Invariance and Stability for Bounded Uncertain Systems

Guaranteed cost control is a method of synthesizing a closed-loop system in which the controlled plant has large parameter uncertainty. This paper gives the basic theoretical development of guaranteed cost control, and shows how it can be incorporated into an adaptive system. The uncertainty in system parameters is reduced first by either: 1) on-line measurement and evaluation, or 2) prior knowledge on the parametric dependence of a certain easily measured situation parameter. Guaranteed cost control is then used to take up the residual uncertainty.It is shown that the uncertainty in system parameters can be taken care of by an additional term in the Riccati equation. A Fortran program for computing the guaranteed cost matrix and control law is developed and applied to an airframe control problem with large parameter variations.

show abstract

“…A slightly different version of this t,heorem was proved in [16], where an example of applicat,ion was also given.…”

Section: System Stabilitymentioning

confidence: 99%

Adaptive guaranteed cost control of systems with uncertain parameters

Chang

Peng

1972

IEEE Trans. Automat. Contr.

655

233

View full text Add to dashboard Cite

show abstract

“…and (3), we However, for our immediate purpose, the class of C 1 functions V suffices. Finally, we remark that Theorem 1 subsumes the invariance principle of [10] wherein, in effect, continuity of the map F is assumed.…”

Section: V(x(t)) -V(x(t))::; It Q(x(s))ds::; 0 Vtt E Jr+ T < T (3)mentioning

confidence: 90%

Discontinuous Feedback and Universal Adaptive Stabilization

Ryan

1990

Control of Uncertain Systems

View full text Add to dashboard Cite

show abstract

“…Among other invariance properties we shall reproduce Peng's invariance results[9] in terms of generalized processes and relaxed controls. Illustrative examples will be given at the end of this section; for various other applications see Peng[9],Wakeman [12] and LaSalle[7].Downloaded 09/30/12 to 152.3.102.242. Redistribution subject to SIAM license or copyright; see http://www.siam.org/journals/ojsa.php…”

mentioning

confidence: 88%

“…This follows from Corollary 4.3 and the density of the ordinary controls in c; indeed, any sequence of ordinary controls u which converges to v will do. COROLLARY 4.5 (Peng's invariance [9]). Suppose that Assumption L holds.…”

Section: /=1mentioning

confidence: 99%

“…Under an appropriate compactness stated in this section we show how the generalized processes are generated by relaxed controls. z. ARTSTEIN is basically a restatement of Peng's original work [9] in terms of generalized processes or relaxed controls. In the nonautonomous case we incorporate the recent developments by Wakeman [12], Dafermos [4], [5], and others (see the survey [2]) and modify them to suit the special structure of control systems.…”

mentioning

confidence: 99%

See 1 more Smart Citation

Relaxed Controls and the Dynamics of Control Systems

Artstein¹

1978

SIAM J. Control Optim.

View full text Add to dashboard Cite

The relationship between relaxed controls and the family of processes or flows generated by ordinary controls is studied. We find that the flows generated by the relaxed controls form a completion of the space of flows generated by ordinary controls. With the aid of this completion we study the asymptotic and limiting behavior of the dynamics of the control system. Invariance properties of the to-limiting sets of admissible solutions are established. Stability, eventual stability and finite time stability properties of solutions with respect to ordinary and relaxed controls are investigated. Invariance properties of to-limit sets for autonomous and nonautonomous systems are treated in 4 and 5 respectively. The invariance in the autonomous case *

show abstract

Invariance and Stability for Bounded Uncertain Systems

Cited by 15 publications

References 6 publications

Adaptive guaranteed cost control of systems with uncertain parameters

Adaptive guaranteed cost control of systems with uncertain parameters

Discontinuous Feedback and Universal Adaptive Stabilization

Relaxed Controls and the Dynamics of Control Systems

Contact Info

Product

Resources

About