Showing papers by "Septimiu E. Salcudean published in 1986"

Algorithms for optimal design of feedback compensators

Abstract: We consider the problem of designing feedback compensators for linear, lumped, time-invariant plants, subject to various frequency and time-domain performance specifications. Our approach is made possible by the development of new algorithms for the constrained optimization of regular, uniformly locally Lipschitz functions in ${\rm I\!R}\sp{N}$. First, we consider the case in which a good nominal plant model is available. We show that complex design probems involving hard bound constraints on the frequency and time domain responses of a multi-input multi-output continuous time feedback system can be formulated as constrained optimization problems in $H\sp\infty$. Since our formulation uses the affine parametrization of all achievable input-output maps obtained from the stable coprime factors of the plant, the constrained $H\sp\infty$ problem we obtain involves only convex functions. We use the continuity properties of these functions, as well as approximations of rational functions in $H\sp\infty$ by polynomials, to show that we can obtain arbitrarily close approximations to a constrained problem in $H\sp\infty$ by solving a sequence of constrained non-differentiable optimization problems of increasing dimension in ${\rm I\!R}\sp{N}$. We present implementable algorithms to obtain solutions to the constrained problems in ${\rm I\!R}\sp{N}$. These algorithms require only the computation of the largest singular value of matrices of low dimension and the simulation of linear dynamical systems. Second, we consider the case in which a reliable nominal model of the plant is not available. We restrict our attention to discrete time single-input single-output plants (ARMA models) of known order but with unknown parameter vector. We show that, if the plant parameter vector is known to belong to a compact set in ${\rm I\!R}\sp{N}$, a worst-case optimal compensator design problem can be reduced to that of the minimization of a regular locally uniformly Lipschitz continuous function for which convergent algorithms exist. Next, we present a new identification scheme that produces such a sequence of uncertainty sets. Furthermore, we show that with appropriate assumptions on the probability distribution of the plant output disturbance, this small set is reduced to a point i.e., the actual parameter vector, with probability 1. (Abstract shortened with permission of author.)