共查询到20条相似文献,搜索用时 31 毫秒
1.
V. I. Maksimov 《Differential Equations》2016,52(11):1442-1452
We study the problem of guaranteed positional guidance of a linear partially observable control system with distributed parameters to a convex target set at a given time. The problem is considered under incomplete information. More precisely, we assume that the system is subjected to an unknown disturbance; in addition, the initial state is assumed to be unknown as well. Further, the sets of admissible disturbances and the set of admissible initial states, which is assumed to be finite, are known. An algorithm for solving the problem is suggested. 相似文献
2.
A. V. Kryazhimskii 《Proceedings of the Steklov Institute of Mathematics》2015,291(1):113-127
The method of open-loop control packages is a tool for stating the solvability of guaranteed closed-loop control problems under incomplete information on the observed states. In this paper, a solution method is specified for the problem of guaranteed closed-loop guidance of a linear control system to a convex target set at a prescribed point in time. It is assumed that the observed signal on the system’s states is linear and the set of its admissible initial states is finite. It is proved that the problem under consideration is equivalent to the problem of open-loop guidance of an extended linear control system to an extended convex target set. Using a separation theorem for convex sets, we derive a solvability criterion, which reduces to solving a finite-dimensional optimization problem. An illustrative example is considered. 相似文献
3.
Self-similar asymptotics describing nonlinear waves in elastic media with dispersion and dissipation
A. G. Kulikovskii A. P. Chugainova 《Computational Mathematics and Mathematical Physics》2010,50(12):2145-2156
Solutions of problems for the system of equations describing weakly nonlinear quasi-transverse waves in an elastic weakly
anisotropic medium are studied analytically and numerically. It is assumed that dissipation and dispersion are important for
small-scale processes. Dispersion is taken into account by terms involving the third derivatives of the shear strains with
respect to the coordinate, in contrast to the previously considered case when dispersion was determined by terms with second
derivatives. In large-scale processes, dispersion and dissipation can be neglected and the system of equations is hyperbolic.
The indicated small-scale processes determine the structure of discontinuities and a set of admissible discontinuities (with
a steady-state structure). This set is such that the solution of a self-similar Riemann problem constructed using solutions
of hyperbolic equations and admissible discontinuities is not unique. Asymptotics of non-self-similar problems for equations
with dissipation and dispersion were numerically found, and it appeared that they correspond to self-similar solutions of
the Riemann problem. In the case of nonunique self-similar solutions, it is shown that the initial conditions specified as
a smoothed step lead to a certain self-similar solution implemented as the asymptotics of the unsteady problem depending on
the smoothing method. 相似文献
4.
B. V. Gera 《Journal of Mathematical Sciences》1997,86(2):2578-2584
We propose a statement and computational scheme for the inverse problem of recovering the temperature field and the moisture
distribution in a body with incompletely known initial conditions. We give additional relations on the integral values of
the unknown functions and introduce a test for the choice of a unique solution of the problem from the set of admissible temperature
and moisture functions. We state conditions for independence of the additional data and obtain systems of equations and conditions
that close the initial indeterminate problem. We study in detail the example of heat-moisture conduction in a layer.
Translated fromMatematichni Metodi ta Fiziko-mekhanichni Polya, Vol. 39, No. 1, 1996, pp. 66–73. 相似文献
5.
External Estimates for Reachable Sets of a Control System with Uncertainty and Combined Nonlinearity
T. F. Filippova 《Proceedings of the Steklov Institute of Mathematics》2018,301(1):32-43
The problem of estimating the trajectory tubes of a nonlinear control dynamic system with uncertainty in the initial data is studied. It is assumed that the dynamic system has a special structure in which the nonlinear terms are defined by quadratic forms in the state coordinates and the values of uncertain initial states and admissible controls are subject to ellipsoidal constraints. The matrix of the linear terms in the velocities of the system is not known exactly; it belongs to a given compact set in the corresponding space. Thus, the dynamics of the system is complicated by the presence of bilinear components in the righthand sides of the differential equations of the system. We consider a complicated case and generalize the author’s earlier results. More exactly, we assume the simultaneous presence in the dynamics of the system of bilinear functions and quadratic forms (without the assumption of their positive definiteness) and we also take into account the uncertainty in the initial data and the impact of the control actions, which may also be treated here as undefined additive disturbances. The presence of all these factors greatly complicates the study of the problem and requires an adequate analysis, which constitutes the main purpose of this study. The paper presents algorithms for estimating the reachable sets of a nonlinear control system of this type. The results are illustrated by examples. 相似文献
6.
