1,721,023 research outputs found
Average and worst-case techniques in convexoptimization with stochastic uncertainty
No full textWe consider two standard philosophies for finding minimizing solutions of convex objective functions affected by uncertainty. In a first approach, the solution should minimize the expected value of the objective w.r.t. uncertainty (average approach), while in a second one it should minimize the worst-case objective (worst-case, or min-max approach). Both approaches are however numerically hard to solve exactly, for general dependence of the cost function on the uncertain data. Here, we discuss two techniques based on uncertainty randomization that permit to solve efficiently some suitable probabilistic relaxation of the indicated problems, with full generality with respect to the way in which the uncertainty enters the problem data. A specific application to uncertain Least-Squares problems is also examined in the pape
Randomization in RH_infty:an Approach to Controller Design with Hard/Soft Performance Specifications
No full textn this paper, we consider a robust controller design problem, where the design objectives are divided into two categories: Hard specifications and soft specifications. Hard specifications need to be met robustly against uncertainties, and axe addressed using a classical H∞μ-synthesis approach. Soft specifications are given as average performance requirements with respect to uncertainty, and are addressed using a probabilistic design method. The key element in this approach is an algorithm for random generation of stable transfer matrices, with a bound on the H∞ nor
Near Optimal Stochastic Solution to Uncertain Least Squares Problems
No full textIn this paper, we present a recursive algorithm for the solution of uncertain least-square problems in a stochastic setting. The algorithm aims at minimizing the expected value with respect to the uncertainty of the least-square residual, and returns with high probability an ε-suboptimal solution in a pre-specified number of iterations. The proposed technique is based on minimization of the empirical mean and on uniform convergence results derived from learning theory inequalities. Comparisons with gradient algorithms for stochastic optimization are also discussed in the paper
Observer design with guaranteed RMS gain for linear parameter varying jump systems
No full textWe consider the problem of designing state observers with guaranteed power-to-power (RMS) gain, for a class of stochastic discrete-time linear systems that possess both measurable parameter variations and Markovian jumps in their dynamics. It is shown in the paper that an upper bound on the RMS gain of the observer can be characterized in terms of robust feasibility of a family of linear matrix inequalities (LMIs). Any feasible solution to these LMIs can then be used to explicitly construct a parameter-varying jump observer that guarantees the desired performance level. This design framework is then specialized to a problem of state estimation for an LPV plant whose state measurements are available trough a lossy Bernoulli channel. A numerical example illustrates the result
- …
