Terminal control in flat systems

The article considers the application of dynamical feedback control to a special class of nonlinear dynamical systems — so-called flat systems. Flat system, linearizing output, and Lie-Backlund isomorphism are among the concepts reviewed. A man-machine algorithm is proposed for solving the terminal control problem for an arbitrary flat system with known linearizing outputs. __________ Translated from Nelineinaya Dinamika i Upravlenie, No. 3, pp. 191–200, 2003.     

Asymptotic Weighted-Periodicity of the Impulsive Parabolic Equation with Time Delay

The main aim of this paper is to investigate the effects of the impulse and time delay on a typeof parabolic equations.In view of the characteristics of the equation,a particular iteration scheme is adopted.The results show that Under certain conditions on the coefficients of the equation and the impulse,the solutionoscillates in a particular manner—called"asymptotic weighted-periodicity".     

Conditional Viability for Impulse Differential Games

We introduce in this paper the concept of “impulse evolutionary game”. Examples of evolutionary games are usual differential games, differentiable games with history (path-dependent differential games), mutational differential games, etc. Impulse evolutionary systems and games cover in particular “hybrid systems” as well as “qualitative systems”. The conditional viability kernel of a constrained set (with a target) is the set of initial states such that for all strategies (regarded as continuous feedbacks) played by the second player, there exists a strategy of the first player such that the associated run starting from this initial state satisfies the constraints until it hits the target. This paper characterizes the concept of conditional viability kernel for “qualitative games” and of conditional valuation function for “qualitative games” maximinimizing an intertemporal criterion. The theorems obtained so far about viability/capturability issues for evolutionary systems, conditional viability for differential games and about impulse and hybrid systems are used to provide characterizations of conditional viability under impulse evolutionary games.     

On optimal control of monotone nonlinear systems with a generalized interaction

We study the problem of the existence of the optimal control of monotone nonlinear distributed systems with generalized interaction. The method proosed allows one to study monotone nonlinear systems with point, impulse, point impulse, and nonstationary controls as well as with their generalizations. Bibliography: 2 titles. Translated fromObcyslyuval'na ta Prykladna Matematyka,, No. 81, 1997, pp 60–61     

On Galilean connections and the first jet bundle

We see how the first jet bundle of curves into affine space can be realized as a homogeneous space of the Galilean group. Cartan connections with this model are precisely the geometric structure of second-order ordinary differential equations under time-preserving transformations — sometimes called KCC-theory. With certain regularity conditions, we show that any such Cartan connection induces “laboratory” coordinate systems, and the geodesic equations in this coordinates form a system of second-order ordinary differential equations. We then show the converse — the “fundamental theorem” — that given such a coordinate system, and a system of second order ordinary differential equations, there exists regular Cartan connections yielding these, and such connections are completely determined by their torsion.     

Mixed Volume Computation for Semi-Mixed Systems

   Abstract. The Li—Li algorithm produced in [11] for the mixed volume computation of fully mixed polynomial systems is reconstructed in this article for general semi-mixed polynomial systems. Taking the special structure of the semi-mixed supports of the systems into account, the resulting algorithm, illustrated by numerical results, can dramatically speed up the mixed volume computation, especially when the systems are unmixed. Even when applied to fully mixed systems, the new algorithm improves the speed of the Li—Li algorithm by a considerable amount.     

Topics in isotopic pairs and their representations. II. The general supercase

Isotopic pairs—algebraic objects suitable for describing some forms of non-Hamiltonian (magnetic-type) interactions of Hamiltonian systems at the quantum level—are considered with maximum generality within the framework of the vector superalgebra formalism. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 111, No. 1, pp. 149–158, April, 1997.     

Relaxation techniques for strictly convex network problems

Gauss—Seidel type relaxation techniques are applied in the context of strictly convex pure networks with separable cost functions. The algorithm is an extension of the Bertsekas—Tseng approach for solving the linear network problem and its dual as a pair of monotropic programming problems. The method is extended to cover the class of generalized network problems. Alternative internal tactics for the dual problem are examined. Computational experiments —aimed at the improved efficiency of the algorithm — are presented. This research was supported in part by National Science Foundation Grant No. DCR-8401098-A0l.     

