A neuroadaptive architecture for model reference control of uncertain dynamical systems with performance guarantees

AIAA Scitech 2019 Forum

Sipahi

et al. 2019

Self Cite

In this paper, we focus on human-in-the-loop physical systems with inner and outer feedback control loops. Specifically, our problem formulation considers that inner loop control laws use a model reference adaptive control approach to suppress the effect of system uncertainties such that the overall physical system operates close to its ideal behavior as desired in the presence of adverse conditions due to failures and/or modeling inaccuracies. Moreover, we consider that the outer loop control laws exist owing to employing either sequential loop closure and/or high-level guidance methods. As it is true in practice, in addition, humans are considered to inject commands directly to the outer loop dynamics in response to the changes in the physical system, where the outer loop commands affect inner loop dynamics in response to the commands received from the humans as well as in response to the changes in the physical system. The presence of humans can result in system instability, even when the resulting physical system augmented with inner and outer feedback control loops yield to stable trajectories in the absence of humans. This paper addresses this problem by proving a sufficient stability condition for the overall physical system with human dynamics modeled as a linear timeinvariant system with human reaction time-delay, where this condition does not depend on system uncertainties similar to our recent theoretical results. Furthermore, inner loop system errors during the transient phase of adaptively suppressing system uncertainties can severely affect the human-outer loop interactions. We also address this issue by utilizing a recently proposed set-theoretic model reference adaptive control approach at the inner loop for enforcing a user-defined performance constraint on the norm of the system error trajectories, where we show how the selection of this constraint affects the overall physical system. Finally, the efficacy of our results is demonstrated through an illustrative numerical example for an adaptive flight control application with a Neal-Smith pilot model.

Section: A Inner Loop Architecturementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Human-in-the-Loop Systems with Inner and Outer Feedback Control Loops: Adaptation, Stability Conditions, and Performance Constraints

AIAA Scitech 2019 Forum

Sipahi

et al. 2019

Self Cite

“…Although model reference adaptive control architectures are capable of guaranteeing closed-loop system stability in the presence of exogenous disturbances and system uncertainties, one of the major drawbacks to adopting these control frameworks is the inability to obtain user-defined performance guarantees. For addressing this limitation, we recently proposed set-theoretic model reference adaptive control architecture in a set of papers [1][2][3][4][5][6][7][8][9][10][11]. The key feature of set-theoretic model reference adaptive control architecture allows the system error bound between the state of an uncertain dynamical system and the state of a reference model, which captures a desired closed-loop system performance, to be less than a-priori, user-defined worstcase performance bound.…”

Section: Introductionmentioning

confidence: 99%

“…Specifically, [1] presents this control framework for achieving time-invariant performance bounds, where in [2,3] this framework is further extended to guarantee time-varying user-defined performance bounds. The generalization of the settheoretic model reference adaptive control architecture to the unstructured system uncertainties is studied in [4,5] and also the extension of this architecture for guaranteeing performance in the presence of actuator failures and actuator dynamics are respectively presented in [6,7]. This framework is also recently employed for decentralized control of large-scale modular systems in [8,9].…”

Section: Introductionmentioning

confidence: 99%

Experimental Results with the Set-Theoretic Model Reference Adaptive Control Architecture on an Aerospace Testbed

AIAA Scitech 2019 Forum

2019

Self Cite

In this paper, we present experimental results of a recently developed set-theoretic model reference adaptive control architecture on an aerospace testbed, which is configured as a conventional dual-rotor helicopter. The key feature of this architecture allows the system error bound between the state of an uncertain dynamical system and the state of a reference model, which captures a desired closed-loop system performance, to be less than a-priori, user-defined worst-case performance bound. This means that this proposed architecture is suitable for enforcing strict performance guarantees during the transient and steady-state response of the adaptation process. Specifically, we first experimentally demonstrate the practical capabilities of this adaptive control algorithm with constant performance bounds on the considered testbed. We then consider the time-varying performance bounds, where we highlight how a control designer is empowered by the set-theoretic model reference adaptive control architecture to control the closed-loop system performance as desired on different time intervals (e.g. transient time interval and steady-state time interval) and also how to handle a possible system initialization error that can happen in practice.

“…To address this challenge, we generalize a recently developed set-theoretic model reference adaptive control architecture [6] (see also [7][8][9][10][11][12][13]), which has the capability to achieve "practical" performance guarantees, for uncertain dynamical systems subject to actuator dynamics using tools and methods from [4,5]. Specifically, we first show that the proposed set-theoretic model reference adaptive control architecture keeps the performance bounds between the uncertain dynamical system trajectories and the "modified" reference model trajectories within an a-priori, user-defined bound (unlike the results in [4,5]).…”

Section: Introductionmentioning

confidence: 99%

On Set-Theoretic Model Reference Adaptive Control of Uncertain Dynamical Systems Subject to Actuator Dynamics

2018 AIAA Guidance, Navigation, and Control Conference

2018

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In applications where the bandwidth of the actuator dynamics is not sufficiently high, the stability of model reference adaptive controllers can be degraded drastically as it is well known. To this end, one of the effective approaches for tackling the challenge of limited actuator bandwidth is the hedging method in which using a "modified" reference model, the adaptation becomes "excluded" from the actuator dynamics. With this approach, however, the performance bounds between the uncertain dynamical system trajectories and the "ideal" reference model trajectories can be conservative and depend on the bounds on the system uncertainties; therefore, no "practical" performance guarantees exist. To address this challenge, we generalize a recently developed set-theoretic model reference adaptive control architecture, which has the capability to achieve "practical" (i.e., user-defined) performance guarantees, for uncertain dynamical systems subject to actuator dynamics. Specifically, we first show that the proposed architecture keeps the performance bounds between the uncertain dynamical system trajectories and the "modified" reference model trajectories within an a-priori, user-defined bound. We next show that the error bounds between the "ideal" reference model trajectories and the uncertain dynamical system trajectories is characterized by this user-defined bound as well as the actuator bandwidth limit, and hence, is "computable" using a given set of adaptive control design parameters. Finally, as a byproduct, our illustrative numerical example shows that the time rate of change of the actual control signal (i.e., the output of the actuator dynamics) becomes less in magnitude as compared with the the set-theoretic model reference adaptive control case without actuator dynamics.