Minimizing Sequences for a Family of Functional Optimal Estimation Problems (English)

In: Journal of Optimization Theory and Applications   ;  147 ,  2  ;  243-262  ;  2010

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Abstract Rates of convergence are derived for approximate solutions to optimization problems associated with the design of state estimators for nonlinear dynamic systems. Such problems consist in minimizing the functional given by the worst-case ratio between the ℒ p -norm of the estimation error and the sum of the ℒ p -norms of the disturbances acting on the dynamic system. The state estimator depends on an innovation function, which is searched for as a minimizer of the functional over a subset of a suitably-defined functional space. In general, no closed-form solutions are available for these optimization problems. Following the approach proposed in (Optim. Theory Appl. 134:445–466, 2007), suboptimal solutions are searched for over linear combinations of basis functions containing some parameters to be optimized. The accuracies of such suboptimal solutions are estimated in terms of the number of basis functions. The estimates hold for families of approximators used in applications, such as splines of suitable orders.

Table of contents – Volume 147, Issue 2

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205
Optimal Control of Second Order Systems with Infinite Time Horizon: Existence of Solutions
Idczak, D. / Walczak, S. | 2010
223
Pseudotransient Continuation for Solving Systems of Nonsmooth Equations with Inequality Constraints
Chen, J. / Qi, L. | 2010
243
Minimizing Sequences for a Family of Functional Optimal Estimation Problems
Alessandri, Angelo / Gnecco, Giorgio / Sanguineti, Marcello | 2010
263
Reverse Convex Programming Approach in the Space of Extreme Criteria for Optimization over Efficient Sets
Thoai, N. V. | 2010
278
Optimal Motion of a Two-Body System in a Resistive Medium
Chernousko, F. L. | 2010
298
Synchronization Criterion for Lur’e Systems via Delayed PD Controller
Ji, D. H. / Park, Ju H. / Lee, S. M. / Koo, J. H. / Won, S. C. | 2010
318
Decentralized Reliable Control of Interconnected Time-Delay Systems Against Sensor Failures
Al-Rayyah, Ali Y. / Mahmoud, Magdi S. | 2010
337
Stochastic and Risk Management Models and Solution Algorithm for Natural Gas Transmission Network Expansion and LNG Terminal Location Planning
Zheng, Qipeng P. / Pardalos, Panos M. | 2010
358
Classical and Impulse Control for the Optimization of Dividend and Proportional Reinsurance Policies with Regime Switching
Wei, Jiaqin / Yang, Hailiang / Wang, Rongming | 2010
378
Uniform Approximation by the Highest Defect Continuous Polynomial Splines: Necessary and Sufficient Optimality Conditions and Their Generalisations
Sukhorukova, Nadezda | 2010
395
Annealing a Genetic Algorithm for Constrained Optimization
Mendivil, F. / Shonkwiler, R. | 2010
411
On an Implicit Method for Nonconvex Variational Inequalities
Noor, M. A. | 2010