State-constrained control problems with neither coercivity norL 1 bounds on the controls

Summary A state-constrained, nonlinear, minimum problem is considered with dynamics depending sublinearly on a control which is not bounded in theL ¹ norm. Because of the lack of coercivity, the value map fails to be continuous, even in the unconstrained case. However, we prove that under suitable assumptions—which guarantee the continuity of the value maps of the problems withL ¹-bounded controls—the value map is upper semicontinuous and solves a Bellman equation with a continuous Hamiltonian. Moreover, the map obtained by by replacing its values at the horizon t=T with the values of the cost function turns out to be the maximal subsolution of the corresponding value problem. Entrata in Redazione il 31 dicembre 1997.     

k-out-of-n-system with repair:T-policy

We consider a k-out-of-n system with repair underT-policy. Life time of each component is exponentially distributed with parameter λ. Server is called to the system after the elapse ofT time units since his departure after completion of repair of all failed units in the previous cycle or until accumulation ofn — k failed units, whichever occurs first. Service time is assumed to be exponential with rateμ.T is also exponentially distributed with parameter α. System state probabilities in finite time and long run are derived for (i) cold (ii) warm (iii) hot systems. Several characteristics of these systems are obtained. A control problem is also investigated and numerical illustrations are provided. It is proved that the expected profit to the system is concave in α and hence global maximum exists.     

Equivalence between Nonlinear H ∞ Control Problems and Existence of Viscosity Solutions of Hamilton—Jacobi—Isaacs Equations rid="*" id="*" This work was written while the author was visiting the University of California at Santa Barbara. He was partially supported by Consiglio Nazionale delle Ricerche of Italy.

In this paper we extend to completely general nonlinear systems the result stating that the suboptimal control problem is solved if and only if the corresponding Hamilton—Jacobi—Isaacs (HJI) equation has a nonnegative (super)solution. This is well known for linear systems, using the Riccati equation instead of the HJI equation. We do this using the theory of differential games and viscosity solutions. Accepted 14 February 1997     

Image synthesis for autostereoscopic systems

The article considers image synthesis for autostereoscopic systems — systems that enable the viewer to perceive three-dimensional images without any special devices, such as glasses. The general image synthesis problem for such systems is stated and an efficient algorithm is proposed for its solution. Some applications of the proposed methodology for two types of units are described: a stereo display and a stereo projection system. We examine the optimization of technical system parameters with the objective of enlarging the region where the viewer sees a three-dimensional image.     

The Expected loss in the discretization of multistage stochastic programming problems—estimation and convergence rate

In the present paper, the approximate computation of a multistage stochastic programming problem (MSSPP) is studied. First, the MSSPP and its discretization are defined. Second, the expected loss caused by the usage of the “approximate” solution instead of the “exact” one is studied. Third, new results concerning approximate computation of expectations are presented. Finally, the main results of the paper—an upper bound of the expected loss and an estimate of the convergence rate of the expected loss—are stated.     

Primitive linear series on curves

In this paper we study a new numerical invariant ℓ of curvesC which is related to the primitive linear series onC. (Primitive series—defined below—are the essential complete and special linear series onC.) The curves with ℓ≤3 are classified, and it is shown that for a given value of ℓ the curve is a double covering if its genus is sufficiently high. The main tool are dimension theorems of H. Martens-Mumford-type for the varieties of special divisors ofC, and we prove two refinements of these theorems.     

Solutions to the systems of functional equations of multivalued logic

General issues concerning solutions to the systems of functional equations of multivalued logic—the dependence of solutions on functional constants and the possibility of constructing the systems of equations having a given unique solution or a given set of solutions—are considered.     

Optimal Control of Elliptic Variational Inequalities

Optimality systems for optimal control problems governed by elliptic variational inequalities are derived. Existence of appropriately defined Lagrange multipliers is proved. A primal—dual active set method is proposed to solve the optimality systems numerically. Examples with and without lack of strict complementarity are included. Accepted 5 March 1999     

Pathology of infinite systems of linear first order differential equations with constant coefficients

Summary The properties of solutions of finite systems are analyzed and it is shown by examples how these properties may be distorted and ultimately lost in passing from finite to infinite systems. To Enrico Bompiani on his Scientific Jubilee This research was supported in part by United States Army through its Office of Ordnance Research under Grant DA-ORD-12. — Most of the results have been presented to various organisations such as Section A of the American Association for the Advancement of Science and mathematics colloquia at the universities of Leningrad, Moscow, and Toronto.     

A Class of Hamilton—Jacobi Equations with Unbounded Coefficients in Hilbert Spaces

We establish existence and comparison theorems for a class of Hamilton—Jacobi equations. The class of Hamilton—Jacobi equations includes and is broader than those studied in [8] We apply the existence and uniqueness results to characterizing the value functions associated with the optimal control of systems governed by partial differential equations of parabolic type. Accepted 11 May 2001. Online publication 5 October 2001.