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Schauder Decompositions, Approximations and Control Problems

SIAM Journal on Control and Optimization, 1980
A Schauder decomposition for a Banach space $X$ is a sequence $\{ P_n \} $ of finite rank continuous projections such that (a) $P_n P_m = P_m P_n = P_{\min \{ m,n\} } $ and (b) $\lim _n P_n x = x$ for each $x$ in $X$. Schauder decompositions can be used to approximate the solution to optimal control problems defined on $X$.
Kaneko, Hideaki, Ruckle, William H.
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Successive Approximations of Linear Control Models

SIAM Journal on Control and Optimization, 1998
Summary: We present a technique for approximating sequences of linear programs with varying right-hand sides and study the geometric properties of this approximation. Our approximation has an efficiency advantage over optimal solutions. When applied to deterministic control problems, the suggested technique outperforms the linear feedback model and ...
Birge, John R., Takriti, Samer
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Duality and approximate controls

Journal of the Franklin Institute, 1968
Abstract The computation of approximate controls for the terminal problem for linear systems is considered. These controls can be made to steer the terminal state vector arbitrarily close to the desired terminal position; their norms will generally be smaller than the norm of the exact optimal control which achieves the desired terminal state. It is
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Robust approximation and control

IEEE Control Systems, 1997
An algorithmic procedure has been implemented. Its input data are the frequency samples of a MIMO high order (possibly infinite dimensional) model and its output is a controller for that system. The procedure considers the approximation error as additive uncertainty and designs for robust performance of a mixed sensitivity problem by using H/sup /spl ...
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Approximation-Based Adaptive Control

2012
This chapter is focused on the design and analysis of adaptive controllers for dynamical systems operating in the presence of nonparametric unknown nonlinear functions and bounded time-varying disturbances. In order to counter these types of uncertainties, we will employ direct adaptive model reference controllers equipped with online function ...
Eugene Lavretsky, Kevin A. Wise
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Approximations of Relaxed Optimal Control Problems

Journal of Optimization Theory and Applications, 2006
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Azhmyakov, V., Schmidt, W.
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Approximate Boundary Null Controllability

2019
In this chapter, we will define the approximate boundary null controllability for system (II) and the D-observability for the adjoint problem, and show that these two concepts are equivalent to each other. Moreover, the corresponding Kalman’s criterion is introduced and studied.
Tatsien Li, Bopeng Rao
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Constrained approximate boundary controllability

IEEE Transactions on Automatic Control, 1997
The author gives necessary and sufficient conditions for constrained approximate boundary controllability for a class of linear systems described by partial differential equations of parabolic type with mixed boundary conditions. Some examples presented in detail illustrate the power of these criteria.
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Adaptive Approximation Based Control

2006
Preface. 1. INTRODUCTION. 1.1 Systems and Control Terminology. 1.2 Nonlinear Systems. 1.3 Feedback Control Approaches. 1.3.1 Linear Design. 1.3.2 Adaptive Linear Design. 1.3.3 Nonlinear Design. 1.3.4 Adaptive Approximation Based Design. 1.3.5 Example Summary. 1.4 Components of Approximation Based Control. 1.4.1 Control Architecture.
Jay A. Farrell, Marios M. Polycarpou
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COAST: Controllable approximative stochastic reaction algorithm

The Journal of Chemical Physics, 2006
We present an approximative algorithm for stochastic simulations of chemical reaction systems, called COAST, based on three different modeling levels: for small numbers of particles an exact stochastic model; for intermediate numbers an approximative, but computationally more efficient stochastic model based on discrete Gaussian distributions; and for ...
Wagner, Holger   +2 more
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