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1
Content available remote On the Fuzzy Control Stochastic Differential Systems
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In this paper, fuzzy control stochastic differential systems are introduced. The existence and some comparison results on solutions of fuzzy control stochastic differential systems and on sheaf-solutions of sheaf fuzzy control stochastic systems are provided. The continuous dependence of solutions and sheaf-solutions on initials and controls is investigated. The results obtained are correct and meaningful for the theory control. (original abstract)
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Content available remote Stabilization of Linear Systems in Random Horizon via Control
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The control problem with random horizon at finie number of events is investigated in this paper, where the general aim of control is the stabilization (in mean square sense) of linear system at minimum cost. This problem is reduced to the task of optima control with established finite horizon. Moreover, the differences between stabilization with fixed and random horizons are also given. To illustrate those differences a numerical example is included. (original abstract)
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In this paper, we introduce four new classes of open sets in general Euclidean space RN. It is shown that every such class of open sets is compact under the Hausdorff distance. The result is applied to a shape optimization problem of p-Laplacian equation. The existence of the optimal solution is presented. (original abstract)
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Content available remote Fractional Order PI Controllers for TCP Packet Flow Ensuring Given Modulus Margins
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An Active Queue Management (AQM) robust control strategy for Traffic Control Protocol (TCP) data transfer is proposed. To this purpose, the TCP behaviour is first approximated by a second-order model with delayed input obtained from the linearization of an efficient and commonly used nonlinear fluid-based model. The adopted feedback control structure uses a fractional-order PI controller. To ensure the desired robustness, the parameter regions where such a controller guarantees a given modulus margin (inverse of the H∞ norm of the sensitivity function) are derived. An example commonly used in the literature is worked out to show that the suggested graphically-based design technique is simple to apply while it limits the effects of disturbances and of the unmodelled dynamics. (original abstract)
We consider a steady-state heat conduction problem P for the Poisson equation with Mied Bondary conditions in a bounded multidimensional domain Ω. We also consider a family of problems Pα for the same Poisson equation with mixed boundary conditions, α > 0 being the heat transfer coefficient defined on a portion Γ1 of the boundary. We formulate simultaneous distributed and Neumann boundary optimal control problems on the internal energy g within Ω and the heat flux q, defined on the complementary portion Γ2 of the boundary of Ω for quadratic cost functional. Here, the control variable is the vector (g,q). We prove existence and uniqueness of the optimal control (g,q) for the system state of P, and (gα,qα) for the system state of Pα, for each α > 0, and we give the corresponding optimality conditions. We prove strong convergence, in suitable Sobolev spaces, of the vectorial optimal controls, system and adjoint states governed by the problems Pα to the corresponding vectorial optimal control, system and adjoint states governed by the problem P, when the parameter α goes to infinity. We also obtain estimations between the solutions of these vectorial optimal control problems and the solution of two scalar optimal control problems characterized by fixed g (with boundary optimal control q) and fixed q (with distributed optimal control g), respectively, for cases both of α > 0 and α = ∞. (original abstract)
This paper considers the problem of designing a robust H∞ fuzzy state-feedback controller for a class of nonlinear Markovian jump systems with time-varying delay. A novel design methodology has been proposed for designing a controller that guarantees the L2-gain of the mapping from the exogenous input noise to the regulated output to be less than some prescribed value. Solutions to the problem are provided in terms of linear matrix inequalities. To illustrate the effectiveness of the design developed in this paper, a numerical example is also provided. (original abstract)
An optimal control problem with a state constraint of inequality type and with dynamics described by a semilinear hyperbolic equation in divergence form with the non-homogeneous boundary condition of the third kind is considered. The state constraint contains a functional parameter that belongs to the class of continuous functions and occurs as an additive term. We study the properties of solutions of linear hyperbolic equations in divergence form with measures in the original data and compute the first variations of functionals on the basis of a so-called two-parameter needle variation of controls. We consider the necessary conditions for minimizing sequences in an optimal control problem with a pointwise in time state constraint of inequality type and with dynamics described by a semilinear hyperbolic equation in divergence form with the non-homogeneous boundary condition of the third kind. For the parametric optimization problem, we also consider regularity and normality conditions stipulated by the differential properties of its value function. (original abstract)