P. G. Surkov 《Proceedings of the Steklov Institute of Mathematics》2017,296(1):218-227
The problem of guaranteed closed-loop guidance by a given time under incomplete information on the initial state is studied for a dynamical control system with delay by means of the method of open-loop control packages. A solvability criterion is proved for this problem in the case of a finite set of admissible initial states. The proposed technique is illustrated by a specific linear control system of differential equations with delay. 相似文献
7.
In this paper, we propose a memory state feedback model predictive control (MPC) law for a discrete-time uncertain state delayed system with input constraints. The model uncertainty is assumed to be polytopic, and the delay is assumed to be unknown, but with a known upper bound. We derive a sufficient condition for cost monotonicity in terms of LMI, which can be easily solved by an efficient convex optimization algorithm. A delayed state dependent quadratic function with an estimated delay index is considered for incorporating MPC problem formulation. The MPC problem is formulated to minimize the upper bound of infinite horizon cost that satisfies the sufficient conditions. Therefore, a less conservative sufficient conditions in terms of linear matrix inequality (LMI) can be derived to design a more robust MPC algorithm. A numerical example is included to illustrate the effectiveness of the proposed method. 相似文献
8.
《Communications in Nonlinear Science & Numerical Simulation》2011,16(11):4153-4157
Robust estimation of the amplitude, frequency and bias of unknown noisy sinusoidal signals is considered in this paper. It is only assumed that the measurements noise is bounded without any additional information such as stationarity, uncorrelation or type of distribution. In this context, the aim is to compute the set of all admissible values that are consistent with the measurements and with the error bound. The estimation problem is formulated as a Constraint Satisfaction Problem (CSP) where the amplitude, frequency and bias constitute the variables and a function relating them to the output is the constraint. Interval constraint propagation techniques are used to solve, in a guaranteed way, this problem. In order to illustrate the principle and the efficiency of the approach, numerical simulations are provided. 相似文献
9.
T. F. Filippova 《Proceedings of the Steklov Institute of Mathematics》2010,271(1):75-84
The problem of estimating trajectory tubes of a nonlinear control dynamical system with uncertainty in initial data is considered. It is assumed that the dynamical system has a special structure, in which nonlinear terms are quadratic in phase coordinates and the values of the uncertain initial states and admissible controls are subject to ellipsoidal constraints. Differential equations are found that describe the dynamics of the ellipsoidal estimates of reachable sets of the nonlinear dynamical system under consideration. To estimate reachable sets of the nonlinear differential inclusion corresponding to the control system, we use results from the theory of ellipsoidal estimation and the theory of evolution equations for set-valued states of dynamical systems under uncertainty. 相似文献
10.
F. Bahrami 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(17):6287-6294
This paper is concerned with two rearrangement optimization problems. These problems are motivated by two eigenvalue problems which depend nonlinearly on the eigenvalues. We consider a rational and a quadratic eigenvalue problem with Dirichlet’s boundary condition and investigate two related optimization problems where the goal function is the corresponding first eigenvalue. The first eigenvalue in the rational eigenvalue problem represents the ground state energy of a nanostructured quantum dot. In both the problems, the admissible set is a rearrangement class of a given function. 相似文献
11.
F. Ben Abdelaziz P. Lang R. Nadeau 《The Journal of the Operational Research Society》1994,45(11):1324-1334
In most of the approaches to the Multiobjective Stochastic Linear Programming problem that have been proposed in the literature, the notion of quality of a solution is not adequately defined. We reconsider this problem from a decision point of view, in contexts where either the decision maker's preference structure cannot be described by a utility function, or where this structure is expressed by an unknown non-decreasing utility function and the probability distribution of the random parameters is unknown. We define a fundamental set of ‘pointwise admissible’ solutions, as well as several subsets of particular interest. We discuss the relevance of these various pointwise efficient sets, their interrelations, and their practical identification. 相似文献
12.
V. I. Maksimov 《Differential Equations》2017,53(11):1449-1457
We study the problem of guaranteed guidance of an elliptic control system to a given objective set at a given time under the assumption that the system is subjected to an unknown disturbance. The case in which only part of the state coordinates are measured is considered. For this problem, we suggest a solution algorithm based on a combination of dynamic inversion theory and the extremal shift principle. 相似文献
13.
ARVANITIS K. G.; TSIRIKOS A. S. 《IMA Journal of Mathematical Control and Information》1999,16(1):1-13
The problem of input-output linearization with simultaneousdecoupling via restricted state feedback for nonsquare nonlinearsystems is investigated in this paper. The problem is treatedon the basis of a new algebraic approach whose main featureis that it reduces the determination of the admissible state-feedbackcontrol laws to the solution of an algebraic and a first-orderpartial differential system of equations. Verifiable necessaryand sufficient conditions of an algebraic nature are establishedfor the solvability of the aforementioned problem, which relyon the solvability of these systems of equations. Moreover,an explicit expression for a special admissible restricted state-feedbackcontroller is analytically derived. 相似文献
14.
