Institute for Systems Research Technical Reports
Permanent URI for this collectionhttp://hdl.handle.net/1903/4376
This archive contains a collection of reports generated by the faculty and students of the Institute for Systems Research (ISR), a permanent, interdisciplinary research unit in the A. James Clark School of Engineering at the University of Maryland. ISR-based projects are conducted through partnerships with industry and government, bringing together faculty and students from multiple academic departments and colleges across the university.
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Item Maximal Range for Generalized Stability- Application to Two Physically Motivated Examples.(1989) Saydy, L.; Tits, A.L.; Abed, Eyad H.; ISRSome recent results on guardian maps and their application to generalized robust stability are reviewed and a characterization of the maximum stability range is obtained. This framework is then applied to the analysis of robust stability in two physically motivated examples.Item On Robust Eigenvalue Location.(1989) Tits, A.L.; Saydy, L.; ISRThe concepts of guardian and semiguardian maps were recently introduced as tools for assessing robust generalized stability of parametrized families of matrices or polynomials. Necessary and sufficient conditions were obtained for stability of parametrized families with respect to a large class of open subsets of the complex plane, namely those with which one can associate a polynomic guardian or semiguardian map. This note focuses on a class of disconnected subsets of the complex plane, of interest in the context of dominant pole assignment and filter design. It is first observed that the robust stability conditions originally put forth are in fact necessary and aufficient for the number of eigenvalues (matrices) or zeros (polynomials) in any given connected component to the same for all the members of the given family. Polynomic semiguardian maps are then identified for a class of disconnected regions of interest. These maps are in fact "essentially guarding with respect to one-parameter families."Item Robustness under Uncertainly with Phase Information.(1989) Lee, Li; Tits, A.L.; Fan, Michael K-H.; ISRThe framework of Doyle's structured angular value is extended to take advantage of possibly available phase information on the dynamic uncertainty. A computable upper bound is obtained for this phase-sensitive structured singular value.Item User's Guite for FSQP Version 1.0: A Fortran Software for Solving Optimization Problems with General Inequality Constraints and Linear Equality Constraints, Generating Feasible Iterates.(1989) Zhou, J.; Tits, A.L.; ISRFSQP is a set of Fortran subroutines for the minimization of a smooth objective function subject to nonlinear smooth inequality constraints, linear inequality and linear equality constraints, and simple bounds on the variables. If the initial guess provided by the user is infeasible, FSQP first generates a feasible point from the given point. Subsequently the successive iterates generated by FSQP all satisfy the constraints. The user also has the option of requiring that the objective value decrease at each iteration after feasibility has been reached. The user must provide subroutines that define the objective and constraint functions and may either provide the subroutines that define the gradients of these functions or require that FSQP estimate them by forward finite differences. FSQP uses an algorithm based on Sequential Quandratic Programming (SQP), modified so as to generate feasible iterates. A certain arc search ensures that the step of one is eventually satisfied, a requirement for superlinear convergence. The merit function used in this arc search is the objective function itself, and either an Armijo- type line search or a nonmonotone line search borrowed from Grippo et al. may be selected.Item Avoiding the Maratos Effect by Means of a Nonrnonotone Line Search: I. General Constrained Problems.(1989) Panier, E.R.; Tits, A.L.; ISRAn essential condition for quasi-Newton optimization methods to converge superlinearly is that a full step of one be taken close to the solution. It is well known that, when dealing with constrained optimization problems, line search schemes ensuring global convergence of such methods may prevent this from occurring (the so called "Maratos effect"). Two types of techniques have been used to circumvent this difficulty. In the watchdog technique, the full step of one is occasionally accepted even when the line search criterion is violated; subsequent backtracking is used if global convergence appears to be lost. In a "bending" technique proposed by Mayne and Polak, backtracking is avoided by performing a search along an arc whose construction requires evaluation of constraint functions at an auxiliary point; along this arc, the full step of one is accepted close to a solution. The main idea in the present paper is to comWne Mayne and Polak's technique with a non-monotone line search proposed by Grippo, Lampariello and Lucidi in the context of unconstrained optimization, in such a way that, asymptotically, function evaluations are no longer performed at auxiliary points. In a companion paper (part II), it is shown that a refinement of this scheme can be used in the context of recently proposed SQP- based methods generating feasible iterates.Item On Feasibility, Descent and Superlinear Convergence in Inequality Constrained Optimization.