J.P. Hespanha and A. S. Morse, "Supervisory control of integral-input-to-state stabilizing controllers," in Proc. of the 1999.  Home/Search   Document Details and Download   Summary   Related Articles   Check

.... see [40] for some preliminary remarks in that direction) For special classes of systems, even output feedback ISS with respect to observation errors is possible, cf. 52] Both ISS and iISS properties have been featured in the analysis of the performance of switching controllers, cf. 17] and [18]. Coprime factorizations are the basis of the parameterization of controllers in the Youla approach. As a matter of fact, as the paper s title indicates, their study was the original motivation for the introduction of the notion of ISS in [63] Some further work can be found in [64] see also ....

Hespanha, J.P, and A.S. Morse, "Supervisory control of integral-input-to-state stabilizing controllers," Proc. of the 5 th European Control Conference, Karlsruhe, September 1999.

....of the disturbances can be directly measured and used for control) the construction involved patching together several control laws defined on appropriate regions of the state space. An interesting source of motivation for the integral input to state stabilization problem is discussed in [7]. The aforementioned formulas for control laws that achieve ISS and iISS disturbance attenuation, with the exception of the pointwise min norm controls considered in [5] are only valid in the case of arbitrary unbounded controls. On the other hand, as we already indicated, the asymptotic ....

.... Let us first consider the simpler case when the values of the disturbances can be used for control, i.e. when the feedback law can take the form u = k(x; d) This situation is not altogether meaningless, for example, it arises in applications to control of uncertain nonlinear systems discussed in [7]. We will assume that a given iISS CLF V satisfies the following variant of the small control property: for each ffl 0 there exists a ffi 0 such that whenever jxj; jdj ffi there exists some u with juj ffl for which a(x) b 1 (x)d Gamma (jdj) b 2 (x)u Gammaff(jxj) 8) Again, note ....

J. P. Hespanha, A. S. Morse, Supervisory control of integral-input-to-state stabilizing controllers, in Proc. 5th European Contr. Conf., 1999.

....fact, the notion of iiss, and the results in this paper, which were previously announced in electronic preprint form, have already played a role in several recent control works. For example, the iiss property appears in the latest approaches to supervisory design in adaptive control. In the paper [7], Hespanha and Morse citing preprints of this work studied the closed loop system obtained when a high level supervisor directs the switching among a family of candidate controllers for an uncertain plant. Their convergence analysis was based on the assumption that each controller ....

Hespanha, J.P, and A.S. Morse, "Supervisory control of integral-input-to-state stabilizing controllers, " 1999 European Control Conference, to appear.

....fact, the notion of iiss, and the results in this paper, which were previously announced in electronic preprint form, have already played a role in several recent control works. For example, the iiss property appears in the latest approaches to supervisory design in adaptive control. In the paper [7], Hespanha and Morse citing preprints of this work studied the closed loop system obtained 2 IEEE TAC when a high level supervisor directs the switching among a family of candidate controllers for an uncertain plant. Their convergence analysis was based on the assumption that each ....

Hespanha, J.P, and A.S. Morse, "Supervisory control of integralinput -to-state stabilizing controllers," Proc. of the 5 th European Control Conference, Karlsruhe, September 1999.

....stability of hysteresis based adaptive control systems in the presence of measurement noise. 1 Introduction Adaptive control algorithms that employ a logic based supervisor to orchestrate the switching between a family of candidate controllers have been quite successful in numerous applications [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]. The need for switching usually arises from the fact that no single candidate controller would be capable, by itself, of guaranteeing stability and good performance when connected with a poorly modeled process. This type of supervisory control results in a switched closedloop system of the form ....

.... systems have therefore avoided a fixed dwelltime, and have been mostly based on hysteresis switch ing [13, 14] or on its more recent scale independent version [8, 15] To date, the analysis of algorithms based on hysteresis switching relied heavily on showing that switching stops in finite time [7, 8, 9, 10, 11, 12]. However, in the presence of noise and disturbance inputs, this is hardly the case. In fact, the only known algorithms for which switching can be proved to stop in finite time, even in the presence of noise disturbances, are those for which an upper bound on these signals is known a priori, or ....

