In this paper, we introduce and investigate a constrained mixed set-valued variational inequality (MSVI) in Hilbert spaces. We prove the solution set of the constrained MSVI is a singleton under strict monotonicity. W...
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In this paper, we introduce and investigate a constrained mixed set-valued variational inequality (MSVI) in Hilbert spaces. We prove the solution set of the constrained MSVI is a singleton under strict monotonicity. We also propose four merit functions for the constrained MSVI, that is, the natural residual, gap function, regularized gap function and D-gap function. We further use these functions to obtain error bounds, i.e. upper estimates for the distance to solutions of the constrained MSVI under strong monotonicity and Lipschitz continuity. The approach exploited in this paper is based on the generalized f-projection operator due to Wu and Huang, but not the well-known proximal mapping.
The present report is devoted to the multicriteria problem of the optimal control for stochastic sequences with the infinite horizon. The general method of attack is based on the method of constraints. The main theore...
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The present report is devoted to the multicriteria problem of the optimal control for stochastic sequences with the infinite horizon. The general method of attack is based on the method of constraints. The main theoretical result is formulated as Kuhn-Tucker theorem which gives the necessary and sufficient conditions of the optirnality; besides, the description of the strategies dass sufficient for the problem's solving is presented. The last section is devoted to the investigation of the linear system with quadratic and linear criteria assuming that the discount factor is fixed.
A modification of the programming iterations method is described here for the discrete-time controlled dynamical systems in which spaces of controls and phase states are the spaces with a priori given notion of limit ...
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A modification of the programming iterations method is described here for the discrete-time controlled dynamical systems in which spaces of controls and phase states are the spaces with a priori given notion of limit of a sequence, i. e. the L * -spaces. For such systems described by nonlinear relations it is to be considered the game problem of keeping back of the system within given phase restrictions during an infinite time interval. The modification of the programming iterations method is used for solving the game problem for the first player on the classes of counterstrategies and quasistrategies.
We introduce nondifferentiable multiobjective programming problems involving the support function of a compact convex set and linear functions. The concept of (properly) efficient solutions are presented. We formulate...
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We introduce nondifferentiable multiobjective programming problems involving the support function of a compact convex set and linear functions. The concept of (properly) efficient solutions are presented. We formulate Mond-Weir-type and Wolfe-type dual problems and establish weak and strong duality theorems for efficient solutions by using suitable generalized convexity conditions. Some special cases of our duality results are given.
This paper considers networked control systems (NCS) with data packet dropout, NCS with data packet dropout is equivalent to a continuous time-delay system. Based on Lyapunov-Krasovskii stability theory, a new conditi...
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ISBN:
(纸本)9781467355322;9781467355339
This paper considers networked control systems (NCS) with data packet dropout, NCS with data packet dropout is equivalent to a continuous time-delay system. Based on Lyapunov-Krasovskii stability theory, a new condition for stabilization of the closed-loop system by output-feedback is presented. Moreover, by using the method of free weights matrix and parameter adjusting, LMI criterion of computing maximum data packets dropout is obtained. In accordance with the criterion, convex optimal condition is obtained, then data packets dropout of the system is estimated. Finally, a simulation experiment illustrates the effectiveness of the proposed method.
Controlled stochastic sequences with countable state and control spaces with restrictions - inequalities - are studied. The main results refer to the instance when the space of admissible strategical measures is a con...
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Controlled stochastic sequences with countable state and control spaces with restrictions - inequalities - are studied. The main results refer to the instance when the space of admissible strategical measures is a convex compact. In this case the initial optimization task is equivalent to a certain task of convex programming on the set of extreme admissible strategical measures. The application of the convex programming theory enables one to achieve new necessary and sufficient conditions of optimality and to describe the class : of strategies sufficient for the solution of the optimal control task.
Results are presented which generalize the known solution to the problem of minimizing the l 1 norm of the error transfer function. The optimization framework is a dual formulation employing the theory of convex funct...
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Results are presented which generalize the known solution to the problem of minimizing the l 1 norm of the error transfer function. The optimization framework is a dual formulation employing the theory of convex functionals applied to the problem of designing optimal compensators for linear feedback control systems. A wide range of cost functions can be optimized using this theory and it allows a rather general treatment of the topic of time-domain shaping of linear systems. The results obtained can be applied to the mathematically equivalent problems of optimal disturbance rejection and optimal tracking.
In this paper, we outline the design of linear controllers by convex programming and demonstrate its merits for an example which has been treated with purely analytic methods before. It is shown that the choice of the...
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In this paper, we outline the design of linear controllers by convex programming and demonstrate its merits for an example which has been treated with purely analytic methods before. It is shown that the choice of the base functions for the series expansion of the Youla parameter is crucial for the success. A modified procedure which reduces this problem is described.
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