By Alexey Victorovich Pavlov, Nathan van de Wouw, Henk Nijmeijer
The challenge of asymptotic law of the output of a dynamical procedure performs a critical function up to the mark concept. a big variation of this challenge is the output law challenge, that are utilized in such parts as set-point keep an eye on, monitoring reference indications and rejecting disturbances generated through an exterior method, managed synchronization of dynamical structures, and observer layout for self reliant platforms. This booklet is among the first systematic experiences at the nonlinear output rules challenge that embraces either the neighborhood and worldwide solvability research, protecting such points as solvability stipulations, controller layout, and functional implementation matters.
The booklet opens with the improvement of the mathematical equipment of convergent systems—very important for learning nonlinear regulate systems—laying the root for many of the consequences offered within the paintings. The examine then proceeds to a brand new challenge statement—the so-called uniform output law challenge. A accomplished solvability research of this challenge is supplied within the subsequent a part of the paintings. according to the solvability research, optimistic controller layout tools for the worldwide uniform output legislation challenge are awarded for numerous periods of nonlinear platforms.
In an try and bridge the space among conception and perform, the authors finish with a presentation of an experimental case examine. The experiment—one of the 1st within the box of nonlinear output regulation—deals with regulate of a translational oscillator with a rotational actuator, illustrating the applicability of the nonlinear output legislation thought in experiments and elevating a couple of inquiries to be addressed in destiny research.
The scope of questions addressed within the booklet, the uniformity in their remedy, the newness of the proposed technique, and the got effects make this quantity exact with recognize to different works at the challenge of nonlinear output legislation. as well as being a superb reference for the uniform output law challenge, the publication has an instructional price on convergent structures. The paintings could be of curiosity to manage engineers, theorists, and scholars, and should be used as a textbook for a graduate path on nonlinear control.
Read or Download Uniform Output Regulation of Nonlinear Systems: A Convergent Dynamics Approach PDF
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Additional resources for Uniform Output Regulation of Nonlinear Systems: A Convergent Dynamics Approach
Example text
Bidirectionally interconnected systems with inputs. 22 2 Convergent systems |y(t)| ≤ βy (|y(t0 )|, t − t0 ). 28) is input-to-state convergent. Proof: Denote z¯w (t) to be the steady-state solution of the z-subsystem corresponding to y = 0 and to some w(·) ∈ PC. 28) that is defined and bounded for all t ∈ R. 13). Remark. 28 in Chapter 5 to prove the separation principle for input-to-state convergent systems. 28) represents a system in closed loop with a state-feedback controller and an observer generating state estimates for this controller.
In this chapter we state several variants of the uniform output regulation problem based on the notion of uniform convergence. 1 we introduce the equations of the systems under consideration and make basic assumptions on these systems. 2 we state the global and local variants of the uniform output regulation problem as well as the problem of robust uniform output regulation. 3. 4. 3) with state x ∈ Rn , input u ∈ Rk , regulated output e ∈ Rlr , and measured output y ∈ Rlm . 4) with some set of initial conditions W ⊂ Rm .
38) for all ω ∈ R. This lemma allows one to check input-to-state convergence for the so-called Lur’e systems, as follows from the example below. Exponential convergence of Lur’e systems with nonlinearities satisfying some incremental sector condition has been studied in [89]. In that work the nonlinearities may even be discontinuous. 38. 39) with the Hurwitz matrix A, scalar output y, and scalar nonlinearity ϕ(y) ∈ R. Suppose the nonlinearity ϕ(y) is C 1 and it satisfies the condition ∂ϕ ∂y (y) ≤ γ for all y ∈ R.
