Robust control with structured perturbations

Abstract

This result has been extended to the parameter space so that one can determine the stability margin, in terms of ranges of parameter variations, of the closed loop system when the nominal stabilizing controller is given. This stability margin can be enlarged by a choice of better stabilizing controller.The second problem this report describes is the lower order stabilization problem.Even though the wide range of stabilizing controller design methodologies are available in both the state space and the transfer function domains, all of these methods produce unnecessarily high order controllers.The motivation of the problem is as follows.In practice, the stabilization is only one of many requirements to be satisfied.Therefore, if the order of a stabilizing controller is excessively high, one can normally expect to have a even higher order controller upon the completion of design such as inclusion of dynamic response requirements, etc. Therefore, it is reasonable to have a lowest possible order stabilizing controller first and then adjust the controller to 3 meet additional requirements.In this report, the algorithm of designing a lower order stabilizing controller is given. The algorithm is not necessarily produce the minimum order controller, however the algorithm is theoretically logical and some simulation results show that the algorithm works in general.The above two problems have been solved and published. These are found in Appendix A and B. Finally, some remarks and on going research are briefly discussed. To appear. 4 PUBLICATIONS S U P P O R T E D BY T H E G R A N T P U B L I C A T I O N S DISCUSSIONS AND DIRECTIONS OF RESEARCHThe stability margin in the parameter space is in general more practical than one in the coefficient space. When parameters enter into coefficients of characteristic polynomial linearly, the stability margin is exact. However, when parameters enter in nonlinear fashion which is the general facts in practical systems, the margin seems to be conservative.The results show that the transfer function approach (or polynomial frame- 1 ABSTRACTThis paper treats the robust stability issue using the characteristic polynomial, for two different cases. First in coefficient space with respect to perturbations in the coefficients of the characteristic polynomial, and then for a control system containing perturbed parameters in the transfer function description of the plant.

Spectral radius minimization for optimal average consensus and output feedback stabilization

“…We now proceed with the following benchmark systems found in the literature [1,13,10,9,12 The first case is particularly interesting in that the set of K which stabilizes the system is very small (see Fig. 5).…”

“…Therefore, all the simulations below are meant for non-symmetric E. Table 2 tabulates the simulation results for (n, m) = (5, 5), (5, 10), (10,20), (10,30) and (10, 40), respectively. Each value represents the average fraction of ρ( W (1) s ), i.e.…”

Stability of Optimal Solutions: Multi- and Single-Objective Approaches

“…One of the first studies in optimal controllers is [17] which has been further developed in [10] and many other papers. One of the studies in robust stability is [35] which is further developed in papers [6], [4], [19] and many others. Robust optimal control is discussed in [44] and [38].…”

“…Special sequences such as produce slightly better results for fewer test points. Here q = (q i1 , q i2 , …, q iN ) is the point in the control space C (27) -a set of controls that determines certain controlling functions (14) and -through the mathematical model of Laddermill -certain objectives (19), (24), i is the number of the point in the sequence, j is the j-th coordinate of the point in C, N is dimension of C. If particular point is near the boundary of C then adjacent points of the boundary should be included into the table, too.…”

“…The problem (24) with objectives (19), (24), controlling functions (14) and constraints (13), (15) and (25) is the optimal control problem with two objectives, fixed start, open end and constraints.…”