1,721,032 research outputs found
Adaptive pole placement by means of a simple, singularity free, identification algorithm.
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The exact feasibility of randomized solutions of robust convex programs
No full textMany optimization problems are naturally delivered in an uncertain framework, and one would like to exercise prudence against the uncertainty elements present in the problem. In previous contributions, it has been shown that solutions to uncertain convex programs that bear a high probability to satisfy uncertain constraints can be obtained at low computational cost through constraint randomization. In this paper, we establish new feasibility results for randomized algorithms. Specifically, the exact feasibility for the class of the so-called fully-supported problems is obtained. It turns out that all fully-supported problems share the same feasibility properties, revealing a deep
kinship among problems of this class. It is further proven that the feasibility of the randomized solutions for all other convex programs can be bounded based on the feasibility for the prototype class of fully-supported problems. The feasibility result of this paper outperforms previous bounds and is not improvable because it is exact for fully-supported problems
Logic-based switching for the stabilization of stochastic systems in presence of unmodeled dynamics.
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A penalized identification criterion for securing controllability in adaptive control.
No full textAbstract in vol. 8, pp. 491-494,
Full paper electronic access code: 2946
Robust Convex Programs: Randomized Solutions and Applications in Control
No full textMany engineering problems can be cast as optimization problems subject to convex constraints that are parameterized by an uncertainty or 'instance' term. A recently emerged successful paradigm for attacking these problems is robust optimization, where one seeks a solution which simultaneously satisfies all possible constraint instances. In practice, however, the robust approach is computationally viable only for problem families with rather simple dependence on the instance parameter (such as affine or polynomial), and leads in general to conservative answers, since the solution is computed transforming the original semi-infinite problem into a standard one, by means of relaxation techniques. In this paper, we take an alternative 'randomized' or 'scenario' approach: by randomly sampling the uncertainty parameter, we substitute the original infinite constraint set with a finite set of N constraints. We show that the resulting randomized solution fails to satisfy only a small portion of the original constraints, provided that a sufficient number of samples is drawn. Our key result is to provide an efficient and explicit bound on the measure (probability or volume) of the original constraints that are possibly violated by the randomized solution. This volume rapidly decreases to zero as N is increased. The proposed paradigm is here applied to the solution of a wide class of NP-hard control problems presentable by means of parameter-dependent linear matrix inequalities
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