By Alexander Poznyak, Andrey Polyakov, Vadim Azhmyakov
This monograph introduces a newly constructed robust-control layout approach for a large classification of continuous-time dynamical platforms referred to as the “attractive ellipsoid method.” in addition to a coherent advent to the proposed keep watch over layout and similar issues, the monograph experiences nonlinear affine keep watch over platforms within the presence of uncertainty and provides a optimistic and simply implementable keep watch over procedure that promises sure balance houses. The authors talk about linear-style suggestions keep watch over synthesis within the context of the above-mentioned structures. the improvement and actual implementation of high-performance robust-feedback controllers that paintings within the absence of whole details is addressed, with a number of examples to demonstrate tips on how to follow the sexy ellipsoid approach to mechanical and electromechanical structures. whereas theorems are proved systematically, the emphasis is on figuring out and employing the speculation to real-world events. beautiful Ellipsoids in powerful regulate will attract undergraduate and graduate scholars with a history in glossy platforms thought in addition to researchers within the fields of keep watch over engineering and utilized mathematics.
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This monograph introduces a newly built robust-control layout procedure for a large category of continuous-time dynamical platforms referred to as the “attractive ellipsoid process. ” in addition to a coherent advent to the proposed regulate layout and similar subject matters, the monograph reports nonlinear affine keep watch over structures within the presence of uncertainty and offers a positive and simply implementable regulate procedure that promises definite balance houses.
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Additional info for Attractive Ellipsoids in Robust Control
In this book, we will consider both of these as interpretations of the basic quasiLipschitz condition. As we can see, the class of the right-hand sides introduced above also contains some possible discontinuous functions. 4) have become a modern application focus of practical control theory; cf. (Bartolini, Fridman, Pisano, & Usai 2008; Poznyak 2008; Utkin 1992). 1) with discontinuous right-hand sides. 2 Examples of Quasi-Lipschitz Systems Let us continue with a brief discussion of some examples of dynamical systems that allow the quasi-Lipschitz modeling framework.
Let gj W Rn ! R be a real-valued function. y/ Ä 0 for j D 1; : : : ; M . y/ N <0 for all j D 1; : : : ; M . 10. y/ Ä 0 for j D 1; : : : ; M and that moreover, the Slater condition for the above system of inequalities is satisfied. y/ 0; where f W Rn ! y/ 0 j D1 for all y 2 Rn . Among additional useful results similar to the S-lemma, let us mention the so-called inhomogeneous S-lemma (please consult Ben-Tal & Nemirovski 2001; Polik & Terlaky 2007 for the exact formulation and proofs). We next give an “algorithmic” formulation of a concrete version of the general S-lemma that we use in some technical proofs in our book.
5 is quadratic. The corresponding robust and/or optimal control design schemes become LMI constraints in this case. 15) where K 2 Rm n is an appropriate gain matrix. 2) is characterized by a matrix pair fP; Kg. t/ Ä 1 holds in an exact or approximate sense. 3). From the point of view of implementable control applications, we are strongly interested in constructing a concrete attractive ellipsoid E of minimal size (in some suitable sense). This requirement can be formalized in the form of a specific minimization problem related to a characteristic parameter of E.