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J.P. Hespanha and A. S. Morse, "Supervisory control of integral-input-to-state stabilizing controllers," in Proc. of the 1999.

.... ] with arbitrary N 0 , and not only for the switching signals in S[ D ] Systems like (1) arise in an adaptive context when a high level, logic based supervisor orchestrates the switching between a family of candidate controllers so as to achieve some desired behavior for the closed loop system [3, 4, 5, 2, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 1]. The need for switching usually arises from the fact that no single candidate controller would be capable, by itself, of guaranteeing stability and good performance when connected with a poorly modeled process. In several of these algorithms the supervisor guarantees, by construction, that there ....

.... system have therefore avoided a xed dwell time, and have been mostly 3 based on hysteresis switching [17, 18] or on its more recent scale independent version [11, 19] To date, the analysis of algorithms based on hysteresis switching relied heavily on showing that switching stops in nite time [10, 11, 12, 13, 14, 15]. However, in the presence of noise and disturbance inputs, this is hardly the case. In fact, the only known switching algorithms for which switching can be proved to stop in nite time, even in the presence of noise disturbances, are those for which an upper bound on these signals is known a ....

J. P. Hespanha and A. S. Morse, \Supervisory control of integral-input-to-state stabilizing controllers," in Proc. of the 1999 European Contr. Conf., Aug. 1999. 11

.... ] with arbitrary N 0 , and not only for the switching signals in S[ D ] Systems like (1) arise in an adaptive context when a high level, logic based supervisor orchestrates the switching between a family of candidate controllers so as to achieve some desired behavior for the closed loop system [2, 3, 1, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13]. The need for switching usually arises from the fact that no single candidate controller would be capable, by itself, of guaranteeing stability and good performance when connected with a poorly modeled process. In several of these algorithms the supervisor guarantees, by construction, that there ....

.... system have therefore avoided a fixed dwell time, and have been mostly 3 based on hysteresis switching [15, 16] or on its more recent scaleindependent version [9, 17] To date, the analysis of algorithms based on hysteresis switching relied heavily on showing that switching stops in finite time [8, 9, 10, 11, 12, 13]. However, in the presence of noise and disturbance inputs, this is hardly the case. In fact, the only known switching algorithms for which switching can be proved to stop in finite time, even in the presence of noise disturbances, are those for which an upper bound on these signals is known a ....

J. P. Hespanha and A. S. Morse. Supervisory control of integral-input-to-state stabilizing controllers. To be presented at the 1999 European Control Conference. , Aug. 1999.

.... is satisfied in the noise disturbance free case, provided P is input output equivalent to a nominal model fsay M p g which is linearizable by output injection [6] Assumptions 3 and 4 enable us to exploit the Hysteresis Switching Lemma [11, 6] and consequently to draw the following conclusion [12]. Lemma 5. For fixed initial states xP (0) 2 XP , xE (0) 2 XE , xC (0) 2 XC , p (0) 0, p 2 P, oe(0) 2 P, the system defined by (4) 5) 6) 7) and (15) with oe the output of S H , has a unique solution fxP ; xE ; xC ; 1 ; 2 ; m ; oeg on a nonempty time interval starting at ....

J. P. Hespanha and A. S. Morse. Supervisory control of integral input-to-state stabilizing controllers. Technical report, Lab. for Control Science & Eng., Yale University, Sept. 1998.

....which a solution to (4) 6) exists. E can typically be constructed so that Assumption 3 is satisfied in the noise disturbance free case, provided P is input output equivalent to a nominal model fsay M p g which is linearizable by output injection [6] The main result of this paper fproved in [12]g is the following. Theorem 1 Let Assumptions 1 to 3 hold. For each initial state xP (0) 2 XP , xE (0) 2 XE , xC (0) 2 XC , p (0) 0, p 2 P, oe(0) 2 P, the solution fxP ; xE ; xC ; 1 ; 2 ; mg to (4) 5) 6) 7) and (15) fwith oe the output of S H g exists and is bounded on ....

J. P. Hespanha and A. S. Morse. Supervisory control of integral input-to-state stabilizing controllers. Technical report, Lab. for Control Science & Eng., Yale University, Sept. 1998.

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