Proceedings ArticleDOI
Explicit optimality conditions for fixed-order dynamic compensation
David C. Hyland,Dennis S. Bernstein +1 more
- Vol. 22, Iss: 22, pp 161-165
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TLDR
In this paper, a linear-quadratic fixed-order dynamic compensation in the presence of disturbance and observation noise is considered and necessary conditions for the optimization problem are derived in a new and highly simplified form.Abstract:
We consider steady-state, linear-quadratic fixed-order dynamic compensation in the presence of disturbance and observation noise. First-order necessary conditions for the optimization problem are derived in a new and highly simplified form. These necessary conditions constitute a system of two modified Riccati equations and two modified Lyapunov equations coupled by a projection which plays an essential role in defining the geometric structure of the compensator. When the order of the compensator is equal to the dimension of the plant, the classical linear-quadratic-Gaussian results are immediately obtained.read more
Citations
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Journal ArticleDOI
The optimal projection equations for fixed-order dynamic compensation
TL;DR: In this paper, the first-order necessary conditions for quadratically optimal, steady-state, fixed-order dynamic compensation of a linear, time-invariant plant in the presence of disturbance and observation noise are derived in a new and highly simplified form.
Journal ArticleDOI
The optimal projection equations for model reduction and the relationships among the methods of Wilson, Skelton, and Moore
TL;DR: In this paper, the first-order necessary conditions for quadratically optimal reduced-order modeling of linear time-invariant systems are derived in the form of a pair of modified Lyapunov equations coupled by an oblique projection which determines the optimal reduced order model.
Journal ArticleDOI
The optimal projection equations for reduced-order state estimation
TL;DR: In this paper, the first-order necessary conditions for optimal, steady-state, reduced-order state estimation for a linear, time-invariant plant in the presence of correlated disturbance and nonsingular measurement noise are derived in a new and highly simplified form.
Journal ArticleDOI
The optimal projection equations for reduced-order, discrete-time modeling, estimation, and control
Proceedings ArticleDOI
The optimal projection/maximum entropy approach to designing low-order, robust controllers for flexible structures
TL;DR: In this paper, the optimal projection equations for fixed-order dynamic compensation in the presence of state-, control-and measurement-dependent noise were derived for high-order systems with parameter uncertainties.
References
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TL;DR: In this paper, it is shown that principal component analysis (PCA) is a powerful tool for coping with structural instability in dynamic systems, and it is proposed that the first step in model reduction is to apply the mechanics of minimal realization using these working subspaces.
Book
Linear Optimal Control Systems
Huibert Kwakernaak,Raphael Sivan +1 more
TL;DR: In this article, the authors provide an excellent introduction to feedback control system design, including a theoretical approach that captures the essential issues and can be applied to a wide range of practical problems.
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Model reduction via balanced state space representations
L. Pernebo,Leonard M. Silverman +1 more
TL;DR: In this article, a model reduction procedure based on balanced state space representations is studied, and the reduced order model is examined from the point of view of stability, controllability, and observability.
Journal ArticleDOI
Optimum solution of model-reduction problem
TL;DR: In this article, conditions for synthetising a reduced model for a multivariable time-invariant linear system by minimizing a functional of the error between the output vector of the reduced model and the original model were given.
Journal ArticleDOI
Optimal limited state variable feedback controllers for linear systems
TL;DR: In this article, the problem of designing compensators, the dimensions of which are fixed a priori, for linear systems is considered, and two types of compensators are considered: static (gain only) compensators which operate directly upon the output signals to generate the controls, and dynamic compensators of fixed dimension.