This paper presents a distributed, guidance and control algorithm for reconfiguring swarms composed of hundreds to thousands of agents with limited communication and computation capabilities. This algorithm solves bot...
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This paper presents a distributed, guidance and control algorithm for reconfiguring swarms composed of hundreds to thousands of agents with limited communication and computation capabilities. This algorithm solves both the optimal assignment and collision-free trajectory generation for robotic swarms, in an integrated manner, when given the desired shape of the swarm ( without pre-assigned terminal positions). The optimal assignment problem is solved using a distributed auction assignment that can vary the number of target positions in the assignment, and the collision-free trajectories are generated using sequential convex programming. Finally, model predictive control is used to solve the assignment and trajectory generation in real time using a receding horizon. The model predictive control formulation uses current state measurements to resolve for the optimal assignment and trajectory. The implementation of the distributed auction algorithm and sequential convex programming using model predictive control produces the swarm assignment and trajectory optimization ( SATO) algorithm that transfers a swarm of robots or vehicles to a desired shape in a distributed fashion. Once the desired shape is uploaded to the swarm, the algorithm determines where each robot goes and how it should get there in a fuel-efficient, collision-free manner. Results of flight experiments using multiple quadcopters show the effectiveness of the proposed SATO algorithm.
In this paper a new approach to H-2 robust filter design is proposed. Both continuous- and discrete-time invariant systems subject to polytopic parameter uncertainty are considered. After a brief discussion on some of...
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In this paper a new approach to H-2 robust filter design is proposed. Both continuous- and discrete-time invariant systems subject to polytopic parameter uncertainty are considered. After a brief discussion on some of the most expressive methods available for H-2 robust filter design, a new one based on a performance certificate calculation is presented. The performance certificate is given in terms of the gap produced by the robust filter between lower and upper bounds of a minimax programming problem where the H-2 norm of the estimation error is maximized with respect to the feasible uncertainties and minimized with respect to all linear, rational and causal filters. The calculations are performed through convex programming methods developed to deal with linear matrix inequality (LMI). Many examples borrowed from the literature to date are solved and it is shown that the proposed method outperforms all other designs. (c) 2007 Elsevier Ltd. All rights reserved.
This work is concerned with generalized convex programming problems, where the objective function and also the constraints belong to a certain class of convex functions. It examines the relationship of two basic condi...
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This work is concerned with generalized convex programming problems, where the objective function and also the constraints belong to a certain class of convex functions. It examines the relationship of two basic conditions used in interior-point methods for generalized convex programming self-concordance and a relative Lipschitz condition-and gives a short and simple complexity analysis of an interior-point method for generalized convex programming. In generalizing ellipsoidal approximations for the feasible set, it also allows a geometrical interpretation of the analysis.
In this paper, we study the global convergence of a large class of primal-dual interior point algorithms for solving the linearly constrained convex programming problem. The algorithms in this class decrease the value...
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In this paper, we study the global convergence of a large class of primal-dual interior point algorithms for solving the linearly constrained convex programming problem. The algorithms in this class decrease the value of a primal-dual potential function and hence belong to the class of so-called potential reduction algorithms. An inexact line search based on Armijo stepsize rule is used to compute the stepsize. The directions used by the algorithms are the same as the ones used in primal-dual path following and potential reduction algorithms and a very mild condition on the choice of the ''centering parameter'' is assumed. The algorithms always keep primal and dual feasibility and, in contrast to the polynomial potential reduction algorithms, they do not need to drive the value of the potential function towards - infinity in order to converge. One of the techniques used in the convergence analysis of these algorithms has its root in nonlinear unconstrained optimization theory.
A new approach for the synthesis of one-dimensional (1D) and 2D reconfigurable sparse arrays generating sum and difference power patterns is presented in this study. In the case of 1D arrays, the design procedure prov...
