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Optimal memoryless control in Gaussian noise: A simple counterexample by Gabriel M. Lipsa; Nuno C. Martins is a Engineering article available to read on EtoBox.
What is Optimal memoryless control in Gaussian noise: A simple counterexample about?
In this paper, we investigate control strategies for a scalar, one-step delay system in discrete-time, i.e., the state of the system is the input delayed by one time unit. In contrast with classical approaches, here the control action must be a memoryless function of the output of the plant, which comprises the current state corrupted by measurement noise. We adopt a first order state-space representation for the delay system, where the initial state is a Gaussian random variable. In addition, we assume that the measurement noise is drawn from a white and Gaussian process with zero mean and constant variance. Performance evaluation is carried out via a finite-time quadratic cost that combines the second moment of the control signal, and the second moment of the difference between the initial state and the state at the final time. We show that if the time-horizon is one or two then the optimal control is a linear function of the plant's output, while for a sufficiently large horizon a control taking on only two values will outperform the optimal affine solution. This paper complements the well-known counterexample by Hans Witsenhausen, which showed that the solution to a linear, qua
Who reads Optimal memoryless control in Gaussian noise: A simple counterexample?
It is typically read by researchers, students, and practitioners in Engineering.
- Author
- Gabriel M. Lipsa; Nuno C. Martins
- Publisher
- Elsevier Science; Elsevier ; Elsevier Ltd.; Test accounts; Elsevier BV (ISSN 0005-1098)
- Published
- 2011
- Language
- EN
- Field
- Engineering (Physical Sciences)