A structural approach to robust control

Nonlinear control algorithms of two types are presented for uncertain linear plants. Controllers of the first type are stabilizing polynomial feedbacks that allow to adjust a guaranteed convergence time of system trajectories into selected neighborhood of the origin independently on initial conditions. The control design procedure uses block control principles and finite-time attractivity properties of polynomial feedbacks. Controllers of the second type are modifications of the second order sliding mode control algorithms. They provide global finite-time stability of the closed-loop system and allow to adjust a guaranteed settling time independently on initial conditions. Control algorithms are presented for both single-input and multi-input systems. Theoretical results are supported by numerical simulations.

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“…The control design for more general case can be done using the robustness analysis of block controllability forms presented in [15].…”

Section: Lemma 3 If the Pair (A B) Is Controllable Then 1) Algorithmentioning

confidence: 99%

Nonlinear Feedback Design for Fixed-Time Stabilization of Linear Control Systems

Polyakov

2012

IEEE Trans. Automat. Contr.

3,186

1,473

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“…If it is stable, then the problem of tracking is solved by the direct choice of the stabilizing control in system (4.3). In what follows we present our block approach-based decomposition procedure to solve the problem of tracking as applied to system (4.2)-(4.4) under the assumption that the proper dynamics of system (4.4) is unstable [10,11].…”

Section: Design Of the Problem Of Tracking By The Output Variables Unmentioning

confidence: 99%

“…Then, the problem of real-time identification of the parameter required to design the tracking system is solved using the estimates of the state vector components [9]. In the problem of tracking under unstable zero dynamics, the feedback proper is designed using decomposition of the design procedure into independently solved smaller subproblem based on the block methodology [10,11].…”

Section: Introductionmentioning

confidence: 99%

Problem of tracking in linear systems with parametric uncertainties under unstable zero dynamics

Utkin

2014

Autom Remote Control

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Proposed was a solution to the problem of tracking in linear SISO systems with unstable zero dynamics in the conditions of parametric uncertainty of the models of plant and reference generator under incomplete information about the state vectors. The approach developed employs the methods of the sliding mode theory in the problems of real-time feedback design, observation, and parameter identification.

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“…Next the decompositional procedure developed by the authors for tracking problem under assumption that the internal dynamics of the system (21) is unstable is proposed. This procedure is using the methodology of block approach (Drakunov et al, 1990), (Krasnova et al, 2011…”

Section: Write (16) In the New Variables Asmentioning

confidence: 99%

“…Then the problem of parameter identification can be solved in real time using the estimates of the state vector components (Utkin, V.I., 1992). Within the framework of the block approach (Drakunov et al, 1990;Krasnova et al, 2011), the decomposition procedure of feedback design in tracking problem under an unstable zero dynamics is developed with the use of the estimates.…”

Section: Introductionmentioning

confidence: 99%

Tracking Problem for Linear Systems with Parametric Uncertainties and Unstable Zero Dynamics

Utkin

Krasnova

2014

IFAC Proceedings Volumes

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A structural approach to robust control

Cited by 17 publications

References 6 publications

Nonlinear Feedback Design for Fixed-Time Stabilization of Linear Control Systems

Nonlinear Feedback Design for Fixed-Time Stabilization of Linear Control Systems

Problem of tracking in linear systems with parametric uncertainties under unstable zero dynamics

Tracking Problem for Linear Systems with Parametric Uncertainties and Unstable Zero Dynamics

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