Finite Horizon H∞ and Related Control Problems by M.Bala Subrahmanyam

By M.Bala Subrahmanyam

HIS e-book provides a generalized state-space concept for the research T and synthesis of finite horizon suboptimal Hoo controllers. We de­ rive expressions for a suboptimal controller in a normal atmosphere and suggest an approximate way to the Hoo functionality robustness challenge. the fabric within the ebook is taken from a suite of analysis papers written through the writer. The booklet is equipped as follows. bankruptcy 1 treats nonlinear optimum regulate difficulties within which the associated fee practical is of the shape of a quotient or a manufactured from powers of convinced integrals. the issues thought of in Chap­ ter 1 are very basic, and the consequences are precious for the computation of the particular functionality of an Hoo suboptimal controller. Such an program is given in Chapters four and five. bankruptcy 2 offers a criterion for the evaluate of the infimal Hoc norm within the finite horizon case. additionally, a differential equation is derived for the possible functionality because the ultimate time is diversified. A basic suboptimal keep an eye on challenge is then posed, and an expression for a subopti­ mal Hoo kingdom suggestions controller is derived. bankruptcy three develops expressions for a suboptimal Hoo output suggestions controller in a really basic case through the answer of 2 dynamic Riccati equations. Assuming the adequacy of linear expressions, bankruptcy four offers an iterative technique for the synthesis of a suboptimal Hoo controller that yields the necessary functionality even less than parameter variations.

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Finite Horizon H∞ and Related Control Problems

HIS publication provides a generalized state-space concept for the research T and synthesis of finite horizon suboptimal Hoo controllers. We de­ rive expressions for a suboptimal controller in a common surroundings and suggest an approximate strategy to the Hoo functionality robustness challenge. the cloth within the ebook is taken from a suite of analysis papers written via the writer.

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Worst-case performance measures for linear control problems," Proc. , 1990, pp. 2439-2443. [10] SUBRAHMANYAM, M. B. , "Model reduction with a finite-interval HOC! criterion," Proc. , 1990, pp. 1419-1427. [11] SAFONOV, M. , LIMEBEER, D. J. , AND CHIANG, R. , "Simplifying the Hoc theory via loop-shifting, matrix-pencil and descriptor concepts," International Journal of Control, 50, 1989, pp. 2467-2488. 52 Ch. 3: Formulae for Suboptimal Hoc Control [12] SUBRAHMANYAM, M. , "Worst-case optimal control over a finite horizon," Journal of Mathematical Analysis and Applications, 171, 1992, pp.

We have From (37) and (38), (56) (57) Incorporating (56) and (57) in (55) and rearranging, the right side of (55) can be written as Since r ~(x*px)dt= ~r T T ~ dt the result follows. 0 {x*px+2x*Px}dt=O, (59) Ch. 3: Formulae for Suboptimal Hoo Control 44 We want to ultimately show that the right side of (54) is larger than -oJo rT v* Rv dt for some 0- > O. It easily follows that e = x - q and r = U - uo satisfy (60) r = Be, (61) where (62) (63). Note that 6 is defined by (45) and L is the gain of the observer.

2] FRANCIS, B. A. AND DOYLE, J. , "Linear Control Theory with an Hoo Optimality Criterion," SIAM J. Control and Optimization, 25, 1987, pp. 815-844. [3] KHARGONEKAR, P. , "State-space Hoo Control Theory," in Mathe- matical System Theory: The Influence of R. E. Kalman, edited by A. C. Antoulas, Springer-Verlag, Berlin, 1991. [4] KHARGONEKAR, P. , NAGPAL, K. , AND POOLLA, K. , "Hoc control with transients," SIAM Journal on Control and Optimization, 29, 1991, pp. 1373-1393. [5] PERKINS, W. R. AND MEDANIC, J.

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