In both practical applications and theoretical analysis, there are many fuzzy chance-constrained optimization problems. Currently, there is short of real-time algorithms for solving such problems. Therefore, in this p...
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In both practical applications and theoretical analysis, there are many fuzzy chance-constrained optimization problems. Currently, there is short of real-time algorithms for solving such problems. Therefore, in this paper, a continuous-time neurodynamic approach is proposed for solving a class of fuzzy chance-constrained optimization problems. Firstly, an equivalent deterministic problem with inequality constraint is discussed, and then a continuous-time neurodynamic approach is proposed. Secondly, a sufficient and necessary optimality condition of the considered optimization problem is obtained. Thirdly, the boundedness, global existence and Lyapunov stability of the state solution to the proposed approach are proved. Moreover, the convergence to the optimal solution of considered problem is studied. Finally, several experiments are provided to show the performance of proposed approach.
In this paper we propose a convex programming based method for computing robust regions of attraction for state-constrained perturbed discrete-time polynomial systems. The robust region of attraction of interest is a ...
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In this paper we propose a convex programming based method for computing robust regions of attraction for state-constrained perturbed discrete-time polynomial systems. The robust region of attraction of interest is a set of states such that every possible trajectory initialized in it will approach an equilibrium state while never violating the specified state constraint, regardless of the actual perturbation. Based on a Bellman equation which characterizes the interior of the maximal robust region of attraction as the strict one sub-level set of its unique bounded and continuous solution, we construct a semi-definite program for computing robust regions of attraction. Under appropriate assumptions, the existence of solutions to the constructed semi-definite program is guaranteed and there exists a sequence of solutions such that their strict one sub-level sets inner-approximate and converge to the interior of the maximal robust region of attraction in measure. Finally, we demonstrate the method by two examples.
This note presents two coupled Lyapunov-like conditions under which a linear discrete-time system can be stabilized by static output feedback. The originality of these conditions is their relation to the well-known co...
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This note presents two coupled Lyapunov-like conditions under which a linear discrete-time system can be stabilized by static output feedback. The originality of these conditions is their relation to the well-known coupled Sylvester equations that describe both the ( A, B ) and ( C, A )-invariance of a subspace. For systems verifying Kimura's condition, we show that output feedback stabilizing gain matrices can be computed through the successive resolution of two standard convex programming problems. Numerical results are provided to show the effectiveness of the proposed approach.
The problems of analysis and synthesis of linear discrete-time control systems subject to actuators amplitude saturation are addressed. The theoretical results are developed by using tools from the absolute stability ...
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The problems of analysis and synthesis of linear discrete-time control systems subject to actuators amplitude saturation are addressed. The theoretical results are developed by using tools from the absolute stability theory for discrete-time systems. Algorithms based on the solution of linear matrix inequalities (LMIs) are proposed both for computing approximations of the basin of attraction for the closed loop system when the control law is given and for designing stabilizing state feedback control laws. Both the analysis and design procedures take into account the effective occurrence of saturation and the nonlinear behavior of the closed-loop system.
The problem of minimax estimation is considered for the linear multivariate statistically indeterminate observation model with mixed uncertainty. It is shown that in the regular case the minimax estimate is defined ex...
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The problem of minimax estimation is considered for the linear multivariate statistically indeterminate observation model with mixed uncertainty. It is shown that in the regular case the minimax estimate is defined explicitly via the solution of the dual optimization problem. For the singular models, the method of dual optimization is developed by means of using the technique of Tikhonov regularization. Several particular cases which are widely used in practice are also examined.
Recently, it was shown how the convergence of a class of multigrid methods for computing the stationary distribution of sparse, irreducible Markov chains can be accelerated by the addition of an outer iteration based ...
