Active optimal vibration control for a lumped system

A dynamic absorber with active torque generating DC motors has been studied as an actively suppressing vibration system. A typical two-level spring-lumped mass system with slider undergoing internal excitation vibrations has been considered. Both the main mass and the secondary absorber mass have DC servo motors planned to suppress the amplitude of vibration. State variable techniques are used to formulate the complete system and three optimal control schemes are used to control such a system. First, the discrete time optimal disturbance rejection control for a system with known disturbance is considered, in the second approach a digital optimal control for a linear quadratic regulator problem is studied and in the last approach a discrete optimal control with selected system characteristic matrix is investigated. The response of the system obtained from these optimal control approaches are compared with the response without control action first. The performance of these optimal control approaches are also compared and the availability of implementations of them are evaluated.     

Optimal Control of the Dynamic Viscoelastic Stress-Strain State of a Composite Body

New optimal control problems for the dynamic viscoelastic stress-strain state of a composite body with quadratic cost functionals are considered. Existence theorems for unique optimal controls are proved for all the cases considered. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 73–92, September–October 2005.     

Complex Optimal Control of a Thermally Stressed State of a Two-Component Body

New problems of optimal control for a thermally stressed state of a two-component solid body are considered in the paper. The body contains a thin and a weakly thermally penetrating inclusion. The existence of unique optimal controls is proved for every described case with quadratic cost functionals.     

Motion control of a rotor with a cavity with a viscous fluid

A formulation and solution procedure of optimal control problems for perturbed relative uniform motion of a body with a cavity filled with a viscous incompressible fluid are proposed. In this paper, the case with a cylinder is considered; however, this approach is basically true for the a cavity of an arbitrary form. The formula for the angular velocity of perturbed motion depending on an external perturbing element is devised. After that, we have a possibility to set different optimal control problems and apply the formalism elaborated in the optimal control theory. Two illustrated problems are given.     

A control for a rotor with a cavity containing an ideal liquid, II

For a motion perturbed with respect to uniform rotation of a body with a cavity containing an ideal liquid, two problems of optimal control with terminal functionals are considered. The model with discontinuous optimal control is studied. Numerical solutions for the problem with constraints on control of the type of inequalities are obtained.     

Constructing a Mean-Variance Optimal Hedge under a Limited Investment Capital

Solution of an optimal mean-variance hedging problem under conditions of a limited initial investment capital is considered. The initial problem is transformed by means of the numéraire-changing method into an equivalent one that corresponds to the martingale case. It is shown that an optimal hedge may be achieved when maximum possible investment recourses are used.     

Time-optimal crossing of a sphere in a viscous medium

Multidimensional controlled motions of a material point in a homogeneous viscous medium are considered. The problem of steering this point to a fixed sphere (from the outside or from the inside) for a minimum time by a force with a bounded absolute value is solved. For an arbitrary initial position and any initial velocity, optimal control both in the open-loop form of the program and in the feedback form, optimal time and Bellman function, as well as optimal phase trajectory are constructed in an explicit form using the Pontryagin’s maximum principle. The solution is studied analytically and numerically, and qualitative mechanical properties of optimal characteristics of motion are found (nonmonotonic dependence of optimal time on the value of initial vector of velocity, discontinuity of the Bellman function, and so on).     

Rate limited time optimal control of a planar pendulum

Time optimal control problems often admit as solution bang-bang controls but they present several drawbacks in real applications where additional degrees of regularity are desirable. In this paper, the rate limited time optimal swing up of an inverted pendulum is considered and necessary conditions that have to be satisfied by optimal trajectories in the presence of rate constraints are derived. A comparison between this approach and the results from the standard time optimal problem is reported.     

Linear optimal control strategies for production systems with a discrete-event demand pattern

A class of production systems are considered in this paper with the aim of determining closed-loop strategies providing the production effort as functions of the system state. The key feature of the considered class of systems is that the demand and the way it is satisfied are asynchronous sequences of part requests and instantaneous withdrawals, respectively, generated by discrete-event processes, whereas the production process has continuous-time dynamics. The optimization problem, whose objective is to minimize inventory and lateness costs, is restated as an optimal control problem by exploiting some structural properties of the optimal solution. Then, optimal closed-loop strategies are found with dynamic programming techniques.     

