A critical problem for adaptive control systems is the characterization of the system re-sponse during transients. In fact a major issue in adaptive system design is the inability to achieve, a-priori, non-conservative user-defined performance guarantees. At present most of the available analysis tools provide performance bounds depending on the norm of uncertain quantities. Since it is extremely difficult to quantify these quantities, conservative upper bounds are used in their place; these, in turn, produce conservative performance bounds of limited practical utility. To face these problems some of the authors have recently introduced a set-theoretic adaptive controller based on generalized restricted potential functions. The key feature of this approach is that it allows the norm of the tracking error to be less than a-priori user-defined worst-case performance bound, and hence, it has the capability to enforce strict per-formance guarantees. Since this performance is expressed as function of the norm of the er-ror vector it is not possible to have the direct control on the amplitude of the single error components. In this paper the method is improved by allowing the control of the shape of the perfor-mance (ellipsoidal) set that is guaranteed to contain the tracking error trajectories. The de-sign problem is formalized as a linear optimization with LMI constraints that allows specify-ing independent componentwise requirements for the error components. Different linear optimization cost functions have been evaluated with the purpose of computing the largest ellipsoidal domain contained in an a-priori specified tracking error polyhedral domain and the smallest ellipsoidal domain containing an a-priori specified ellip-soidal initial condition set. A detailed simulation study in the aeronautic context has been used to highlight the efficacy of the method and the role of the different design parameters.
A model reference adaptive control approach for uncertain dynamical systems with strict component-wise performance guarantees
Fravolini, Mario L;
2018
Abstract
A critical problem for adaptive control systems is the characterization of the system re-sponse during transients. In fact a major issue in adaptive system design is the inability to achieve, a-priori, non-conservative user-defined performance guarantees. At present most of the available analysis tools provide performance bounds depending on the norm of uncertain quantities. Since it is extremely difficult to quantify these quantities, conservative upper bounds are used in their place; these, in turn, produce conservative performance bounds of limited practical utility. To face these problems some of the authors have recently introduced a set-theoretic adaptive controller based on generalized restricted potential functions. The key feature of this approach is that it allows the norm of the tracking error to be less than a-priori user-defined worst-case performance bound, and hence, it has the capability to enforce strict per-formance guarantees. Since this performance is expressed as function of the norm of the er-ror vector it is not possible to have the direct control on the amplitude of the single error components. In this paper the method is improved by allowing the control of the shape of the perfor-mance (ellipsoidal) set that is guaranteed to contain the tracking error trajectories. The de-sign problem is formalized as a linear optimization with LMI constraints that allows specify-ing independent componentwise requirements for the error components. Different linear optimization cost functions have been evaluated with the purpose of computing the largest ellipsoidal domain contained in an a-priori specified tracking error polyhedral domain and the smallest ellipsoidal domain containing an a-priori specified ellip-soidal initial condition set. A detailed simulation study in the aeronautic context has been used to highlight the efficacy of the method and the role of the different design parameters.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
