Optimal data placement in two-headed disk systems

A problem inherent to the performance of disk systems is the data placement in cyinders in such a way that the seek time is minimized. If successive searchers are independent, then the optimal placement for conventional one-headed disk systems is the organ-pipe arrangement. According to this arrangement the most frequent cylinder is placed in the central location, while the less frequent cylinders are placed right and left alternatively. This paper proves that the optimal placement for two-headed disk systems is the camel arrangement, which may be viewed as two consecutive organ-pipe arrangements. It is also proved that, for a two-headed disk system withN=2(2n+1) cylinders, the total number of these optimal camel arrangements is exp₂ (N/2+1).Professor J. G. Kollias died untimely December 1989.     

Optimal coefficient control in parabolic systems

We consider an optimal coefficient control problem for a linear parabolic equation. For this problem, we study well-posedness issues and obtain necessary optimality conditions.     

Optimal feedback control of bilinear systems

Feedback synthesis of optimal constrained controls for single-input bilinear systems is considered. Quadratic cost functionals (with and without quadratic control penalization) are modified by the inclusion of additional nonnegative state penalizing functions in the respective cost integrands. The latter functions are chosen so as to regularize the problems, in the sense that feedback solutions of particularly simple form are obtained. Finite and infinite time horizon problem formulations are treated, and associated aspects of feedback stabilization of bilinear systems are discussed.     

Optimal control of infinite-dimensional uncertain systems

In this paper, we consider a minimax problem of optimal control for a class of strongly nonlinear uncertain evolution equations on a Banach space. We prove the existence of optimal controls. A nontrivial example of a class of systems governed by a nonlinear partial differential equation with uncertain spatial parameters is presented for illustration.This work was supported in part by the National Science and Engineering Research Council of Canada under Grant No. A7109 and The Engineering Faculty Development Fund, University of Ottawa.The authors would like to thank the anonymous reviewers for their valuable comments and suggestions.     

Optimal control of impulsive hybrid systems

In this paper, we deal with optimization techniques for a class of hybrid systems that comprise continuous controllable dynamics and impulses (jumps) in the state. Using the mathematical techniques of distributional derivatives and impulse differential equations, we rewrite the original hybrid control system as a system with autonomous location transitions. For the obtained auxiliary dynamical system and the corresponding optimal control problem (OCP), we apply the Lagrange approach and derive the reduced gradient formulas. Moreover, we formulate necessary optimality conditions for the above hybrid OCPs, and discuss the newly elaborated Pontryagin-type Maximum Principle for impulsive OCPs. As in the case of the conventional OCPs, the proposed first order optimization techniques provide a basis for constructive computational algorithms.     

Optimal guaranteed control of delay systems

A linear problem of optimal guaranteed control of a delay system is considered in which geometric constraints on control actions and terminal constraints on states are present. A new concept of a state of the problem that represents a finite-dimensional vector is introduced. Three kinds of optimal feedback are defined. We describe methods for implementing open-loop and closable optimal feedbacks. They are based on a fast dual method for the correction of optimal programs. The results are illustrated by examples.     

Optimal control of nonlinear hereditary systems

A function space Λ is introduced for the study of nonlinear hereditary differential equations. The properties of Λ include: it is a Banach space under the supremum norm, the continuous functions constitute a closed proper subspace, and the unit ball is sequentially compact in the weak-¹ topology. Existence, uniqueness, and continuous dependence results are obtained for solutions of a broad class of initial value problems. An optimization problem is formulated for systems which are affine in the control, and solutions are approximated by means of a sequence of problems which are finite-dimensional in the control.     

Optimal observation and control in linear systems

The paper consists of two parts. In Part I, we consider the optimal observation problem for a nondeterministic linear system by examining results of a deep processing of an output signal of a dynamical measurement device (sensor). The problem studied is an auxiliary problem for studying the optimal control problem for dynamical systems under set-uncertainty conditions in Part II. The methods for the construction of a posteriori, program, and positional solutions are described. The results are illustrated by examining an example of an optimal observation and control problem of a fourth-order mechanical system. __________ Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 23, Optimal Control, 2005.     

Robust pole placement controller design in LMI region for uncertain and disturbed switched systems

This paper concerns the state feedback control for continuous-time, disturbed and uncertain linear switched systems with arbitrary switching rules. The main result of this work consists in getting a LMI (Linear Matrix Inequalities) condition guaranteeing a robust pole placement according to some desired specifications. Then, external disturbance attenuation with a fixed rate according to the H_∞ criterion is ensured. This is obtained thanks to the existence of a common quadratic Lyapunov function for all sub-systems. Finally, an academic example illustrates the efficiency of the developed approach.     

