A New Adaptive Control Architecture for Uncertain Dynamical Systems with Actuator Dynamics: Beyond Pseudo-Control Hedging

Gruenwald, Benjamin C.; Yucelen, Tansel; Dogan, K. Merve; Muse, Jonathan A.

doi:10.2514/6.2018-0845

Cited by 6 publications

(11 citation statements)

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“…Through an illustrative numerical example on a benchmark mechanical system (Example ), in addition, we discuss that the sufficient stability condition of this architecture can be satisfied more easily compared with the sufficient stability condition of the standard MRAC architecture. (iii) We then focus on the expanded MRAC architecture. In particular, this method uses a reference model predicated on the weight estimation and a copy of the actuator dynamics (Section 2.3) in order to offer a better closed‐loop system performance as compared with the hedging method for the actuator dynamics problem alone . Here, once again, we show sufficient stability conditions (Assumptions and ) that yield bounded closed‐loop system trajectories in the presence of both actuator and unmodeled dynamics (Section 3.3).…”

Section: Introductionmentioning

confidence: 86%

“…Building on the results in the works of Johnson et al, Gruenwald et al develop sufficient stability conditions that guarantee the stability of the hedged, modified reference model trajectories and, therefore, the stability of the closed‐loop system trajectories. Gruenwald et al further extend the results in their aforementioned works . Specifically, they propose an approach based on an extended reference model to the adaptive control literature that can achieve a better closed‐loop system performance in the presence of actuator dynamics when it is compared with the hedging method.…”

Section: Introductionmentioning

confidence: 93%

“…Remark For the clarity of the exposition, the same bandwidth for all actuator channels is considered in this paper. This is without loss of generality since one can readily replace λ in with a positive‐definite diagonal matrix (see, for example, the works of Gruenwald et al) by following the system‐theoretical analysis steps given later in this paper. In addition, one can also consider an unknown control effectiveness matrix

normalΛ \in {double-struckR}_{+}^{m \times m} \cap {double-struckD}^{m \times m}

in by replacing the term “ v ( t )” with “Λ v ( t ).” This is also without loss of generality by following the system‐theoretical analysis steps of this paper along with the results, for example, in the work of Dogan et al…”

Section: Problem Formulationmentioning

confidence: 99%

“…In the expanded MRAC architecture, the objective is to drive the augmented state vector

{false[x^{normalT} false(t false), v^{normalT} false(t false) false]}^{normalT} \in {double-struckR}^{n + m}

to the state vector

χ_{normalr} false(t false) = {false[x_{normalr}^{normalT} false(t false), v_{normalr}^{normalT} false(t false) false]}^{normalT} \in {double-struckR}^{n + m}

of the expanded reference model given by

\underset{{\overset{χ}{true}}_{normalr} false(t false)}{\underset{⏟}{([], \begin{matrix} center \\ array {\dot{x}}_{r} (t) \\ array {\dot{v}}_{r} (t) \end{matrix})}} = \underset{{scriptA}_{normalr} false(Ŵ false(t false), λ false)}{\underset{⏟}{([], \begin{matrix} center center \\ array A + B Ŵ^{T} (t) & array B \\ array - λ (K_{1} + Ŵ^{T} (t)) & array - λ I_{m} \end{matrix})}} \underset{χ_{normalr} false(t false)}{\underset{⏟}{([], \begin{matrix} center \\ array x_{r} (t) \\ array v_{r} (t) \end{matrix})}} + ([], \begin{matrix} center \\ array 0_{n \times m} \\ array λ K_{2} \end{matrix})

…”

Section: Problem Formulationmentioning

confidence: 99%

“…Remark Assumption , which is also stated in (25) in the work of Gruenwald et al, captures the system‐theoretic trade‐off between system uncertainties and actuator dynamics. Assumption , in addition, is the sufficient condition that depends on Assumption as well as the matrices resulting from the unmodeled dynamics.…”

Section: Problem Formulationmentioning

confidence: 99%

See 4 more Smart Citations

Adaptive architectures for control of uncertain dynamical systems with actuator and unmodeled dynamics

Dogan

Gruenwald

Yucelen

et al. 2019

Intl J Robust & Nonlinear

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Summary In adaptive control of uncertain dynamical systems, it is well known that the presence of actuator and/or unmodeled dynamics in feedback loops can yield to unstable closed‐loop system trajectories. Motivated by this standpoint, this paper focuses on the analysis and synthesis of multiple adaptive architectures for control of uncertain dynamical systems with both actuator and unmodeled dynamics. Specifically, we first analyze model reference adaptive control architectures with standard, hedging‐based, and expanded reference models for this class of uncertain dynamical systems and develop sufficient stability conditions. We then synthesize a robustifying term for the latter architecture and analytically show that this term can allow for a relaxed sufficient stability condition. The proposed theoretical treatments involve Lyapunov stability theory, linear matrix inequalities, and matrix mathematics. Finally, we compare the resulting sufficient stability conditions of the considered adaptive control architectures on a benchmark mechanical system subject to actuator and unmodeled dynamics.

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Section: Introductionmentioning

confidence: 86%