Read e-book online Perspectives in Control Theory: Proceedings of the Sielpia PDF

By B. Jakubczyk

ISBN-10: 1475721056

ISBN-13: 9781475721058

ISBN-10: 1475721072

ISBN-13: 9781475721072

The quantity comprises papers in response to lectures added in the course of the tuition "Per spectives on top of things conception" held in Sielpia, Poland on September 19-24, 1988. the purpose of the varsity used to be to offer the cutting-edge presentation of contemporary achievements as weH as views in such fields of regulate thought as optimum keep watch over and optimization, linear structures, and nonlinear structures. for this reason, the quantity contains survey papers including displays of a few fresh effects. The particular emphasis is wear: - nonlinear platforms (algebraic and geometric methods), - optimum keep an eye on and optimization (general difficulties, dispensed parameter systems), - linear platforms (linear-quadratic challenge, strong stabilization). a huge function of the varsity (and accordingly of the quantity) used to be its particularly "international" personality because it introduced jointly prime keep an eye on theoriests from West and East. All jointly the college was once attended by means of 108 contributors from 18 international locations. in the course of the tuition 21 one-hour invited lectures have been introduced. additionally, 5 half-an-hour talks got and 30 contributions have been provided in frames of poster classes. the varsity used to be geared up and supported by means of: Institute of arithmetic of the Polish Academy of Sciences, Committee of computerized keep watch over and Robotics of the Polish Academy of Sciences, - Institute of automated keep watch over, Warsaw collage of expertise (as Co ordinator of the fundamental examine software R.P.I.02 "Theory of keep an eye on of continuing Dynamic structures and Discrete procedures" ).

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Additional resources for Perspectives in Control Theory: Proceedings of the Sielpia Conference, Sielpia, Poland, September 19–24, 1988

Sample text

1. The regular semidefinite case. A complete solution of the regular semidefinite finite-horizon problem is given by: THEOREM (Reqular semidefinite finite-horizon case). 8, in whieh D is injeetive. : O. , t 1 P(t 1 ) ::SP(t 2 »). 42 Define the time-variable feedback matrix F(t) := - (D'D)-l(B'P(T-t)+D'C) (0 s t s T) Then we have for every function u: J(x ,u,T) = x'P(T)x + ST11D(u(t) - F(t)X(t))~2dt o 0 0 0 There exists a unique optimal control u': [O,T] .. 3) (1. 4) iii) . 5) The minimal value of J(xo,u,T) equals iv) J'(x ,T) (1.

Math. Optimization 1 (1974) 163-188 [19] H. O. FATTORINI, Exact controllability of linear systems in infinite dimensional spaces, Springer Lecture Notes in Mathematics 466 (1975) 166-183 [20] H. O. FATTORINI, The time optimal control problem for boundary control of the heat equation, Calculus of Variations and Control Theory, Academic Press, New York (1976) 305-319 [21] H. O. FATTORINI, The time optimal problem for distributed control of systems described by the wave equation, Control Theory of Systems Governed by Partial Differential Equations, Academic Press, New York (1977) 151-175 [22] H.

The relations transfer matrix from the input that y is represents choose, in independent of "'1. 5) reduces is "'1 Hence, the part of the optimal 0, [G-2, Section imply that the zero, so of the input control. If we to a regular LQ problem, which can be solved as in the previous section. 5). 3) is v* : = [(F ol; + "':)', 0] " which is also a regular function. The optimal control of the original problem, in terms of the original variables is u* := H(p)v*, input which is in ~imp , that and hence an but in general not regular.

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