Abstract
Optimization of linear systems of the type (7.1) usually relies upon minimization of the quadratic criterion
where Q is a positive semi-definite symmetric matrix, and R is a positive definite symmetric matrix. If the controlled variable is of the form y = Dx where y∈ℝk, k<n, and D is constant kxn matrix, then taking
one obtains that the first term in the criterion (9.1) is yTy and characterizes the degree of deviation of the controlled variable from the zero state. The second term in the criterion defines the penalty for controll “expenses”. The relation between the weight matrices Q and R defines the tradeoff between the two contradictory desires such as to have a rapidly decaying control process and to reduce power consumption for its realization.
Keywords
- Asymptotic Stability
- Dynamic Optimization
- Bellman Equation
- Discontinuity Surface
- Positive Definite Symmetric Matrix
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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© 1992 Springer-Verlag Berlin, Heidelberg
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Utkin, V.I. (1992). Dynamic Optimization. In: Sliding Modes in Control and Optimization. Communications and Control Engineering Series. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-84379-2_9
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DOI: https://doi.org/10.1007/978-3-642-84379-2_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-84381-5
Online ISBN: 978-3-642-84379-2
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