Simplified Techniques for Adaptive Control of Robotic Systems

Successful implementations of simple direct adaptive control techniques in various domains of application have been presented over the last two decades in the technical literature. The theoretical background concerning basic conditions needed for stability of the controller and the open questions relating the convergence of the adaptive gains have been clarified recently, yet only for the continuous‐time algorithms. Apparently, asymptotic tracking in discrete time systems has been possible only with step input commands and the scope of the so called “almost strictly positive real (ASPR)” condition has also remained not clear. This paper expands the feasibility of discrete simple adaptive control methodology to include any desired input commands and almost all real‐world systems. The proofs of stability are also rigorously revised to solve the ultimate adaptive gain values question that has remained open until now. Finally, a complex algebraic loop that seemed to be inherent in discrete ASPR systems and might prevent the use of passivity properties in discrete systems has also been eliminated.

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“…Relations (14)- (16) can also be written in a more concise form. Substituting L T from (15) into (14) and using (16) gives…”

Section: Passivity In Discrete Linear Systemsmentioning

confidence: 99%

Almost Passivity and Simple Adaptive Control in Discrete‐Time Systems

Barkana¹,

Rusnak²,

Weiss³

2013

Asian Journal of Control

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“…Copyright For the purpose of this paper and to keep the rather elaborate mathematical presentation within some limits, we assume here that the command generator uses a step input. For the same reason, this paper assumes that the plant is LTI with unknown parameters, although same techniques can be used to extend the scope of the presentation to time-varying and non-linear plants, along the lines shown in References [22,25,30,40].…”

Section: Formulation Of the Problemmentioning

confidence: 99%

“…These techniques have also been extended by Wen and Balas [5], and Balas [6] to infinite-dimensional systems. The SAC methodology has found implementation in such diverse applications as flexible structures [2][3][4][5][6][7][8][9][10][11][12][13][14], flight control of flexible aircraft [15] or reconfiguration after control surface failure [16] and with various degrees of non-linearity and uncertainty [17][18][19][20], reentry vehicle [21], missile control [22,23], power systems with varying parameters [24], non-linear systems such as robotic manipulators [25], motor control [26,27], drug infusion [28,29] and other systems with timevarying uncertainties [30]. SAC methodology requires the controlled plant to satisfy a so-called 'almost strictly positive realness (ASPR)' condition [4] (to be defined below).…”

Section: Introductionmentioning

confidence: 99%

“…A structural decomposition method has also been developed that allows satisfaction of the ASPR condition without the use of parallel feedforward [37]. The methodology has also been shown to be feasible in time-varying and non-linear system, when the ASPR property is replaced by 'almost strictly passivity (ASP)' [22,25]. Some references present the robustness of the simple adaptive control algorithms in noisy environments [7,14,22,38,39] and some present the extension of the method to time-varying and non-linear systems [22,25].…”

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confidence: 99%

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Gain conditions and convergence of simple adaptive control

Barkana

2005

Int. J. Adapt. Control Signal Process.

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Recent publications have presented successful implementations of simple direct adaptive control techniques in various applications. However, they also expose the fact that the convergence of the adaptive gains has remained uncertain. The gains may not converge to the ideal constant control gains predicted by the underlying linear time-invariant system considerations. As those prior conditions that were also needed for stability may not hold, this conclusion may raise doubts about the robustness of the adaptive system. This paper intends to show that the adaptive control performs perfect tracking even when the linear time-invariant solution does not exist. It is shown that the adaptation performs a 'steepest descent' minimization of the errors, ultimately ending with the appropriate set of control gains that fit the particular input command and initial conditions. The adaptive gains do asymptotically reach an appropriate set of bounded constant ideal gain values that solve the problem at task.

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“…4,5 These techniques have also been extended by Wenn and Balas 6 and Balas 7 to infinite-dimensional systems. Those successful applications of low-order adaptive controllers to large-scale examples have led to successful implementations of SAC in such diverse applications as flexible structures, 8−15 flight control, 16,17 power systems, 18 robotics, 19 motor control, 20,21 drug infusion, 22,23 and other. 24 SAC methodology had started with an apparently restricted range of applications because it seemed to be feasible only for step input commands and required the controlled plant to be almost strictly passive (ASP) and its transfer function almost strictly positive real (ASPR).…”

Section: Introductionmentioning

confidence: 99%

Classical and Simple Adaptive Control for Nonminimum Phase Autopilot Design

Barkana

2005

Journal of Guidance, Control, and Dynamics

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A recent publication uses a difficult design example to show that fuzzy logic might have advantages when compared with classical compensators. Although in this particular case the application was shown to be successful, convergence of the fuzzy-logic algorithm, as well as other time-varying controllers, cannot not be guaranteed unless some preliminary conditions are satisfied. It will be shown that further exploitation of the classical design can improve robust performance. This result is then used to create sufficient conditions that guarantee convergence with time-varying controllers, and it is then shown that simple adaptive control methods can further improve performance and maintain it in changing environments.

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Simplified Techniques for Adaptive Control of Robotic Systems

Cited by 13 publications

References 59 publications

Almost Passivity and Simple Adaptive Control in Discrete‐Time Systems

Almost Passivity and Simple Adaptive Control in Discrete‐Time Systems

Gain conditions and convergence of simple adaptive control

Classical and Simple Adaptive Control for Nonminimum Phase Autopilot Design

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