The problem of robust energy-to-peak filtering for linear systems with convex bounded uncertainties is investigated in this paper. The main purpose is to design a full order stable linear filter that minimizes the wor...
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The problem of robust energy-to-peak filtering for linear systems with convex bounded uncertainties is investigated in this paper. The main purpose is to design a full order stable linear filter that minimizes the worst-case peak value of the filtering error output signal with respect to all bounded energy inputs, in such way that the filtering error system remains quadratically stable Necessary and sufficient conditions arc formulated in terms of Linear Matrix Inequalities - LMIs, for both continuous- and discrete-time cases.
Conditions for existence of maximal and stabilizing liermitian solutions for a set of discrete-time coupled algebraic Riccati equations are considered. Such equations play an important role in optimal control of discr...
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Conditions for existence of maximal and stabilizing liermitian solutions for a set of discrete-time coupled algebraic Riccati equations are considered. Such equations play an important role in optimal control of discrete-time Markovian jump linear systems. The matrix cost is only assumed to be liermitian. First, conditions for existence of a maximal liermitian solution are derived in terms of the concept of mean square stabilizability and a convex set not being empty. A connection with convex optimization is also established, leading to a numerical algorithm. Next, a necessary and sufficient condition for existence of a stabilizing solution (in the mean square sense) is derived. These results generalize and unify several previous results presented in the literature of discrete-time coupled Riccati equations of Markovian jump linear systems.
This paper proposes a method to determine trajectories of dynamic systems that steer between two end points while satisfying linear inequality constraints arising from limits on states and inputs. The method exploits ...
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This paper proposes a method to determine trajectories of dynamic systems that steer between two end points while satisfying linear inequality constraints arising from limits on states and inputs. The method exploits the structure of the dynamic system to eliminate the state equations. The linear inequalities on inputs and states are replaced by a finite set of linear inequalities on the mode coefficients and changing the problem of trajectory generation to finding a convex polytope on the mode coefficients. The procedure is demonstrated in an example and verified experimentally.
In the present paper the logarithmic barrier method applied to the linearly constrained convex optimization problems is studied from the view point of classical path-following algorithms. In particular, the radius of ...
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This paper investigates and unifies several relative nonlinear optimization problems in locally convex topological vector spaces or in convex spaces. The main generalization including some unified forms is the weaking...
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A detailed description of a path-following Interior point algorithm for constrained convex programs is presented. The algorithm employs a truncated logarithmic barrier function, which is particularly suitable to probl...
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A detailed description of a path-following Interior point algorithm for constrained convex programs is presented. The algorithm employs a truncated logarithmic barrier function, which is particularly suitable to problems with many nonactive constraints. A special version of the algorithm is adopted to minmax problems. Extensive testing of the algorithms on large-scale Structural Optimization problems (truss topology design, shape design with optimized material) demonstrate their efficiency.
In a generalised H 2 optimal control problem, the conventional H 2 norm is replaced by an operator norm, A stabilising controller is sought such that the closed loop gain from time domain input disturbances in L 2 to ...
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In a generalised H 2 optimal control problem, the conventional H 2 norm is replaced by an operator norm, A stabilising controller is sought such that the closed loop gain from time domain input disturbances in L 2 to time domain regulated outputs in L ∞ is minimised, A solution to this problem can be obtained by using a finite dimensional convex programme for weight selection in an LQR problem. Both continuous- and discrete-time versions of problem are considered, and, following the technique of Rotea (1993) the problem is reduced to one of finding a state feedback controller for an auxiliary system. In general, the weight selection method offers a potentially reduced computational burden compared with that in Rotea (1993).
We give an algorithm for minimizing the sum of a strictly convex function and a convex piecewise linear function. It extends several dual coordinate ascent methods for large-scale linearly constrained problems that oc...
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We give an algorithm for minimizing the sum of a strictly convex function and a convex piecewise linear function. It extends several dual coordinate ascent methods for large-scale linearly constrained problems that occur in entropy maximization, quadratic programming, and network flows. In particular, it may solve exact penalty versions of such (possibly inconsistent) problems, and subproblems of bundle methods for nondifferentiable optimization. It is simple, can exploit sparsity, and in certain cases is highly parallelizable. Its global convergence is established in the recent framework of B-functions (generalized Bregman functions).
Synchronous vibration is the most common form of vibration in rotorbearing systems. Open-loop controllers, in conjunction with magnetic bearings, have been shown to be very effective in controlling synchronous vibrati...
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Synchronous vibration is the most common form of vibration in rotorbearing systems. Open-loop controllers, in conjunction with magnetic bearings, have been shown to be very effective in controlling synchronous vibration in flexible rotor-bearing systems. A well-known open-loop controller, called a mini-least-squares controller, minimises the measured rotor vibration in a least-squares sense. In this paper, it is shown how convex programming can be used to design mini-major-axis controllers, which minimise the largest measured rotor displacement. A numerical example illustrates the potential improvement in performance of mini-major-axis controllers compared to mini-least-squares controllers.
The minimum covering hypersphere problem is defined as to find a hypersphere of minimum radius enclosing a finite set of given points in IRn. A hypersphere is a set S(c,r) = {x is an element of IRn : d(x,c) less than ...
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The minimum covering hypersphere problem is defined as to find a hypersphere of minimum radius enclosing a finite set of given points in IRn. A hypersphere is a set S(c,r) = {x is an element of IRn : d(x,c) less than or equal to r}, where c is the center of S, r is the radius of S and d(x,c) is the Euclidean distance between x and c, i.e., d(x,c) = l(2)(x - c). We consider the extension of this problem when d(x,c) is given by any l(pb)-norm, where 1 < p < infinity and b = (b(1),..., b(n)) with b(j) > 0, j = 1,..., n, then S(c,r) is called an l(pb)-hypersphere. in particular for p = 2 and b(j) = 1, j = 1,..., n, we obtain the l(2)-norm. We study some properties and propose some primal and dual algorithms for the extended problem, which are based on the feasible directions method and on the Wolfe duality theory. By computational experiments, we compare the proposed algorithms and show that they can be used to approximate the smallest l(pb)-hypersphere enclosing a large set of points in IRn.
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