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Content available remote A simple proof of the maximum principle with endpoint constraints
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The paper presents a new, relatively simple proof of Pontryagin's maximum principle for the canonical problem of optimal control, with equality and inequality constraints imposed on the trajectory endpoints. The proof combines together two ideas, which appeared separately in the earlier works: application of the Karush-John conditions for finite-dimensional problems, and using packages of needle variations. (original abstract)
Niniejszy referat analizuje kierunki rozwoju narodowych systemów nadzoru korporacyjnego. Ramy teoretyczne przedstawiają kilka rożnych ujęć, z których można analizować role mechanizmów nadzorczych stosowanych w poszczególnych systemach. W ostatnich czasach w dobie postępującej globalizacji gospodarki oraz internacjonalizacji rynków kapitałowych obserwuje się wiele zmian powodujących zacieranie granic pomiędzy rożnymi systemami. Zdania autorów odnośnie rozwoju narodowych mechanizmów regulacyjnych są podzielone, jednakże większość wskazuje na stopniową ewolucje tych systemów w kierunku modelu amerykańskiego. (abstrakt oryginalny)
Obok tradycyjnych już pytań, który model lepiej sprosta wymaganiom coraz trudniejszego rynku i z jakich źródeł przedsiębiorstwa powinny pozyskiwać kapitał, zaczęto stawiać pytania czy posiadanie kontrolnego pakietu głosów w przedsiębiorstwie: - wpływa na "dystrybucję" wartości przedsiębiorstwa; - przynosi dodatkowe korzyści kontrolującym; - czy jakie są determinanty tych korzyści. W opracowaniu podejmuję tę tematykę starając się przedstawić genezę problemu i rozważania teoretyczne. Celem opracowania jest również dostarczenie dowodów na istnienie korzyści z posiadania kontroli, zmierzenie wartość kontroli w Polsce i zbadanie jej determinantów. (fragment tekstu)
W praktyce najczęściej kontrola w przedsiębiorstwie lokuje się pomiędzy dwiema koncepcjami: kontrolą biurokratyczną i kontrolą klanu, które zostały szczegółowo przedstawione w artykule. Autorka jednak zaznaczyła, że większość organizacji nie ogranicza się tylko do jednego z wymienionych sposobów projektowania kontroli. Najczęściej organizacja wybiera jedną z nich, a następnie wprowadza pewne instrumenty kontroli rynkowej. Kluczową sprawą w każdym, ze sposobów jest zaprojektowanie odpowiedniego systemu kontroli, który pomoże organizacji w osiąganiu jej celów.
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Content available remote Generalized α-V-univex Functions for Multiobjective Variational Control Problems
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The purpose of this paper is to introduce a new class of α-V-univex / generalized α-V-univex functions for a class of multiobjective variational control problems. Moreover, sufficient optimality conditions and Mond-Weir type duality results, associated with the multiobjective variational control problem, are established under aforesaid assumptions. (original abstract)
This paper analyses a trajectory tracking control problem for a wheeled mobile robot, Rusing integration of a kinematic neural controller (KNC) and a torque neural controller (TNC), in which both the kinematic and dynamic models contain uncertainties and disturbances. The proposed adaptive neural controller (PANC) is composed of the KNC and the TNC and is designed with use of a modeling technique of Gaussian radial basis function neural networks (RBFNNs). The KNC is a variable structure controller, based on the sliding mode theory and is applied to compensate for the disturbances of the wheeled mobile robot kinematics. The TNC is an inertia-based controller composed of a dynamic neural controller (DNC) and a robust neural compensator (RNC) applied to compensate for the wheeled mobile robot dynamics, bounded unknown disturbances, and neural network modeling errors. To minimize the problems found in practical implementations of the classical variable structure controllers (VSC) and sliding mode controllers (SMC), and to eliminate the chattering phenomenon, the nonlinear and continuous KNC and RNC of the TNC are applied in lieu of the discontinuous components of the control signals that are present in classical forms. Additionally, the PANC neither requires the knowledge of the wheeled mobile robot kinematics and dynamics nor the timeconsuming training process. Stability analysis, convergence of the tracking errors to zero, and the learning algorithms for the weights are guaranteed based on the Lyapunov method. Simulation results are provided to demonstrate the effectiveness of the proposed approach. (original abstract)
An optimal control problem with a state constraint of inequality type and with dynamics described by a semilinear hyperbolic equation in divergence form with the non-homogeneous boundary condition of the third kind is considered. The state constraint contains a functional parameter that belongs to the class of continuous functions and occurs as an additive term. We study the properties of solutions of linear hyperbolic equations in divergence form with measures in the original data and compute the first variations of functionals on the basis of a so-called two-parameter needle variation of controls. We consider the necessary conditions for minimizing sequences in an optimal control problem with a pointwise in time state constraint of inequality type and with dynamics described by a semilinear hyperbolic equation in divergence form with the non-homogeneous boundary condition of the third kind. For the parametric optimization problem, we also consider regularity and normality conditions stipulated by the differential properties of its value function. (original abstract)
