Robust H2/H∞-state estimation for systems with error variance constraints: the continuous-time case

Copyright [1999] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.The paper is concerned with the state estimator design problem for perturbed linear continuous-time systems with H∞ norm and variance constraints. The perturbation is assumed to be time-invariant and norm-bounded and enters into both the state and measurement matrices. The problem we address is to design a linear state estimator such that, for all admissible measurable perturbations, the variance of the estimation error of each state is not more than the individual prespecified value, and the transfer function from disturbances to error state outputs satisfies the prespecified H∞ norm upper bound constraint, simultaneously. Existence conditions of the desired estimators are derived in terms of Riccati-type matrix inequalities, and the analytical expression of these estimators is also presented. A numerical example is provided to show the directness and effectiveness of the proposed design approac

Norm Based Optimally Robust Control of Constrained Discrete Time Linear Systems

Most realistic control problems involve both some type of time-domain constraints and model uncertainty. However, the majority of controller design procedures currently available focus only on one aspect of the problem, with only a handful of method capable of simultaneously addressing, albeit in a limited fashion, both issues. In this paper we propose a simple design procedure that takes explicitly into account both time domain constraints and model uncertainty. Specifically, we use a operator norm approach to define a simple robustness measure for constrained systems. The available degrees of freedom are then used to optimize this measure subject to additional performance specifications. We believe that the results presented here provide a useful new approach for designing controllers capable of yielding good performance under substantial uncertainty while meeting design constraints

Finite-time behavior of inner systems

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Online-Computation Approach to Optimal Control of Noise-Affected Nonlinear Systems with Continuous State and Control Spaces

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During the last few years there has been considerable interest in the use of trainable controllers based upon the use of neuron-like elements, with the expectation being that these controllers can be trained, with relatively little effort, to achieve good performance. However, good performance hinges on the ability of the neural net to generate a "good" control law even when the input does not belong to the training set, and it has been shown that neural-nets do not necessarily generalize well. It has been proposed that this problem can be solved by essentially quantizing the state-space and then using a neural-net to implement a table look-up procedure. However, there is little information on the effect of this quantization upon the controllability properties of the system. In this paper we address this problem by extending the theory of control of constrained systems to the case where the controls and measured states are restricted to finite or countably infinite sets. These results provide the theoretical framework for recently suggested neuromorphic controllers but they are also valuable for analyzing the controllability properties of computer-based control systems

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