Abstract
In linear quadratic control the objective of the controller is to minimize the effect of the initial condition on the (quadratic) cost functional. However, in many systems, uncontrolled inputs, known as disturbances are present. A controller can reduce the response to the disturbances. Even with the same cost function as for linear quadratic control, the problem statement changes. The problems of a single disturbance, and also of an unknown disturbance are considered. The solutions to these problems lead to \(H_2\) and \(H_\infty \) control problems respectively. The framework for approximation is described, as are appropriate computation methods. As for other control system objectives, actuator location is part of control system design.
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References
Morris KA, Demetriou MA, Yang SD (2015) Using \(\mathbb{H}_2\)-control performance metrics for infinite-dimensional systems. IEEE Trans Autom Control 60(2):450–462
Kasinathan D, Morris KA (2013) \({H}_\infty \)-optimal actuator location. IEEE Trans Autom Control 58(10):2522–2535
Ito K, Morris KA (1998) An approximation theory for solutions to operator Riccati equations for \({H}_{\infty }\) control. SIAM J Control Optim 36(1):82–99
Colaneri P, Geromel JC, Locatelli A (1997) Control theory and design. Academic
Morris KA (2001) An introduction to feedback controller design. Harcourt-Brace Ltd
Zhou K, Doyle JC, Glover K (1996) Robust and optimal control. Prentice-Hall, Englewood Cliffs, NJ
Khargonekar PP, Petersen IR, Rotea MA (1988) \({H}_{\infty }\)-control with state feedback. IEEE Trans Autom Control 33(8):786–788
Bensoussan A, Bernhard P (1993) On the standard problem of \({H}_{\infty }\)-optimal control for infinite-dimensional systems. In: Identification and control in systems governed by partial differential equations. SIAM, pp 117–140
Keulen BV (1993) \(H^{\infty }-\) control for distributed parameter systems: a state-space approach. Birkhauser, Boston
Arnold WF, Laub AJ (1984) Generalized eigenproblem algorithms and software for algebraic Riccati equations. Proc IEEE 72(12):1746–1754
Kasinathan D, Morris KA, Yang S (2014) Solution of large descriptor \({H}_\infty \) algebraic Riccati equations. J Comput Sci 5(3):517–526
Lanzon A, Feng Y, Anderson BDO, Rotkowitz M (2008) Computing the positive stabilizing solution to algebraic Riccati equations with an indefinite quadratic term via a recursive method. IEEE Trans Auto Control 53(10):2280–2291
Varga A (1995) On stabilization methods of descriptor systems. Syst Control Lett 24:133–138
Bergeling C, Morris KA, Rantzer A (2020) Direct method for optimal \({H}_\infty \) control of infinite-dimensional systems, Automatica.
Naylor AW, Sell GR (1982) Linear operator theory in science and engineering. Springer, New York
Zaitsev VF, Polyanin AD (2002) Handbook of exact solutions for ordinary differential equations. CRC Press
Darivandi N, Morris K, Khajepour A (2013) An algorithm for LQ-optimal actuator location. Smart Mater Struct 22(3):035001
Yang SD, Morris KA (2015) Comparison of actuator placement criteria for control of structural vibrations. J Sound Vib 353:1–18
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Morris, K.A. (2020). Disturbances. In: Controller Design for Distributed Parameter Systems. Communications and Control Engineering. Springer, Cham. https://doi.org/10.1007/978-3-030-34949-3_5
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DOI: https://doi.org/10.1007/978-3-030-34949-3_5
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