(1989) Panier, E.R.; Tits, A.L.; ISRExtension of quasi-Newton techniques from unconstrained to constrained optimization via Sequential Quadratic Programming (SQP) presents several difficulties. Among these are the possible inconsistency, away from the solution, of first order approximations to the constraints, resulting in infeasibility of the quadratic programs; and the task of selecting a suitable merit function, to induce global convergence. In the case of inequality constrained optimization, both of these difficulties disappear if the algorithm is forced to generate iterates that all satisfy the constraints, and that yield monotonically decreasing objective function values. It has been recently shown that this can be achieved while preserving local superlinear convergence. In this note, the essential ingredients for an SQP- based method exhibiting the desired properties are highlighted. Correspondingly, a class of such algorithms is described and analyzed.Item On Robust Stability of Linear State Space Models.(1988) Fan, Michael K-H.; Doyle, John C.; Tits, A.L.; ISRThe structured singular value (MU), introduced by Doyle [1] allows to analyze robust stability and performance of linear systems affected by parametric as well as dynamic uncertainty. While exact computation of MU can be prohibitively complex, an efficiently computable upper bound was obtained in [2], yielding a practical sufficient condition for robust stability and performance. In this note, the results of [2] are used to study the case of state space models of the form x{WITH DOT ABOVE IT}=(A_0={SIGMA i=1 to m of DELTA_i * A_i}) where the A_i's are n X n real matrices and the DELTA_i's are uncertain real parameters. The case where the A_i's have low rank is given special attention. When the A_i's all have rank one, (1) is equivalent to the model used by Qiu and Davison [3], which itself generalizes that used by Yedavalli [4]. By means of two examples, we compare our bound to those proposed in [3] and [4].Item On Stabilization with a Prescribed Region of Asymptotic Stability.(1988) Saydy, L.; Abed, Eyad H.; Tits, A.L.; ISRAn important unsolved problem in nonlinear control is that of stabilization with a prescribed region of stability. In this paper, sufficient conditions are obtained for the existence of a linear feedback stabilizing an equilibrium point of a given nonlinear system with the resulting region of asymptotic stability (RAS) containing a ball of given radius. Conditions for global stabilization are also given. Feedback stabilization is achieved while satisfying a certain robustness property. The technique is applied to planar systems, resulting in a complete design methodology for this case. Examples and simulations illustrating the method are presented.Item Aspects of Optimization-Based CADCS.(1988) Tits, A.L.; Fan, Michael K-H.; Panier, E.R.; ISRWith the recent dramatic increase in available computing power, numerical optimization has become an attractive tool for the design of complex engineering systems. Yet, generalized use of numerical optimization techniques in design has been hindered by (i) the difficulty to translate in a faithful manner the actual design problem into any kind of rigid mathematical optimization problem, (ii) the inability of classical optimization tools to efficiently take into account the many distinctive features of optimization problems arising in a design context, and (iii) the unavailability of software tools offering to the designer a powerful as well as congenial environment supporting such capabilities. In this paper, some aspects of these questions are touched upon and avenues are suggested to address them. In particular, a recently proposed interaction driven design methodology is briefly described and numerical optimization schemes satisfying two specific requirements of many design problems are sketched. As an example, the design of a controller for a copolymerization reactor using the Maryland developed CONSOLE system is considered.Item Robustness in the Presence of Joint Parametric Uncertainty and Unmodeled Dynamics.(1988) Fan, Michael K-H.; Tits, A.L.; Doyle, John C.; ISRIt is shown that, in the case of joint real parametric and complex uncertainty, Doyle's structured singular value can be obtained as the solution of a smooth constrained optimization problem. While this problem may have local maxima, an improved computable upper bound to the structured singular value is derived, leading to a sufficient condition for robust stability and performance.
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