The problem of the boundary kinematic control of one-dimensional oscillatory systems with distributed parameters in a finite time interval is investigated. The displacement of one of the ends is assumed to be controlled; the other end is assumed to be free. The system is subjected to additional disturbing actions, distributed and concentrated at the ends. The problem is stated by selecting an admissible control to transfer the system from an arbitrary state to the required final state, provided that the integral quadratic functional is minimal. Using the Fourier method, the maximum principle method and the L-problem of moments method, the problem of optimal control is solved explicitly in closed form, and, by d’Alembert's wave propagation method, is represented in terms of the initial functions. The requirements concerning the disturbing actions are established, and also those concerning the initial and final distributions and the duration of the control process, leading to smooth solutions of the problem. The problem of synthesizing the optimal control is discussed. The results are of interest when investigating problems of precision control of mechanical systems possessing considerable elastic compliance (shafts, beams, springs, strings, etc.) 相似文献
15.
O. I. Kushlyk 《Ukrainian Mathematical Journal》1991,43(12):1533-1538
The optimal control problem for a linear system of differential equations with delay for which the initial function on the initial set is the control function is considered. Phase constraints with variable times are imposed on the trajectory of the object. Necessary optimality conditions of controls in admissible classes are obtained.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 12, pp. 1647–1652, December, 1991. 相似文献
16.
Robust output feedback stabilization for two-dimensional continuous systems in roesser form 总被引:1,自引:0,他引:1
James Lam Shengyuan Xu Yun Zou Zhiping Lin K. Galkowski 《Applied Mathematics Letters》2004,17(12):81-1341
This paper considers the problem of robust stabilization via dynamic output feedbackcontrollers for uncertain two-dimensional continuous systems described by the Roesser's state space model. The parameter uncertainties are assumed to be norm-bounded appearing in all the matrices of the system model. A sufficient condition for the existence of dynamic output feedback controllers guaranteeing the asymptotic stability of the closed-loop system for all admissible uncertainties is proposed. A desired dynamic output feedback controller can be constructed by solving a set of linear matrix inequalities. Finally, an illustrative example is provided to demonstrate the applicability and effectiveness of the proposed method. 相似文献
17.
The authors consider the problem of constructing an admissible open-loop control of bounded energy steering a nonlinear system
from a given initial state to a given final state under the condition that the first-approximation system is completely controllable.
The convergent iterative procedure for computing an admissible control is verified. It is shown that a nonlinear system locally
controllable with respect to the first approximation becomes globally completely controllable for any boundary conditions
from the stability region if the initial nonlinear system is stabilizable up to the asymptotic stability in the large and
in the whole and the nonlinear terms either satisfy the global Cauchy-Lipschitz condition or are polynomials of a certain
degree in state coordinates with arbitrary coefficients. The nonlinear system of algebraic equations to computation of whose
solutions the problem of constructing the admissible control reduces is indicated.
__________
Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 26, Nonlinear
Dynamics, 2005. 相似文献
18.
The problem of transferring a controlled linear system with a disturbance to a prescribed target set (a hyperplane at a prescribed time instant) is considered. The control and disturbance are subject to geometrical constraints. The original transfer problem is reduced to a scalar one. Then, for a given transferring linear feedback strategy, the respective transferable set is studied, i.e. the set of all the initial positions in the time/state plane, from which the target set is reached, respecting the control constraints, against any admissible disturbance. Necessary and sufficient conditions for the existence of the transferable set are derived, its set-theoretical properties are established, the algorithm of its boundary construction is proposed, the boundary smoothness is studied. Illustrative examples are presented. 相似文献
19.
The paper deals with a linear time-dependent dynamic system with scalar control and input uncertainty (disturbance). Two admissible classes of input uncertainty realizations are considered: the class of measurable bounded functions and the class of measurable quadratically integrable functions. The problem to be studied is the existence of a state feedback control with measurable bounded time realizations transferring the system to a given hyperplane (a target set) from any initial position in a prescribed time for any admissible input uncertainty realization. Necessary and sufficient conditions for the existence of such a control are derived, based on the explicit construction of this control by using an auxilary zero-sum linear-quadratic differential game with a cheap control for the minimizing player. Examples illustrting the theoritical results are presented. 相似文献
20.
V. I. Maksimov 《Proceedings of the Steklov Institute of Mathematics》2017,297(1):147-158
We discuss the problem of guaranteed guidance of a linear control system by a fixed time under the assumption that the system is subject to an unknown disturbance. We consider the case when a part of state coordinates are measured and the set of unknown initial states is finite. We specify a solution algorithm based on the combination of the package approach, the theory of dynamic inversion, and the extremal shift method. 相似文献