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A new approach for the synthesis of one-dimensional (1D) and 2D reconfigurable sparse arrays generating sum and difference power patterns is presented in this study. In the case of 1D arrays, the design procedure provides solutions in which only one set of amplitude coefficients is required and the reconfigurability is obtained by modifying only the excitation phases. In the case of 2D arrays, the simplification of the antenna system is investigated by sharing some excitations for the sum and difference channels. An iterative scheme is used where the array response in the main lobe direction is cast as a multi-convex problem at each step that the non-convex lower bound constraint is relaxed while concurrently minimising a reweighted objective function based on the magnitudes of the element excitations. To ensure the robustness of the array, worst-case performance optimisation technique and white noise gain constraint are introduced in the array. Numerical tests and electromagnetic simulations, referred to known optimal solutions, show that the proposed design is able to obtain good radiation performance with a smaller number of elements.
A shaped beam synthesis methodology for planar arrays with control of the ripple amplitude in the shaped region, and constraints on the sidelobe and cross-polar levels, is proposed in this paper. A previously develope...
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A shaped beam synthesis methodology for planar arrays with control of the ripple amplitude in the shaped region, and constraints on the sidelobe and cross-polar levels, is proposed in this paper. A previously developed synthesis formulation for designing finite impulse response (FIR) filters by transforming a nonconvex synthesis problem to a convex optimization scheme enforcing conjugate symmetric excitation weights, is extended to real and coupled radiating elements of complex geometry, taking into account mutual coupling effects. The optimization procedure is integrated with a finite array approach simulating different array environments. This approach is based on the infinite array model through a Floquet modal- and general scattering matrix (GSM)-based analysis, where the periodic radiating element is characterized from a hybrid and full-wave analysis procedure combining the FEM, modal analysis, and domain decomposition technique. Numerical results of different synthesized beam patterns are presented for arrays of open-ended apertures and microstrip antennas.
In this paper we consider minimizing the spectral condition number of a positive semidefinite matrix over a nonempty closed convex set Omega. We show that it can be solved as a convex programming problem, and moreover...
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In this paper we consider minimizing the spectral condition number of a positive semidefinite matrix over a nonempty closed convex set Omega. We show that it can be solved as a convex programming problem, and moreover, the optimal value of the latter problem is achievable. As a consequence, when Omega is positive semidefinite representable, it can be cast into a semidefinite programming problem. We then propose a first-order method to solve the convex programming problem. The computational results show that our method is usually faster than the standard interior point solver SeDuMi [J. F. Sturm, Optim. Methods Softw., 11/12 (1999), pp. 625-653] while producing a comparable solution. We also study a closely related problem, that is, finding an optimal preconditioner for a positive definite matrix. This problem is not convex in general. We propose a convex relaxation for finding positive definite preconditioners. This relaxation turns out to be exact when finding optimal diagonal preconditioners.
We give some new regularity conditions for Fenchel duality in separated locally convex vector spaces, written in terms of the notion of quasi interior and quasi-relative interior, respectively. We provide also an exam...
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We give some new regularity conditions for Fenchel duality in separated locally convex vector spaces, written in terms of the notion of quasi interior and quasi-relative interior, respectively. We provide also an example of a convex optimization problem for which the classical generalized interior-point conditions given so far in the literature cannot be applied, while the one given by us is applicable. By using a technique developed by Magnanti, we derive some duality results for the optimization problem with cone constraints and its Lagrange dual problem, and we show that a duality result recently given in the literature for this pair of problems has self-contradictory assumptions.
A finite-dimensional mathematical programming problem with convex data and inequality constraints is considered. A suitable definition of condition number is obtained via canonical perturbations of the given problem, ...
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A finite-dimensional mathematical programming problem with convex data and inequality constraints is considered. A suitable definition of condition number is obtained via canonical perturbations of the given problem, assuming uniqueness of the optimal solutions. The distance among mathematical programming problems is defined as the Lipschitz constant of the difference of the corresponding Kojima functions. It is shown that the distance to ill-conditioning is bounded above and below by suitable multiples of the reciprocal of the condition number, thereby generalizing the classical Eckart-Young theorem. A partial extension to the infinite-dimensional setting is also obtained.
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