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Recently, it was shown how the convergence of a class of multigrid methods for computing the stationary distribution of sparse, irreducible Markov chains can be accelerated by the addition of an outer iteration based on iterant recombination. The acceleration was performed by selecting a linear combination of previous fine-level iterateswith probability constraints to minimize the two-norm of the residual using a quadratic programming method. In this paper we investigate the alternative of minimizing the one-norm of the residual. This gives rise to a nonlinear convex program which must be solved at each acceleration step. To solve this minimization problem we propose to use a deep-cuts ellipsoid method for nonlinear convex programs. The main purpose of this paper is to investigate whether an iterant recombination approach can be obtained in this way that is competitive in terms of execution time and robustness. We derive formulas for subgradients of the one-norm objective function and the constraint functions, and show how an initial ellipsoid can be constructed that is guaranteed to contain the exact solution and give conditions for its existence. We also investigate using the ellipsoid method to minimize the two-norm. Numerical tests show that the one-norm and twonorm acceleration procedures yield a similar reduction in the number of multigrid cycles. The tests also indicate that onenorm ellipsoid acceleration is competitive with two-norm quadratic programming acceleration in terms of running time with improved robustness.
A robust design method for uncertain single-input-single-output systems is presented. Both structured and unstructured uncertainties are considered. Optimal performance is described as maximum achievable bandwidth. A ...
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A robust design method for uncertain single-input-single-output systems is presented. Both structured and unstructured uncertainties are considered. Optimal performance is described as maximum achievable bandwidth. A controller for robust optimal performance is determined through a convex optimization problem where the constraints come from frequency domain performance criteria. The theoretical framework is developed. Uniqueness of the solution is shown. The design method is applied on two problems.
A whole variety of robust analysis and synthesis problems can be formulated as robust Semi-Definite Programs (SDPs), i.e. SDPs with data matrices that are functions of an uncertain parameter which is only known to be ...
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A whole variety of robust analysis and synthesis problems can be formulated as robust Semi-Definite Programs (SDPs), i.e. SDPs with data matrices that are functions of an uncertain parameter which is only known to be contained in some set. We consider uncertainty sets described by general polynomial semi-definite constraints, which allows to represent norm-bounded and structured uncertainties as encountered in μ-analysis, polytopes and various other possibly non-convex compact uncertainty sets. As the main novel result we present a family of Linear Matrix Inequalities (LMI) relaxations based on sum-of-squares (sos) decompositions of polynomial matrices whose optimal values converge to the optimal value of the robust SDP. The number of variables and constraints in the LMI relaxations grow only quadratically in the dimension of the underlying data matrices. We demonstrate the benefit of this a priori complexity bound by an example and apply the method in order to asses the stability of a fourth order LPV model of the longitudinal dynamics of a helicopter.
In hyperthermia treatments, the possibility of generating a specific absorption rate distribution peaked into the tumor and bounded elsewhere represents the main clinical need. As multi-frequency applicators can be ex...
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In hyperthermia treatments, the possibility of generating a specific absorption rate distribution peaked into the tumor and bounded elsewhere represents the main clinical need. As multi-frequency applicators can be exploited to reduce the occurrence of undesired hot-spots, an optimal multi-frequency approach is proposed and discussed. Being formulated in terms of a convex programming problem, the globally optimal solution can be determined (only for very special cases). The procedure, presented for the case of scalar fields, can be extended both to the case of vector fields and to the more interesting problem of shaping (rather than just focusing) the specific absorption rate distribution.
The form-closure and force-closure properties of robotic grasping can be loosely defined as the capability of the robot to inhibit motions of the workpiece in spite of externally applied forces. In this paper, the for...
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The form-closure and force-closure properties of robotic grasping can be loosely defined as the capability of the robot to inhibit motions of the workpiece in spite of externally applied forces. In this paper, the form-closure property of robotic grasping is considered as a purely geometric property of a set of unilateral (contact) constraints, such as those applied on a workpiece by a mechanical fixture. The concept of partial form-closure is introduced and discussed in relation with other concepts appeared in literature, such as accessibility and detachability. An algorithm is proposed to obtain a synthetic geometric description of partial form-closure constraints.
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