Optimal control over nonlinear stochastic systems

The synthesis of optimal control over nonlinear stochastic systems that are described by the Itô equations is reduced to the solution of recurrence relations derived from the Bellman stochastic equation.     

Optimal control of undamped Sobolev-type retarded systems

The optimal control problem for a system whose evolution is described by a Sobolev-type second-order retarded operator-differential equation is studied. The main assumption is that a restriction is imposed on the derivatives of the resolvent of the quadratic operator pencil on a ray in the right half-plane. Several applications to systems described by non-Kovalevskaya-type partial differential equations are considered.     

Optimal trajectories of infinite-horizon deterministic control systems

We study the infinite-horizon deterministic control problem of minimizing ₀ ^T L(z, ) dt, T, whereL(z, ·) is convex in for fixedz but not necessarily jointly convex in (z, ). We prove the existence of a solution to the infinite-horizon Bellman equation and use it to define a differential inclusion, which reduces in certain cases to an ordinary differential equation. We discuss cases where solutions of this differential inclusion (equation) provide optimal solutions (in the overtaking optimality sense) to the optimization problem.A quantity of special interest is the minimal long-run average-cost growth rate. We compute it explicitly and show that it is equal to min _x L(x, 0) in the following two cases: one is the scalar casen = 1 and the other is' when the integrand is in a separated form      

Optimal control of discrete systems involving delays

For a class of discrete systems with delays and additional state-dependent constraints, a maximum principle is derived. The existing general results in the field of discrete optimal control theory make it possible to deal with this class of optimization problems in a straight-forward way. The formulation of the results presented is fairly general and includes a number of cases when the constraints are specified in more detail.     

Optimal resource consumption control of perturbed systems

A method for calculating the optimal resource consumption control of perturbed dynamic systems is developed. This method includes both normal and singular solutions. According to the method proposed, the problem is subdivided into three independent tasks: (1) consideration of the effects of perturbations on the system, (2) computation of the optimal control structure, and (3) computation of the switching instants of the optimal control. The consideration of the influence of perturbations on the system and the transfer to a nonzero final state are reduced to the transformation of the initial and final states of the system. The control structure calculation is based on a specific method of quasi-optimal control formation. The control switching instants are found by using the relationship between deviations in the initial conditions of the conjugate system and deviations of the phase trajectory at the final instant. An iterative algorithm is developed, and its characteristics are considered. Results of modeling and numerical calculations are presented.     

Optimal control of vibrationally excited locomotion systems

Optimal controls are constructed for two types of mobile systems propelling themselves due to relative oscillatory motions of their parts. The system of the first type is modelled by a rigid body (main body) to which two links are attached by revolute joints. All three bodies interact with the environment with the forces depending on the velocity of motion of these bodies relative to the environment. The system is controlled by high-frequency periodic angular oscillations of the links relative to the main body. The system of the other type consists of two bodies, one of which (the main body) interacts with the environment and with the other body (internal body), which interacts with the main body but does not interact with the environment. The system is controlled by periodic oscillations of the internal body relative to the main body. For both systems, the motions with the main body moving along a horizontal straight line are considered. Optimal control laws that maximize the average velocity of the main body are found.     

Optimal control of time delay parabolic systems

Various optimal control problems for linear parabolic systems with multiple constant time delays are considered. Necessary and sufficient conditions of optimality are derived for the Neumann problem. The optimal control is obtained in the feedback formMaking use of the results of Schwartz's, the representation of the optimal feedback control is given. A simple example of application is also provided     

Optimal periodic control of lumped parameter systems

Some subsidiary conditions for determining the superiority of the periodic control to the steady control are derived. The necessary condition for the optimality of period is established by adding a new condition to the well-known condition which can yield merely the stationary value of the objective function. Some considerations are also given for a system having a single state variable and a single control variable and for the linear control problem, which very often appears in many practical cases.     

Optimal nonlinear feedback control of quasi-Hamiltonian systems

An innovative strategy for optimal nonlinear feedback control of linear or nonlinear stochastic dynamic systems is proposed based on the stochastic averaging method for quasi-Hamiltonian systems and stochastic dynamic programming principle. Feedback control forces of a system are divided into conservative parts and dissipative parts. The conservative parts are so selected that the energy distribution in the controlled system is as requested as possible. Then the response of the system with known conservative control forces is reduced to a controlled diffusion process by using the stochastic averaging method. The dissipative parts of control forces are obtained from solving the stochastic dynamic programming equation. Project supported by the National Natural Science Foundation of China (Grant No. 19672054) and Cao Guangbiao High Science and Technology Development Foundation of Zhejiang University.