposed. This method involves the second-order derivative of the state constraint function and is based on the notion of the extended Hamilton-Pontryagin function and on the related optimality conditions.