By Yury V. Orlov, Luis T. Aguilar
This compact monograph is targeted on disturbance attenuation in nonsmooth dynamic structures, constructing an H∞ technique within the nonsmooth surroundings. just like the traditional nonlinear H∞ approach, the proposed nonsmooth layout promises either the interior asymptotic balance of a nominal closed-loop method and the dissipativity inequality, which states that the dimensions of an mistakes sign is uniformly bounded with appreciate to the worst-case measurement of an exterior disturbance sign. This warrantly is accomplished by means of developing an power or garage functionality that satisfies the dissipativity inequality and is then applied as a Lyapunov functionality to make sure the inner balance requirements.
Advanced H∞ regulate is detailed within the literature for its remedy of disturbance attenuation in nonsmooth structures. It synthesizes a variety of instruments, together with Hamilton–Jacobi–Isaacs partial differential inequalities in addition to Linear Matrix Inequalities. in addition to the finite-dimensional therapy, the synthesis is prolonged to infinite-dimensional surroundings, concerning time-delay and dispensed parameter structures. to aid illustrate this synthesis, the e-book makes a speciality of electromechanical functions with nonsmooth phenomena as a result of dry friction, backlash, and sampled-data measurements. designated cognizance is dedicated to implementation issues.
Requiring familiarity with nonlinear structures conception, this e-book could be obtainable to graduate scholars drawn to structures research and layout, and is a welcome boost to the literature for researchers and practitioners in those areas.
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Extra info for Advanced H∞ Control: Towards Nonsmooth Theory and Applications
28) and some " > 0. Theorem 14. A4/. T 2/, coupled together, are satisfied. 34) yields a T -periodic solution to the problem in question. Proof. Necessity is demonstrated based on a periodic version of the strict bounded real lemma. Let the H1 suboptimal control problem possess a solution. T 2/. 28) and some " > 0. T 2/. The detailed proof of the sufficiency follows the line of reasoning used in the proof of Theorem 4 and is left to the reader. Chapter 4 Nonlinear H1 Control In this chapter, the H1 (sub)optimal control problem is reformulated for an autonomous nonlinear system in terms of its L2 -induced norm.
8). 7) at a time instant t t0 . Definition 1. 11) Consider Lyapunov–Krasovskii functionals, which depend on x and xP . Œ h; 0; H/ ! t; ; P /: Lemma 4. Œ h; 0; H/ ! 11) holds with K D ˇ. Proof. 14) or fast-varying with no restrictions on P . Let A1–A3 be in force. A/ ! 16) 28 2 The LMI Approach in an Infinite-Dimensional Setting for some positive constants ˇ; P ; Q ; S ; R . 12) of Lemma 4 is satisfied. 16) allows one to use not only bounded operators P (like those considered in [35, p. 16).
S t / z2 . s t / z2 . ; s/ds d ; > 0, and q 0. 0; /. It should be noted that the above choice of P , depending on the slack variable P3 , is different from that of the ODEs (where these matrices are independent). Thus, the slack variable allows one to construct an appropriate Lyapunov–Krasovskii functional. A/. 3). 1). 1 d /qe 2ıh 2ıh : We have thus proved the following result. Theorem 8. 38) hold. 14), and the inequality p1 R 0 z2 . t t0 / n ap3 R 0 z2 . ; t0 /d p3 a C hq C hs; h3 r=2 o R 2 2 h;t0 0 Œz .
Advanced H∞ Control: Towards Nonsmooth Theory and Applications by Yury V. Orlov, Luis T. Aguilar
Categories: System Theory