Download Attractive Ellipsoids in Robust Control by Alexander Poznyak, Andrey Polyakov, Vadim Azhmyakov PDF

By Alexander Poznyak, Andrey Polyakov, Vadim Azhmyakov

This monograph introduces a newly built robust-control layout process for a large classification of continuous-time dynamical platforms referred to as the “attractive ellipsoid method.” in addition to a coherent creation to the proposed regulate layout and comparable themes, the monograph stories nonlinear affine keep watch over structures within the presence of uncertainty and provides a confident and simply implementable regulate method that promises yes balance homes. The authors speak about linear-style suggestions regulate synthesis within the context of the above-mentioned platforms. the advance and actual implementation of high-performance robust-feedback controllers that paintings within the absence of entire details is addressed, with a number of examples to demonstrate tips to practice the horny ellipsoid approach to mechanical and electromechanical platforms. whereas theorems are proved systematically, the emphasis is on knowing and utilizing the speculation to real-world events. appealing Ellipsoids in strong regulate will attract undergraduate and graduate scholars with a historical past in sleek platforms thought in addition to researchers within the fields of keep watch over engineering and utilized mathematics.

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Extra info for Attractive Ellipsoids in Robust Control

Example text

1 (LPV, LTV and Uncertain Systems). 2 (Affine Control System). 5). 3 (Nonlinear Mechanical Systems). t// P is Lipschitz continuous and does not increase faster than linear in the second and third arguments. 5) and is quasi-Lipschitz. 4 (Relay and Sliding Mode Control Systems). 3), and hence is quasi-Lipschitz too. 4). 4) discontinuous right-hand side, one needs to extend a classical solution concept in order to develop a consistent modeling framework for the systems under consideration. Later, we will examine briefly a common technique for dealing with discontinuous dynamic behavior.

R is said to be proper if it satisfies the following conditions: • Iy id continuously differentiable in Rn . 0/ D 0). • Iy is radially unbounded (kxk ! x/ ! C1). 2). Here P is a symmetric positive definite n n matrix, called the shape (or configuration) matrix of the ellipsoid. 3). Based on the classical concepts mentioned above, we now introduce our local definition of the attractive ellipsoid. 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.

3 Elements of LMIs 39 (a) It must be strictly convex on the interior of !. (b) It must approach C1 along each sequence of points fxn g1 nD1 in the interior of ! that converges to a boundary point of !. Given such a specific barrier function . x/ over all x 2 ! x/; where t > 0 is the penalty parameter. Note that ft is strictly convex on Rn . The main idea is to determine a mapping t 7! t/ of ft . Subsequently, we consider the behavior of this mapping as the penalty parameter t varies. In almost all interior point methods, the latter unconstrained optimization problem is solved with the classical Newton–Raphson iteration technique Atkinson & Han 2005 to approximate the minimum of ft .

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