Coherent control of a qubit is trap-free

There is a strong interest in optimal manipulating of quantum systems by external controls. Traps are controls which are optimal only locally but not globally. If they exist, they can be serious obstacles to the search of globally optimal controls in numerical and laboratory experiments, and for this reason the analysis of traps attracts considerable attention. In this paper we prove that for a wide range of control problems for two-level quantum systems all locally optimal controls are also globally optimal. Hence we conclude that two-level systems in general are trap-free. In particular, manipulating qubits—two-level quantum systems forming a basic building block for quantum computation—is free of traps for fundamental problems such as the state preparation and gate generation.     

Quantum Optimal Control Problems with a Sparsity Cost Functional

In this article, the investigation of a class of quantum optimal control problems with L¹ sparsity cost functionals is presented. The focus is on quantum systems modeled by Schrödinger-type equations with a bilinear control structure as it appears in many applications in nuclear magnetic resonance spectroscopy, quantum imaging, quantum computing, and in chemical and photochemical processes. In these problems, the choice of L¹ control spaces promotes sparse optimal control functions that are conveniently produced by laboratory pulse shapers. The characterization of L¹ quantum optimal controls and an efficient numerical semi-smooth Newton solution procedure are discussed.     

Maximum principle for optimal control problems involving impulse controls with nonsmooth data

This paper is concerned with the stochastic maximum principle for impulse optimal control problems of forward–backward systems, where the coefficients of the forward part are Lipschitz continuous. The domain of the regular controls is not necessarily convex. We establish a Pontryagins maximum principle for this control problem by applying Ekelands variational principle to a sequence of approximated control problems with smooth coefficients of the initial problems.     

Controllability of nonlinear discrete systems without differentiability assumption

The paper gives another approach to studying controllability of nonlinear discrete systems, which is based on proving the support principle for some boundary problems involving locally Lipschitzian set-valued maps. The approach enables us to develop sufficient conditions for various types of local controllability of nonlinear non-stationary discrete systems without differentiability assumption. For linear discrete systems with constrained states and controls, necessary and sufficient conditions for local controllability are given.     

Robust H∞ output dynamic observer-based control of uncertain time-delay systems

In this paper, the robustness and H_∞ control problems of output dynamic observer-based control for a class of uncertain linear systems with time delay are considered. Under no disturbance input, the asymptotic stabilization for uncertain time-delay systems will be guaranteed. Linear matrix inequality (LMI) optimization approach is used to design three classes of the H_∞ output dynamic controls. Based on the results of this paper, the constraint of matrix equality is not necessary for designing the observer-based controls.     

Time-optimal control of parabolic systems with boundary conditions involving time delays

The present paper is concerned with the control of certain parabolic systems whose boundary conditions involve time delays. The optimal controls are characterized in terms of an adjoint system and shown to be unique and bang-bang. These results extend to certain cases of nonlinear control and to fixed-time, minimum-norm control problems.     

Optimization of a Class of Nonlinear Dynamic Systems: New Efficient Method without Lagrange Multipliers

This paper deals with optimization of a class of nonlinear dynamic systems with n states and m control inputs commanded to move between two fixed states in a prescribed time. Using conventional procedures with Lagrange multipliers, it is well known that the optimal trajectory is the solution of a two-point boundary-value problem. In this paper, a new procedure for dynamic optimization is presented which relies on tools of feedback linearization to transform nonlinear dynamic systems into linear systems. In this new form, the states and controls can be written as higher derivatives of a subset of the states. Using this new form, it is possible to change constrained dynamic optimization problems into unconstrained problems. The necessary conditions for optimality are then solved efficiently using weighted residual methods.     

Solvability of mixed-type optimal control problems for distributed systems

In this paper we consider optimal control problems for distributed systems which are not solved with respect to the time derivative, where performance functionals take a quadratic form. We concurrently use the distributed and starting controls.     

Necessary conditions for optimality of singular controls in systems governed by partial differential equations

In this paper, we present a method to obtain necessary conditions for optimality of singular controls in systems governed by partial differential equations (distributed-parameter systems). The method is based on the one developed earlier by the author for singular control problems described by ordinary differential equations. As applications, we consider conditions for optimality of singular controls in a Darboux-Goursat system and in control systems that describe chemical processes.This research was supported in part by the National Science Foundation under Grant No. NSF-MCS-80-02337 at the University of Michigan.The author wishes to express his deep gratitude to Professor L. Cesari for his valuable guidance and constant encouragement during the preparation of this paper.     

Multi-parallel work centers scheduling optimization with shared or dedicated resources in low-volume low-variety production systems

A new methodology for modeling large-scale scheduling problems in low-volume low-variety production systems is proposed through this paper. Such scheduling problems are constrained by limited time and resources, where each work center is assigned a unique statement of work, to be completed on-time with the budgeted number of resources. Products assembled in low-volume low-variety production systems are processed through a series of stations referred to as work centers, where varying levels and classifications of resources are deployed onto the product. Aircraft, heavy aero-structures, and heavy military equipment are examples of products assembled in low-volume low-variety production systems. To ensure products are delivered on-time and on-budget, it is crucial to execute to a detailed schedule, such that all precedence, resource, zonal, and other constraints and characteristics inherent in such production systems are successfully satisfied. Despite the criticality of detailed schedules in delivering products on-time and on-budget, limited research is reported on mixed-integer programming approaches for scheduling optimization of activities in low-volume low-variety production systems. The discrete-time linear mixed-integer mathematical programming model developed in this paper fills the gap in the current literature with a direct impact on the organizations’ service levels and bottom line. The proposed mathematical programming models are validated through a real-world case-study of the assembly process of a narrow body aircraft to ensure compatibility in the modeling of large-scale industrial problems.     

