Practical novel tests for ensuring safe adaptive control

Abstract

In this paper, we further illustrate the versatility and effectiveness of our novel tests for ensuring safe adaptive control in practice. The tests utilize a limited amount of experimental and possibly noisy data obtained from a closedloop-consisting of an existing known stabilizing controller connected to an unknown plant-to infer if the introduction of a prospective controller will stabilize the unknown plant. The need and importance of this arise in iterative identification and control algorithms, multiple-model adaptive control (MMAC), and multi-controller adaptive switching.

Verifying closed-loop performance before inserting a new controller

“…Our earlier results in [4], [5], [6] verify that C 1 will be stabilizing (in place of C 0 ) if the Nyquist plot of T : r → z in Fig. 2 does not encircle the origin.…”

“…This aimed to address the so-called transient instability problem in the context of multiple model adaptive control (MMAC) and iterative identification and control ideas discussed in the introduction. We shall outline the results in [4], [5], [6] (applicable to the MIMO case) for ease of reference.…”

“…Note that the mapping T : r → z in (8) can also be expressed in terms of the graph symbols (see [4], [5], [6] for details) G andK i given in (1),…”

“…In order to project the internal stability of [P, C 1 ] before the insertion of C 1 into the loop, we introduced validation tests in [4], [5], [6] utilizing a limited amount of experimental data obtained from the stable closed-loop interconnection [P, C 0 ]. Our earlier results propose a type of phase test analogous to the Nyquist criterion and utilize the noisy frequency response information of the closed-loop mapping T : r → z in Fig.…”

Verifying closed-loop performance before inserting a new controller

“…Our earlier results in [4], [5], [6] verify that C 1 will be stabilizing (in place of C 0 ) if the Nyquist plot of T : r → z in Fig. 2 does not encircle the origin.…”

“…This aimed to address the so-called transient instability problem in the context of multiple model adaptive control (MMAC) and iterative identification and control ideas discussed in the introduction. We shall outline the results in [4], [5], [6] (applicable to the MIMO case) for ease of reference.…”

“…Note that the mapping T : r → z in (8) can also be expressed in terms of the graph symbols (see [4], [5], [6] for details) G andK i given in (1),…”

“…In order to project the internal stability of [P, C 1 ] before the insertion of C 1 into the loop, we introduced validation tests in [4], [5], [6] utilizing a limited amount of experimental data obtained from the stable closed-loop interconnection [P, C 0 ]. Our earlier results propose a type of phase test analogous to the Nyquist criterion and utilize the noisy frequency response information of the closed-loop mapping T : r → z in Fig.…”

Validating Controllers for Internal Stability Utilizing Closed-Loop Data

“…Obviously, but importantly, even with uncertainty of around 3 dB error in magnitude and 30 degrees error in phase, one could draw the same conclusion with confidence, and hence the measurement can tolerate error. The versatility of our proposed tests for ensuring safe adaptive control in practice are further illustrated in [39] via presenting two benchmark examples.…”

Verifying closed-loop performance before inserting a new controller

“…Our earlier results in [4], [5], [6] verify that C 1 will be stabilizing (in place of C 0 ) if the Nyquist plot of T : r → z in Fig. 2 does not encircle the origin.…”

“…This aimed to address the so-called transient instability problem in the context of multiple model adaptive control (MMAC) and iterative identification and control ideas discussed in the introduction. We shall outline the results in [4], [5], [6] (applicable to the MIMO case) for ease of reference.…”

“…Note that the mapping T : r → z in (8) can also be expressed in terms of the graph symbols (see [4], [5], [6] for details) G andK i given in (1),…”

“…In order to project the internal stability of [P, C 1 ] before the insertion of C 1 into the loop, we introduced validation tests in [4], [5], [6] utilizing a limited amount of experimental data obtained from the stable closed-loop interconnection [P, C 0 ]. Our earlier results propose a type of phase test analogous to the Nyquist criterion and utilize the noisy frequency response information of the closed-loop mapping T : r → z in Fig.…”

Validating Controllers for Internal Stability Utilizing Closed-Loop Data

“…Obviously, but importantly, even with uncertainty of around 3 dB error in magnitude and 30 degrees error in phase, one could draw the same conclusion with confidence, and hence the measurement can tolerate error. The versatility of our proposed tests for ensuring safe adaptive control in practice are further illustrated in [39] via presenting two benchmark examples.…”

Verifying closed-loop performance before inserting a new controller

“…Our earlier results in [4], [5], [6] verify that C 1 will be stabilizing (in place of C 0 ) if the Nyquist plot of T : r → z in Fig. 2 does not encircle the origin.…”

“…This aimed to address the so-called transient instability problem in the context of multiple model adaptive control (MMAC) and iterative identification and control ideas discussed in the introduction. We shall outline the results in [4], [5], [6] (applicable to the MIMO case) for ease of reference.…”

“…Note that the mapping T : r → z in (8) can also be expressed in terms of the graph symbols (see [4], [5], [6] for details) G andK i given in (1),…”

“…In order to project the internal stability of [P, C 1 ] before the insertion of C 1 into the loop, we introduced validation tests in [4], [5], [6] utilizing a limited amount of experimental data obtained from the stable closed-loop interconnection [P, C 0 ]. Our earlier results propose a type of phase test analogous to the Nyquist criterion and utilize the noisy frequency response information of the closed-loop mapping T : r → z in Fig.…”

Validating Controllers for Internal Stability Utilizing Closed-Loop Data

“…Obviously, but importantly, even with uncertainty of around 3 dB error in magnitude and 30 degrees error in phase, one could draw the same conclusion with confidence, and hence the measurement can tolerate error. The versatility of our proposed tests for ensuring safe adaptive control in practice are further illustrated in [39] via presenting two benchmark examples.…”