By Alexander Poznyak, Andrey Polyakov, Vadim Azhmyakov
This monograph introduces a newly constructed robust-control layout approach for a large type of continuous-time dynamical structures referred to as the “attractive ellipsoid method.” in addition to a coherent creation to the proposed keep watch over layout and similar subject matters, the monograph experiences nonlinear affine regulate structures within the presence of uncertainty and offers a optimistic and simply implementable keep watch over approach that promises convinced balance houses. The authors talk about linear-style suggestions regulate synthesis within the context of the above-mentioned structures. the advance and actual implementation of high-performance robust-feedback controllers that paintings within the absence of entire info is addressed, with a number of examples to demonstrate the best way to practice the horny ellipsoid approach to mechanical and electromechanical structures. whereas theorems are proved systematically, the emphasis is on figuring out and utilising the idea to real-world occasions. beautiful Ellipsoids in powerful keep an eye on will attract undergraduate and graduate scholars with a history in sleek platforms conception in addition to researchers within the fields of regulate engineering and utilized mathematics.
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Extra resources for Attractive Ellipsoids in Robust Control
0 if t ! C1: Note that the attractivity property mentioned above does not imply in general the Lyapunov asymptotic stability of the invariant set under consideration. Well-known counterexamples are given in Blanchini (1999). t/; Dg < ; t 0: It is notable that the various versions of the basic Lyapunov function method provide the main tools for stability and robustness analysis and the corresponding control design for nonlinear control systems. In that connection, let us recall the fundamental Lyapunov function concept.
8. 3). The analytic background of the attractive ellipsoid method we developed for the class of systems with quasi-Lipschitz right-hand sides is given by the following simple conceptual result. 5. Let assumptions (A1), (A2) hold, and let u W Rn ! Rm be a continuous function. If there exists a proper function V W Rn ! x/. Proof. 3) has solutions for every set of initial conditions. t/ be an arbitrary solution. t// hold for almost all t. t// > 1. So the set is invariant and asymptotically attractive.
X// are defined, upper semicontinuous, compact, and convex-valued for every t 2 R, x 2 Rn , and u 2 Rm . 11) with quasi-Lipschitz right-hand side (Aubin & Celina 1984; Berkovitz 1974; Deimling 1992; Filippov 1988). 4. An absolutely continuous vector function x W R ! x// almost everywhere on some time interval or segment I. The above definition gives rise to the corresponding existence result. 4. t0 / D x0 has at least one solution, and each solution is defined for all t > t0 . 2 and the following fundamental lemma.