Optimal Control of a System Described by Hyperbolic Equation with Conjugation Conditions

New problems of optimal control of distributed systems described by a hyperbolic equation with conjugation conditions and a quadratic cost function are considered in the paper. Unique optimal control existence theorems are proved for all the analyzed cases.     

On the structure of optimal sets for a quantum channel

Special sets of states, called optimal, which are related to the Holevo capacity and to the minimal output entropy of a quantum channel, are considered. By methods of convex analysis and operator theory, structural properties of optimal sets and conditions of their coincidence are explored for an arbitrary channel. It is shown that strong additivity of the Holevo capacity for two given channels provides projective relations between optimal sets for the tensor product of these channels and optimal sets for the individual channels.     

Optimal traffic flow schedules in a semi-parallel tree network

Scheduling of traffic through a tree-structured model under a semi-parallel constraint is considered. The problem of finding the optimal root without resort to exhaustive search is studied. Several sufficient conditions to exclude a node as a optimal root candidate are presented.     

Optimal control of a poisson source

Controlled Poisson sources with known rate and with unknown rate but known prior rate distribution are considered and optimal controls are computed in special cases for each.     

Optimal control of an elliptic system with a nonsymmetric state operator

New optimal control problems for elliptic systems with contact conditions and nonsymmetric state operators are considered. Existence theorems for optimal solutions are proved. High-accuracy schemes for approximating optimal controls are proposed for the case where the set of admissible controls coincides with a complete Hilbert space. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 67–85, November–December 2005.     

非线性椭圆型种群模型的最优控制问题

The optimal control problem for a nonlinear elliptic population system is considered. First, under certain hypotheses, the existence and uniqueness of coexistence state solutions are shown. Then the existence of the optimal control is given and the optimality system is established.     

On the Optimal Control Problem of a Nonlinear Elliptic Population System

The optimal control problem for a nonlinear elliptic population system is considered. First, under certain hypotheses, the existence and uniqueness of coexistence state solutions are shown. Then the existence of the optimal control is given and the optimality system is established.     

Optimal Choice of Prices and Flows in a Complex Open Industrial System

Production processes are very important subject of economic study. These processes are irreversible. Processes in nonhomogenious systems are considered taking into account restrictions on the finite intensities of the resources flows. The problem on determination of optimal prices is considered for a firm with given internal structure.     

Optimal control laws for lot-sizing and timing of jobs on a single production facility

The optimal control of a single machine processing a certain number of jobs and modeled as a discrete-event dynamic system is considered. The number of jobs and their sequence are fixed, whereas their timing and sizes represent the control variables of the system. The objective function to be optimized is a weighted sum of the quadratic earliness and tardiness of each job, and of the quadratic deviations of job lot sizes and actual machine service speeds from those specified by the production demand and by the regular machine speeds. An optimization problem with quadratic cost function and nonlinear constraints is stated and formalized as a multistage optimal control problem. Necessary conditions to be satisfied by an optimal control sequence are derived. A simpler model is also considered in which the machine speeds are fixed; in this case, the control problem is solved by a procedure making use of dynamic programming techniques. The optimal control laws at each stage are thus obtained.     

Structure of the Optimal Organization of a Continuum of Executives

The problem of designing the optimal structure of an organization was considered as that of determining a graph with the minimum cost of a group of executives realizing the given functions. Design of the optimal organizational structure of a continuum of executives was considered. The cost of the optimal organizational tree of one function was determined. The notion of ideally coordinated collection of functions for which determination of the optimal structure is substantially simpler was introduced.     

The mean squared loss control problem for a partially observed Markov chain

In this article, we study the optimal control of a partially observed Markov chain for which a mean squared cost functional is minimised. Both the terminal cost and the running cost are considered. Minimum principles are established. In both cases, if the optimal control is Markov feedback, more explicit forms for the stochastic integrands and adjoint processes are obtained.