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Multivariate polynomial matrices arise from the treatment of linear systems of partial differential equations, delay-differential equations or multidimensional discrete equations. In this paper we generalize some of the results obtained for the equivalence to the Smith normal form for a class of multivariate polynomial matrices. (original abstract)
16
Content available remote Robust L2 Consensus of High-Order Swarm Systems with Time-Varying Delays
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Consensus problems for high-order continuous-time swarm systems in directed networks with time delays, uncertainties and external disturbances are investigated. Firstly, the state space of a swarm system is decomposed into a consensus subspace (CS) and a complement consensus space (CCS). A necessary and sufficient condition for the system with time delays and uncertainties to achieve consensus is presented based on the state projection on CCS, and an explicit expression of the consensus function is shown on the basis of the state projection on CS. Then, a sufficient condition for the system to achieve consensus with a desired L2 performance is given. Finally, numerical simulations are shown to demonstrate theoretical results. (original abstract)
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Content available remote Novel Robust Control Design for Unstable Systems with Dual Pole and Dual Zero
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In this note, a novel robust control design for a class of unstable systems with dual pole and dual zero is addressed. In the algorithm, αfeedback node was moved from the interior of the controlled plant to its right-hand side. Then, the closed-loop gain shaping algorithm was used to design the feedback transfer function. Consequently, controller and the controlled plant have clear physical meaning and are easily tuned. Simulation results show that the control effects are better than for the previous modification, the system can have rapid settling time with no overshoot, zero steadystate error and satisfactory robust stability to model perturbation and disturbance. The method has the advantages of simple and efficient design, and it was also successfully applied to control static unstable missile. (original abstract)
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Content available remote Fusion Filtration in LQG Control for Multisensor Systems
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In the paper, state filtration in a LQG problem formulated for a multisensor system is considered. Control is determined by a central node as a linear form of a state estimate. It is assumed that control values are not available to local nodes. Because of the drawbacks of centralized filtration an optimal fusion of decentralized local Kalman filters is proposed. When control values are not available to local nodes, then control should be treated as a random variable in the synthesis of local state estimates. This leads to a non-classical estimation. It is shown that the proposed filter is equivalent to the centralized one. (original abstract)
The paper aims at a critical presentation of basic algorithms used for solving linear-quadratic optimal control models. The assumptions concerning the random disturbances allow us to use the certainty equivalence theorem and to ignore disturbances in computing optimal solutions. Thus, the problem to be solved is a deterministic one. The paper presents three algorithms representative for global and stage - wise mode i.e. the. Nestor algorithm and algorithms by Chow and Pindyck. The author investigates the case of solving a nonlinear-quadratic optimal control model by an algorithm invented by Chow. Finally, she reviews published criticism of the optimal control theory and its economic applications, including the most important critical remarks made by Lucas, which led to the invention of the generalized theory of optimal control. (original abstract)
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Content available remote Stability Analysis of Variational Inequalities for Bang-Singular-Bang Controls
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The paper is related to parameter dependent optimal control problems for control-affine systems. The case of scalar reference control with bang-singular-bang structure is considered. The analysis starts from a variational inequality (VI) formulation of Pontryagin's Maximum Principle. In a first step, under appropriate higher-order sufficient optimality conditions, the existence of solutions for the linearized problem (LVI) is proven. In a second step, for a certain class of right-hand side perturbation, it is show that the controls from LVI have bang-singular-bang structure and, in L1 topology, depend Lipschitz continuously on the data. Applying finally a common fixed-point approach to VI, the results are brought together to obtain existence and structural stability results for extremals of the original control problem under parameter perturbation. (original abstract)
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