Robustness of adaptive controllers—A survey

Ortega, Roméo; Tang, Yu

doi:10.1016/0005-1098(89)90023-x

“…This choice yields the adaptive I&I control law . Selecting the update law as (30), that is , yields the error equations (31), (32), which, in this case, become…”

Section: E Examplesmentioning

confidence: 99%

Immersion and Invariance: A New Tool for Stabilization and Adaptive Control of Nonlinear Systems

Astolfi

¹

2001

IFAC Proceedings Volumes

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Abstract-A new method to design asymptotically stabilizing and adaptive control laws for nonlinear systems is presented. The method relies upon the notions of system immersion and manifold invariance and, in principle, does not require the knowledge of a (control) Lyapunov function. The construction of the stabilizing control laws resembles the procedure used in nonlinear regulator theory to derive the (invariant) output zeroing manifold and its friend. The method is well suited in situations where we know a stabilizing controller of a nominal reduced order model, which we would like to robustify with respect to higher order dynamics. This is achieved by designing a control law that asymptotically immerses the full system dynamics into the reduced order one. We also show that in adaptive control problems the method yields stabilizing schemes that counter the effect of the uncertain parameters adopting a robustness perspective-this is in contrast with most existing adaptive designs that (relying on certain matching conditions) treat these terms as disturbances to be rejected. It is interesting to note that our construction does not invoke certainty equivalence, nor requires a linear parameterization, furthermore, viewed from a Lyapunov perspective, it provides a procedure to add cross terms between the parameter estimates and the plant states. Finally, it is shown that the proposed approach is directly applicable to systems in feedback and feedforward form, yielding new stabilizing control laws. We illustrate the method with several academic and practical examples, including a mechanical system with flexibility modes, an electromechanical system with parasitic actuator dynamics and an adaptive nonlinearly parameterized visual servoing application.

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“…Examples of these modifications are the modification [22] and the e modification [23]. A good survey on the topic can be found in [24]. While all of these modifications offered some improvement in terms of robustness, none of them provided the means to 1) quantify the transient response of the closed-loop adaptive system, 2) develop a framework for analysis of its performance and robustness characteristics, or 3) provide systematic guidelines for its design.…”

Section: Introductionmentioning

confidence: 99%

Experimental Validation of L1 Adaptive Control: The Rohrs Counterexample in Flight

Dobrokhodov¹,

Kaminer²,

Kitsios³

et al. 2011

Journal of Guidance, Control, and Dynamics

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This paper presents flight-test results that examine the performance and robustness properties of an L 1 control augmentation loop implemented onboard a small unmanned aerial vehicle. The framework used for in-flight control evaluation is based on the Rohrs counterexample, a benchmark problem presented in the early 1980s, to show the limitations of adaptive controllers developed at that time. Hardware-in-the-loop simulations and flight-test results confirm the ability of the L 1 flight control system to maintain stability and predictable performance of the closed-loop adaptive system in the presence of general (artificially injected) unmodeled dynamics. The results demonstrate the advantages of L 1 control as a robust adaptive control architecture with the potential of facilitating the transition of adaptive control into advanced flight control systems.

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“…Writing this equation in terms of the off-the-manifold coordinates and adding and subtracting yields the first error equation (26). The off-the-manifold dynamics is obtained differentiating the variable taking into account (18), (23), and the fact that is constant, as Thus, selecting the parameter update law as (30) yields (27). The proof of the first part of the proposition is completed with the use of assumption H8).…”

Section: H8) (Manifold Attractivity and Trajectory Boundedness)mentioning

confidence: 99%

“…These kind of parameter update laws were called in early references PI adaptation. Although it was widely recognized that PI update laws were superior to purely integral adaptation, except for the notable exception of output error identification, their performance improvement was never clearly established, see, e.g., [30] for a tutorial account of these developments. The I&I framework contributes then to put PI adaptation in its proper perspective.…”

Section: H8) (Manifold Attractivity and Trajectory Boundedness)mentioning

confidence: 99%

Immersion and invariance: a new tool for stabilization and adaptive control of nonlinear systems

Astolfi

¹

,

Ortega

²

2003

IEEE Trans. Automat. Contr.

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Abstract-A new method to design asymptotically stabilizing and adaptive control laws for nonlinear systems is presented. The method relies upon the notions of system immersion and manifold invariance and, in principle, does not require the knowledge of a (control) Lyapunov function. The construction of the stabilizing control laws resembles the procedure used in nonlinear regulator theory to derive the (invariant) output zeroing manifold and its friend. The method is well suited in situations where we know a stabilizing controller of a nominal reduced order model, which we would like to robustify with respect to higher order dynamics. This is achieved by designing a control law that asymptotically immerses the full system dynamics into the reduced order one. We also show that in adaptive control problems the method yields stabilizing schemes that counter the effect of the uncertain parameters adopting a robustness perspective-this is in contrast with most existing adaptive designs that (relying on certain matching conditions) treat these terms as disturbances to be rejected. It is interesting to note that our construction does not invoke certainty equivalence, nor requires a linear parameterization, furthermore, viewed from a Lyapunov perspective, it provides a procedure to add cross terms between the parameter estimates and the plant states. Finally, it is shown that the proposed approach is directly applicable to systems in feedback and feedforward form, yielding new stabilizing control laws. We illustrate the method with several academic and practical examples, including a mechanical system with flexibility modes, an electromechanical system with parasitic actuator dynamics and an adaptive nonlinearly parameterized visual servoing application.

show abstract

Robustness of adaptive controllers—A survey

Cited by 235 publications

References 92 publications

Immersion and Invariance: A New Tool for Stabilization and Adaptive Control of Nonlinear Systems

Immersion and Invariance: A New Tool for Stabilization and Adaptive Control of Nonlinear Systems

Experimental Validation of L1 Adaptive Control: The Rohrs Counterexample in Flight

Immersion and invariance: a new tool for stabilization and adaptive control of nonlinear systems

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