Feedback Kalman-Yakubovich lemma and its applications to adaptive control

Andrievsky, Boris; Churilov, Alexander N.; Fradkov, Alexander L.

doi:10.1109/cdc.1996.577581

Cited by 32 publications

(35 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This "squaring down" procedure changes the number of unknowns which may be important to preserve, e.g. for adaptive control, where reducing the number of adjustable parameters may decrease transient performance of adaptive systems, see [1]. To summarize, G-passification of W (s, ∆) is not equivalent to passification of GW (s, ∆), thus justifying the terminology.…”

Section: Definition 1 System (1) Is Called Robustly Strictly G-passivmentioning

confidence: 99%

“…∆ ∈ ¡ there exists a unique quadratic function V (x) = x * Hx (storage function) with H = H * > H and a unique scalar ρ > 0 such that (3) holds for all uncertainties ∆ ∈ ¡ and for any solution of the system (1).…”

Section: Definition 2 System (1) Is Called Uniformly Robustly Strictlmentioning

confidence: 99%

“…Parameters of the state-space model (1) Note that for this data some coefficients of the matrix A(∆) vary in an order of magnitude.…”

Section: Examplementioning

confidence: 99%

“…One of the most powerful passivity-based design methods is passification (sometimes called passivation) -finding a state or output feedback rendering the closed loop system passive [21,6,13]. Among applications of passification approach are adaptive control [1]; control of partially linear composite systems [19,13], flight control [12,8], process control [25,9].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Robust Passification via Static Output Feedback – Lmi Results

Peaucelle

Fradkov

Andrievsky

2005

IFAC Proceedings Volumes

View full text Add to dashboard Cite

show abstract

Section: Definition 1 System (1) Is Called Robustly Strictly G-passivmentioning

confidence: 99%

Section: Definition 2 System (1) Is Called Uniformly Robustly Strictlmentioning

confidence: 99%

“…Parameters of the state-space model (1) Note that for this data some coefficients of the matrix A(∆) vary in an order of magnitude.…”

Section: Examplementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Robust Passification via Static Output Feedback – Lmi Results

Peaucelle

Fradkov

Andrievsky

2005

IFAC Proceedings Volumes

View full text Add to dashboard Cite

show abstract

“…First introduced in 1974 for linear systems [9,10,1] and later extended to nonlinear systems [29,30,18,13] it provides efficient design procedures and simple controller structures. Compared to adaptive schemes with combined parameter estimation and controller tuning [16,4], PBAC needs no estimation and tuning is performed via a simple differential equation.…”

Section: Introductionmentioning

confidence: 99%

Passification‐based adaptive control of linear systems: Robustness issues

Peaucelle

Fradkov

Andrievsky

2007

Adaptive Control & Signal

View full text Add to dashboard Cite

Passivity is a widely used concept in control theory having lead to many significant results. The manuscript concentrates on one characteristic of passivity, namely passification-based adaptive control. This concept applies to MIMO systems for which exists a combination of outputs that renders the open-loop system hyper-minimum-phase. Under such assumptions, the system may be passified by both high-gain static output-feedback and by a particular adaptive control algorithm. This last control law is modified here to guarantee its coefficients to be bounded. The contribution of the paper is to investigate its robustness with respect to parametric uncertainty. Time response characteristics are illustrated on examples including realistic situations with noisy output and saturated input. Theoretical results are formulated as linear matrix inequalities and can hence be readily solved with semi-definite programming solvers.

show abstract

Decentralized simple adaptive control of nonlinear systems

Ulrich

Sąsiadek

2013

Adaptive Control & Signal

View full text Add to dashboard Cite

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...

show abstract

Feedback Kalman-Yakubovich lemma and its applications to adaptive control

Cited by 32 publications

References 18 publications

Robust Passification via Static Output Feedback – Lmi Results

Robust Passification via Static Output Feedback – Lmi Results

Passification‐based adaptive control of linear systems: Robustness issues

Decentralized simple adaptive control of nonlinear systems

Contact Info

Product

Resources

About