Stability of self‐tuning control based on Lyapunov function

Patete, Anna; Furuta, K.; Tomizuka, Masayoshi

doi:10.1002/acs.1027

Cited by 15 publications

(4 citation statements)

References 19 publications

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“…Journal of Electrical and Computer Engineering Using (14) and (15) and adding and subtracting ( +1) ( + 1)̂( ) to the right member of (16), we obtain…”

Section: Modified Recursive Least Square Algorithm M-rls With -Modifimentioning

confidence: 99%

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Self-Tuning Control Scheme Based on the Robustnessσ-Modification Approach

Touijer

Kamoun

Essounbouli

et al. 2017

Journal of Electrical and Computer Engineering

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This paper deals with the self-tuning control problem of linear systems described by autoregressive exogenous (ARX) mathematical models in the presence of unmodelled dynamics. An explicit scheme of control is described, which we use a recursive algorithm on the basis of the robustnessσ-modification approach to estimate the parameters of the system, to solve the problem of regulation tracking of the system. This approach was designed with the assumptions that the norm of the vector of the parameters is well-known. A new quadratic criterion is proposed to develop a modified recursive least squares (M-RLS) algorithm withσ-modification. The stability condition of the proposed estimation scheme is proved using the concepts of the small gain theorem. The effectiveness and reliability of the proposed M-RLS algorithm are shown by an illustrative simulation example. The effectiveness of the described explicit self-tuning control scheme is demonstrated by simulation results of the cruise control system for a vehicle.

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“…Journal of Electrical and Computer Engineering Using (14) and (15) and adding and subtracting ( +1) ( + 1)̂( ) to the right member of (16), we obtain…”

Section: Modified Recursive Least Square Algorithm M-rls With -Modifimentioning

confidence: 99%

“…Stability theory was introduced. In this context, several studies have been developed [5][6][7][8][9][10][11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Self-Tuning Control Scheme Based on the Robustnessσ-Modification Approach

Touijer

Kamoun

Essounbouli

et al. 2017

Journal of Electrical and Computer Engineering

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“…[15,16] adopted the method of adding an "attenuated excitation signal" to ensure the stability and convergence of random pole assignment self-tuning control, while [7,8] provided that it does not need an external excitation signal, but uses a self-convergent weighted least squares parameter estimation algorithm to ensure the stability and convergence of random pole assignment self-tuning control. The literature [17][18][19][20] analyzed the stability and convergence of the adaptive decoupling control system, and the literature [21] analyzed the stability and convergence of generalized minimum variance selftuning control for minimum phase objects and some non-minimum phase objects based on the Lyapunov function. The literature [22] proposed a theory of virtual equivalent systems, but it mainly focused on single-variable systems and did not study multivariable systems.…”

Section: Introductionmentioning

confidence: 99%

From Nonlinear Dominant System to Linear Dominant System: Virtual Equivalent System Approach for Multiple Variable Self-Tuning Control System Analysis

Pan

Peng

Zhang

2023

Entropy

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The stability and convergence analysis of a multivariable stochastic self-tuning system (STC) is very difficult because of its highly nonlinear structure. In this paper, based on the virtual equivalent system method, the structural nonlinear or nonlinear dominated multivariable self-tuning system is transformed into a structural linear or linear dominated system, thus simplifying the stability and convergence analysis of multivariable STC systems. For the control process of a multivariable stochastic STC system, parameter estimation is required, and there may be three cases of parameter estimation convergence, convergence to the actual value and divergence. For these three cases, this paper provides four theorems and two corollaries. Given the theorems and corollaries, it can be directly concluded that the convergence of parameter estimation is a sufficient condition for the stability and convergence of stochastic STC systems but not a necessary condition, and the four theorems and two corollaries proposed in this paper are independent of specific controller design strategies and specific parameter estimation algorithms. The virtual equivalent system theory proposed in this paper does not need specific control strategies, parameters and estimation algorithms but only needs the nature of the system itself, which can judge the stability and convergence of the self-tuning system and relax the dependence of the system stability convergence criterion on the system structure information. The virtual equivalent system method proposed in this paper is proved to be effective when the parameter estimation may have convergence, convergence to the actual value and divergence.

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“…One of them resorts to external excitation or internal excitation [9][10][11][12][13][14][15][16][17], and the other is based on modification of the parameter estimates [18][19][20][21][22][23][24][25]. Recently, a new result for a class of non-minimum phase plant based on generalized minimum variance is presented in [26]. Despite the fundamental progress achieved so far, a general theory of STC is still absent.…”

Section: Introductionmentioning

confidence: 99%

The convergence of parameter estimates and the real structure information of plant are both unnecessary for a general self-tuning control system - Arbitrary deterministic plant

Zhang

et al. 2012

2012 24th Chinese Control and Decision Conference (CCDC)

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This paper is concerned with the stability and convergence of a general deterministic self-tuning control (STC) system, which consists of arbitrary control strategy and arbitrary estimation algorithm. The plant may be linear or non-linear, time-invariant or time varying. The conditions required for global stability and convergence are relaxed, i.e., the convergence of parameter estimates and the real structure information of plant are both removed. It is therefore argued that external excitation signal is not necessary for deterministic STC system. In other words, feedback information of STC system itself is sufficient to achieve the control objective (regulation or tracking). The key point is that with the help of Virtual Equivalent System (VES) concept, the original nonlinear dominant (nonlinear in structure) problem of STC is converted to a linear dominant (linear in structure) problemdeterministic slow switching control system.

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Stability of self‐tuning control based on Lyapunov function

Cited by 15 publications

References 19 publications

Self-Tuning Control Scheme Based on the Robustnessσ-Modification Approach

Self-Tuning Control Scheme Based on the Robustnessσ-Modification Approach

From Nonlinear Dominant System to Linear Dominant System: Virtual Equivalent System Approach for Multiple Variable Self-Tuning Control System Analysis

The convergence of parameter estimates and the real structure information of plant are both unnecessary for a general self-tuning control system - Arbitrary deterministic plant

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