Mixed $H_2/H_\infty$ control in a stochastic framework

M.A. Peters, A.A. Stoorvogel

Abstract

This paper deals with a mixture of H_2 and H_\infty. We have two inputs and one output. One input signal is a white noise stochastic process, and represents errors e.g. resulting from measurement noise. The other input has a more deterministic character. If one has a reference signal (e.g. a step) as input one can not model this as white noise, but it fits nicely into this new class of inputs. The objective is to minimize the effect of these exogenuous signals on the output ofthe system. We define a cost function which enables us to combine the structural difference between these two exogenuous inputs. The analysis of this function leads to a standard H_\infty Riccati equation. We will motivate this cost function by looking at two theoretical applications: the derivation of robust performance bounds and a tracking problem.
Original language English Eindhoven Technische Universiteit Eindhoven 18 Published - 1992

Publication series

Name Memorandum COSOR 9213 0926-4493

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White noise
Cost functions
Riccati equations
Random processes

Cite this

Peters, M. A., & Stoorvogel, A. A. (1992). Mixed $H_2/H_\infty$ control in a stochastic framework. (Memorandum COSOR; Vol. 9213). Eindhoven: Technische Universiteit Eindhoven.
Peters, M.A. ; Stoorvogel, A.A. / Mixed $H_2/H_\infty$ control in a stochastic framework. Eindhoven : Technische Universiteit Eindhoven, 1992. 18 p. (Memorandum COSOR).
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Peters, MA & Stoorvogel, AA 1992, Mixed $H_2/H_\infty$ control in a stochastic framework. Memorandum COSOR, vol. 9213, Technische Universiteit Eindhoven, Eindhoven.

Mixed $H_2/H_\infty$ control in a stochastic framework. / Peters, M.A.; Stoorvogel, A.A.

Eindhoven : Technische Universiteit Eindhoven, 1992. 18 p. (Memorandum COSOR; Vol. 9213).

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AU - Stoorvogel, A.A.

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N2 - This paper deals with a mixture of H_2 and H_\infty. We have two inputs and one output. One input signal is a white noise stochastic process, and represents errors e.g. resulting from measurement noise. The other input has a more deterministic character. If one has a reference signal (e.g. a step) as input one can not model this as white noise, but it fits nicely into this new class of inputs. The objective is to minimize the effect of these exogenuous signals on the output ofthe system. We define a cost function which enables us to combine the structural difference between these two exogenuous inputs. The analysis of this function leads to a standard H_\infty Riccati equation. We will motivate this cost function by looking at two theoretical applications: the derivation of robust performance bounds and a tracking problem.

AB - This paper deals with a mixture of H_2 and H_\infty. We have two inputs and one output. One input signal is a white noise stochastic process, and represents errors e.g. resulting from measurement noise. The other input has a more deterministic character. If one has a reference signal (e.g. a step) as input one can not model this as white noise, but it fits nicely into this new class of inputs. The objective is to minimize the effect of these exogenuous signals on the output ofthe system. We define a cost function which enables us to combine the structural difference between these two exogenuous inputs. The analysis of this function leads to a standard H_\infty Riccati equation. We will motivate this cost function by looking at two theoretical applications: the derivation of robust performance bounds and a tracking problem.

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Peters MA, Stoorvogel AA. Mixed $H_2/H_\infty$ control in a stochastic framework. Eindhoven: Technische Universiteit Eindhoven, 1992. 18 p. (Memorandum COSOR).