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Some results on bilinear control systems with rank-one inputs

Chou, Yonggang
http://rave.ohiolink.edu/etdc/view?acc_num=case1058456992

Abstract Details

1995, Doctor of Philosophy, Case Western Reserve University, Mathematics.
We shall be treating bilinear single-input control systems in n-space, dot x = (A + uB)x, u: R1→[-1,1],with the special property that the 'control' matrix B has rank 1, i.e., B = bc* for nonzero n-vectors b, c. Let cal At cdot p denote the set attainable from an initial point p at time t ge 0 by admissible controls u(.). It is known that the 'extremal' controls are directly available: a measurable control u: (0, t) → (-1, 1) steers p to the boundary of the attainable set cal At cdot p if, and only if, u takes on the extreme values ±1 only, is piecewise constant, and has at most n - 1 switches (under mild generic conditions on the data A, b, c, and for small t > 0; this is a strong version of the bang-bang principle, see (9)). Naturally, every time-optimal control is extremal; however, usually the converse fails, so that not all extremal controls are time-optimal (unless the initial point p is locally controllable; see Fig. 2). Chapter 2 solves the 'recognition problem', this suggests: to determine completely, in terms of the system data A, b, c and the initial point p, which extremal controls are indeed time-optimal. In the second part (Chapter 3), we assume that the initial point p is local ly controllable. We introduce and study the terminal manifolds of these attainable sets cal At cdot p for small times t, and then construct the optimal feedback equation corresponding to the system. Finally (Chapter 4) we apply the theory of discontinuous differential equations to study the so-called measurement-stability of this optimal feedback equation, and we will prove that the equation is measurement-stable
Otomar Hajek (Advisor)
61 p.
Mathematics
Bilinear control systems; Rank-one inputs

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Citations

  • Chou, Y. (1995). Some results on bilinear control systems with rank-one inputs [Doctoral dissertation, Case Western Reserve University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=case1058456992

    APA Style (7th edition)

  • Chou, Yonggang. Some results on bilinear control systems with rank-one inputs. 1995. Case Western Reserve University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=case1058456992.

    MLA Style (8th edition)

  • Chou, Yonggang. "Some results on bilinear control systems with rank-one inputs." Doctoral dissertation, Case Western Reserve University, 1995. http://rave.ohiolink.edu/etdc/view?acc_num=case1058456992

    Chicago Manual of Style (17th edition)

case1058456992
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© 1995, all rights reserved.
This open access ETD is published by Case Western Reserve University School of Graduate Studies and OhioLINK.