### Abstract

In this paper the model reference adaptive control (MRAC) problem of a class of linear time-varying (LTV) plants is considered. The plant parameters are assumed to be smooth, bounded functions of time which satisfy the usual assumptions of MRAC for time-invariant plants, at each frozen time instant. It is first shown that if the plant parameters are sufficiently slowly varying with time, a control parameter vector with smooth elements exists, such that the closed-loop plant behaves almost like a linear time-invariant reference model. The robust adaptive law proposed in Ioannou and Tsakalis (1986) IEEE Trans. Aut. Control, AC-31, 1033 is then used to adjust the controller parameters and establish boundedness of all signals in the adaptive loop for any bounded initial conditions. It is shown that the bound for the residual tracking error depends on the speed of the plant parameter variations in such a way that as these parameters become constant the bound reduces to zero.

Original language | English (US) |
---|---|

Pages (from-to) | 459-468 |

Number of pages | 10 |

Journal | Automatica |

Volume | 23 |

Issue number | 4 |

DOIs | |

State | Published - 1987 |

Externally published | Yes |

### Fingerprint

### Keywords

- Adaptive system
- differential operators
- Lyapunov methods
- model reference adaptive control
- robust adaptive law
- time-varying systems

### ASJC Scopus subject areas

- Control and Systems Engineering
- Electrical and Electronic Engineering

### Cite this

*Automatica*,

*23*(4), 459-468. https://doi.org/10.1016/0005-1098(87)90075-6

**Adaptive control of linear time-varying plants.** / Tsakalis, Konstantinos; Ioannou, Petros.

Research output: Contribution to journal › Article

*Automatica*, vol. 23, no. 4, pp. 459-468. https://doi.org/10.1016/0005-1098(87)90075-6

}

TY - JOUR

T1 - Adaptive control of linear time-varying plants

AU - Tsakalis, Konstantinos

AU - Ioannou, Petros

PY - 1987

Y1 - 1987

N2 - In this paper the model reference adaptive control (MRAC) problem of a class of linear time-varying (LTV) plants is considered. The plant parameters are assumed to be smooth, bounded functions of time which satisfy the usual assumptions of MRAC for time-invariant plants, at each frozen time instant. It is first shown that if the plant parameters are sufficiently slowly varying with time, a control parameter vector with smooth elements exists, such that the closed-loop plant behaves almost like a linear time-invariant reference model. The robust adaptive law proposed in Ioannou and Tsakalis (1986) IEEE Trans. Aut. Control, AC-31, 1033 is then used to adjust the controller parameters and establish boundedness of all signals in the adaptive loop for any bounded initial conditions. It is shown that the bound for the residual tracking error depends on the speed of the plant parameter variations in such a way that as these parameters become constant the bound reduces to zero.

AB - In this paper the model reference adaptive control (MRAC) problem of a class of linear time-varying (LTV) plants is considered. The plant parameters are assumed to be smooth, bounded functions of time which satisfy the usual assumptions of MRAC for time-invariant plants, at each frozen time instant. It is first shown that if the plant parameters are sufficiently slowly varying with time, a control parameter vector with smooth elements exists, such that the closed-loop plant behaves almost like a linear time-invariant reference model. The robust adaptive law proposed in Ioannou and Tsakalis (1986) IEEE Trans. Aut. Control, AC-31, 1033 is then used to adjust the controller parameters and establish boundedness of all signals in the adaptive loop for any bounded initial conditions. It is shown that the bound for the residual tracking error depends on the speed of the plant parameter variations in such a way that as these parameters become constant the bound reduces to zero.

KW - Adaptive system

KW - differential operators

KW - Lyapunov methods

KW - model reference adaptive control

KW - robust adaptive law

KW - time-varying systems

UR - http://www.scopus.com/inward/record.url?scp=0023382819&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0023382819&partnerID=8YFLogxK

U2 - 10.1016/0005-1098(87)90075-6

DO - 10.1016/0005-1098(87)90075-6

M3 - Article

AN - SCOPUS:0023382819

VL - 23

SP - 459

EP - 468

JO - Automatica

JF - Automatica

SN - 0005-1098

IS - 4

ER -