Necessary conditions for optimality of singular controls

The present paper is concerned with the study of controls which are singular in the sense of the maximum principle. We obtain necessary conditions for optimality of singular controls in systems governed by ordinary differential equations. A useful feature of the method considered here is that it can be applied to optimal control problems with distributed parameters.this research was supported in part by the National Science Foundation under Grant No. NSF-MCS-80-02337 at the University of Michigan.The author wishes to express his deep gratitude to Professor L. Cesari for his valuable guidance and constant encouragement during the preparation of this paper.     

Prediction of swerving motion of a dual-spin projectile with lateral pulse jets in atmospheric flight

Using the linear theory for a dual-spin projectile in atmospheric flight, closed form expressions are obtained for swerving motion under the action of lateral pulse jets. Trajectory results generated by the linear theory equations and a fully nonlinear seven degree-of-freedom dual spin projectile model agree favorably. The analytic solution provides a relatively straightforward and computationally efficient means of trajectory estimation which is useful within smart weapon flight control systems. In order to accurately predict the impact point using the analytic solution, the dual-spin projectile linear model must be updated periodically. Terminal impact point prediction degrades rapidly as the linear model update interval is increased beyond a critical value. Control authority, as defined by the change in impact location due to a pulse jet firing, steadily decreases as a function of projectile down range position.     

Variational problems in the theory of optimum processes

This paper presents a review of the optimization problems for control processes described by ordinary differential equations and of the variational methods for solving these problems. The following cases are studied: problems with constraints on the controls or the coordinates, problems described by equations with discontinuous right-hand sides, problems with functionals depending on intermediate coordinates, and problems with given discontinuities in the coordinates. Variational problems of synthesis of optimal systems are also discussed. The method of solution is based on the multiplier rule and the Weierstrass necessary condition for the strong minimum of a functional. In some cases, the Legendre-Clebsch necessary condition for the weak minimum of a functional is used.     

Generalized green operator of a boundary-value problem with degenerate pulse influence

We establish necessary and sufficient conditions for the solvability of inhomogeneous linear boundaryvalue problems for systems of ordinary differential equations with pulse influence in the case where the number of boundary conditions is not equal to the order of the differential system (Noetherian problems). We construct a generalized Green operator for boundary-value problems not all solutions of which can be extended from the left endpoint to the right endpoint of the interval where these solutions are constructed.     

Chatter dynamic analysis for Van der Pol Equation with impulsive effect via the theory of flow switchability

In this paper, the phenomenon of free vibrations in LC circuit was introduced as well as some restrictions in the application of triode. Then we optimize the problems and present a certain kind of Van der Pol Equations which can be considered as a class of second-order impulsive switched systems. To investigate the chatter dynamics on such system, we turn to look for conditions that keep the complex pulse phenomena absent. We introduce several conceptions of theory of flow switchability and analyze the flow’s dynamical behaviors such as transversal property at a boundary in the normal direction of separation surface by constructing generic mappings. Some sufficient conditions for the absence of pulse phenomena and numerical illustrations of periodic motions are obtained.     

Asymptotic behavior of solutions of pulse systems with small parameter and markov switchings. I. Uniform boundedness of solutions

We consider pulse systems with Markov switchings. We study the problems of uniform boundedness of solutions of these systems and the stability of the systems with respect to the limit equation.     

A differential game formulation of a controlled network

This paper considers multiclass queueing network systems with fixed routing. With the service control as one player and the arrival and service rates as the other, the problem of network regulation can be formulated as a differential game. Representations of the value function are developed by studying the geometric properties of the associated Hamiltonians and are expressed in terms of related simpler halfspace problems. Also, a method of constructing the optimal feedback controls through the representation and the projected Isaacs equations is provided. The controls so constructed give both a guaranteed level of performance and robust stability over a range of rate perturbations.     

Error Estimates for the Approximation of a Class of Optimal Control Systems Governed by Linear PDEs

This paper deals with a class of optimal control problems in which the system is governed by a linear partial differential equation and the control is distributed and with constraints. The problem is posed in the framework of the theory of optimal control of systems. A numerical method is proposed to approximate the optimal control. In this method, the state space as well as the convex set of admissible controls are discretized. An abstract error estimate for the optimal control problem is obtained that depends on both the approximation of the state equation and the space of controls. This theoretical result is illustrated by some numerical examples from the literature.     

Dynamic vehicle routing: Status and prospects

Although most real-world vehicle routing problems are dynamic, the traditional methodological arsenal for this class of problems has been based on adaptations of static algorithms. Still, some important new methodological approaches have recently emerged. In addition, computer-based technologies such as electronic data interchange (EDI), geographic information systems (GIS), global positioning systems (GPS), and intelligent vehicle-highway systems (IVHS) have significantly enhanced the possibilities for efficient dynamic routing and have opened interesting directions for new research. This paper examines the main issues in this rapidly growing area, and surveys recent results and other advances. The assessment of possible impact of new technologies and the distinction of dynamic problems vis-à-vis their static counterparts are given emphasis.