Simple and robust adaptive control

Barkana, Itzhak; Fradkov, Alexander L.

doi:10.1002/acs.2477

Cited by 11 publications

(8 citation statements)

References 17 publications

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“…Now, define the domain Ω where the Lyapunov derivative is identically zero (i.e., not just equal zero),

Ω MathClass-rel= {x MathClass-rel| \overset{V}{true} (x MathClass-punc, t) MathClass-rel\equiv 0) MathClass-close}

. Then, if one of the Assumptions A or B holds, the entire state vector x ( t ) ultimately reaches the domain

Ω_{f} MathClass-rel= Ω_{0} MathClass-op\cap Ω

.…”

Section: Old and New Developments In Stability Analysis Of Nonlinear mentioning

confidence: 99%

“…However, the examples earlier show that in many practical situation one cannot define Ω as in the former text, yet nonetheless Ω can be defined as Ω = { x | W ( x ) g ( t ) ≡ 0},

Ω MathClass-rel= {x MathClass-rel| MathClass-op\sum W_{i} (x) g_{i} (t) MathClass-rel\equiv 0}

, or just

Ω MathClass-rel= {x MathClass-rel| \overset{V}{true} (x MathClass-punc, t) MathClass-rel\equiv 0}

. As one can prove , any one of the definitions earlier is legitimate definition that is covered by the new invariance principle.…”

Section: Old and New Developments In Stability Analysis Of Nonlinear mentioning

confidence: 99%

“…Theorem 6 (The modified invariance principle): Under the same assumptions as the new invariance principle, assume that the derivative of the PD Lyapunov function has the form

\overset{V}{true} (t) MathClass-rel= W_{1} (x MathClass-punc, t) MathClass-bin+ W_{2} (x MathClass-punc, t)

where W 1 ( x , t ) ⩽ 0 and W 2 ( x , t ) vanishes as time goes to infinity along bounded trajectories. Then, all bounded trajectories ultimately reach that domain in space where W 1 ( x , t ) ≡ 0 .…”

Section: Old and New Developments In Stability Analysis Of Nonlinear mentioning

confidence: 99%

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Simple adaptive control – a stable direct model reference adaptive control methodology – brief survey

Barkana¹

2013

Adaptive Control & Signal

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In spite of successful proofs of stability and even successful demonstrations of performance, the eventual use of model reference adaptive control methodologies in practical real-world systems has met a rather strong resistance from practitioners and has remained very limited. Apparently, the practitioners have a hard time understanding the conditions that can guarantee stable operations of adaptive control systems under realistic operational environments. Besides, it is difficult to measure the robustness of adaptive control system stability and allow it to be compared with the common and widely used measure of phase margin and gain margin that is utilized by present, mainly LTI, controllers. Furthermore, recent counterexamples seem to show that adaptive systems may diverge even when all required conditions are fulfilled. This paper attempts to revisit the fundamental qualities of the common direct model reference adaptive control methodology based on gradient and to show that some of its basic drawbacks have been addressed and eliminated within the so-called simple adaptive control methodology. The sufficient conditions that guarantee stability are clearly stated and lead to similarly clear proofs of stability. The main claim of the paper is that if sufficient information exists for a robust classical design control, same information can be used to implement robust simple adaptive controllers. As many real world applications show, the added value of using add-on adaptive control techniques, the use is pushing the desired performance beyond any previous limits. The paper also shows that the previous counterexamples to model reference adaptive control become just simple, successful, and stable applications of simple adaptive control.

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“…Now, define the domain Ω where the Lyapunov derivative is identically zero (i.e., not just equal zero),

Ω MathClass-rel= {x MathClass-rel| \overset{V}{true} (x MathClass-punc, t) MathClass-rel\equiv 0) MathClass-close}

. Then, if one of the Assumptions A or B holds, the entire state vector x ( t ) ultimately reaches the domain

Ω_{f} MathClass-rel= Ω_{0} MathClass-op\cap Ω

.…”

Section: Old and New Developments In Stability Analysis Of Nonlinear mentioning

confidence: 99%

“…However, the examples earlier show that in many practical situation one cannot define Ω as in the former text, yet nonetheless Ω can be defined as Ω = { x | W ( x ) g ( t ) ≡ 0},

Ω MathClass-rel= {x MathClass-rel| MathClass-op\sum W_{i} (x) g_{i} (t) MathClass-rel\equiv 0}

, or just

Ω MathClass-rel= {x MathClass-rel| \overset{V}{true} (x MathClass-punc, t) MathClass-rel\equiv 0}

. As one can prove , any one of the definitions earlier is legitimate definition that is covered by the new invariance principle.…”

Section: Old and New Developments In Stability Analysis Of Nonlinear mentioning

confidence: 99%

“…Theorem 6 (The modified invariance principle): Under the same assumptions as the new invariance principle, assume that the derivative of the PD Lyapunov function has the form

\overset{V}{true} (t) MathClass-rel= W_{1} (x MathClass-punc, t) MathClass-bin+ W_{2} (x MathClass-punc, t)

Section: Old and New Developments In Stability Analysis Of Nonlinear mentioning

confidence: 99%

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Simple adaptive control – a stable direct model reference adaptive control methodology – brief survey

Barkana¹

2013

Adaptive Control & Signal

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“…This basic knowledge can be used to test the Almost Strictly Positive Real (ASPR) properties of the plant or to build the proper parallel feedforward that renders the plant ASPR and makes the use of SAC safe and robust (see [1] and [9]. In [10] it is shown that the information required rendering a plant ASPR (robust ASPR) is exactly the same information as is required for stabilization (robust stabilization) of the plant.…”

Section: Review Of the Sac Algorithmmentioning

confidence: 99%

“…(1) (K e ) eq =K e +K 10 is bounded below by K 10 where K Ie (0)=0.. The design of the SAC controller involves the synthesis of D(s).…”

Section: Fig 2: Sac Schemementioning

confidence: 99%

Real-time implementation of Add-On Simple Adaptive Control Algorithm to linear stage

Rusnak

Nesher

Dana

2013

2013 International Conference on Process Control (PC)

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Abstract² Application of the Add-On Simple Adaptive Control Algorithm in real time is presented. The algorithm is applied to a real linear drive system. The algorithm has been implemented in SIMULINK ® within the dSPACE ® Real-Time Control Environment. The Add-On simple adaptive control algorithm is briefly reviewed and design procedure is outlined. The performance in real-time shows the ability of the Add-On simple adaptive control algorithm to perform on real hardware in noisy environment while improving the performance and robustness.

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Decentralized simple adaptive control of nonlinear systems

Ulrich

Sąsiadek

2013

Adaptive Control & Signal

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Recently, the passivity results for linear time-invariant systems were successfully extended to nonlinear and nonstationary systems, thus guaranteeing stability of adaptive control of nonlinear square systems. Based on this theoretical development, this paper presents the development of a new class of direct adaptive controllers, which employ a new decentralized adaptation law mechanism that is developed from the simple adaptive control technique. The resulting direct adaptive control methodology is referred to as decentralized simple adaptive control. A simplification of this new control algorithm, referred to as decentralized modified simple adaptive control, is also presented. In addition, it is shown that both control methodologies can be modified to avoid divergence in practical situations, where the trajectory tracking errors cannot reach zero. Using Lyapunov direct method and Lasalle's invariance principle for nonautonomous systems, the formal proof of stability is established. As well, a numerical simulation study for a trajectory tracking problem by a rigid-joint manipulator is presented to illustrate the new adaptive control approaches. DECENTRALIZED SIMPLE ADAPTIVE CONTROL 751 CB be a positive definite symmetric (PDS). A recent algebraic proof of this important statement can be found in [10].Over the years, a variety of direct adaptive control laws have been developed to address the problem of time varying the gains of a controller so that the plant closed-loop characteristics match those defined by a reference model. However, most of the research in this area is based on the assumption that prior knowledge of the unknown plant to be controlled is available, and/or requires the plant to be of the same order as the reference model, and/or requires full-state feedback or observers. To mitigate these stringent requirements, the simple adaptive control (SAC) approach was developed by Sobel et al. [11], Barkana et al. [12] and Barkana and Kaufman [13]. Using the ASP results, the stability of the SAC technique for square LTI systems was rigorously established by Kaufman, Barkana and Sobel [14]. This direct adaptive output feedback method is based upon the command generator tracker methodology [15] and requires the plant to track the ideal model, which is an ideal representation of the plant only as far as its outputs represent the desired output behavior of the plant. For this reason, this direct adaptive control methodology has been successfully applied for the control of number of large-scale systems without requiring large-order adaptive controllers.However, although greatly reduced when compared with standard model following techniques, in some applications the SAC technique may still present a design complexity issue arising from the large number of parameters and coefficients to select. In fact, the calculation of the control input involves a stabilizing output feedback control gain and two feedforward control gains, each calculated as the summation of a proportional and an integral control gain compo...

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Simple and robust adaptive control

Cited by 11 publications

References 17 publications

Simple adaptive control – a stable direct model reference adaptive control methodology – brief survey

Simple adaptive control – a stable direct model reference adaptive control methodology – brief survey

Real-time implementation of Add-On Simple Adaptive Control Algorithm to linear stage

Decentralized simple adaptive control of nonlinear systems

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