Publications in systems theory Papers

• V. Yadav, P. Voulgaris, and M. V. Salapaka. “Stabilization of nested systems with uncertain subsystem communication channels” Proceedings of the IEEE Conference on Decision and Control. pp. 2853-2858, Hawaii, December 2003. 
  • This paper addresses the design of stabilizing controllers for a nested control system where the controller is realized in a distributed manner, considering uncertainty not only in the controller-to-plant and plant-to-controller channels but also in the nest-to-nest, subcontroller-to-subcontroller communication. An input-output approach is taken. Two appropriate controller architectures that stabilize the entire system with the various components subject to uncertainty and noise are addressed. We present controller synthesis procedures to address deterministic uncertainty and stochastic uncertainty, that model packet-loss in the Internet. 
• V. Yadav, P. Voulgaris, and M. V. Salapaka. “Controller Architectures for Distributed Implementation and Performance Optimization” Submitted to IEEE Conference on Decision and Control. Bahamas, December 2004.
  • In this paper we consider how to distribute and implement an unstructured or structured overall controller K to various stations (sub-controllers). In doing so In doing so we assume that noise is present in the sub-controller to subcontroller communication and thus, its effect on stability and performance has to be addressed. Using an observer based controller parameterization, we provide suitable stabilizing sub-controller architectures that directly take into account the effect of communication noise on performance. In particular, the overall performance optimization can be cast as a convex problem in the Youla-Kucera parameter Q. Similar results hold for banded controller structures, i.e., when there is also a delay in the subsystem to subsystem communication. 
• M. Khammash, M.V. Salapaka, T. VanVoorhis, "Robust Synthesis in l1: A globally optimal solution", IEEE Trans. Automatic Control, Volume: 46 Issue: 11 , Nov. 2001, Page(s): 1744 -1754.
• M. V. Salapaka, M. Khammash, M. Dahleh,  “Solution of MIMO H2/l1 problem without zero interpolation”, SIAM Journal on Optimization and Control, V37, no. 6, pp.1865-1873.
• M. V. Salapaka, M. Dahleh, and P. Voulgaris,  Mimo optimal control design: the interplay of the H2 and the l1 norms IEEE Transactions on Automatic Control, V43, no. 10:pp.1374-1388, 1998.
  • In this paper we consider controller design methods which can address directly the interplay between the H2 and l1 performance of the closed loop. The development is devoted to multi-input multi-output (MIMO) systems. Two relevant multiobjective performance problems are considered each being of interest in its own right. In the first, termed as the combination problem, a weighted sum of the l1 norms and the square of the H2 norms of a given set of input-output transfer functions constituting the closed loop is minimized. It is shown that, in the 1-block case, the problem solution can be obtained via a finite dimensional quadratic optimization with a priori known dimension. In the 4-block case, a method of computing approximate solutions within any a priori given tolerance is provided. In the second, termed as the mixed problem, the H2 performance of the closed loop is minimized subject to a l1 constraint. It is shown that approximating solutions within any a priori given tolerance can be obtained via the solution to a related combination problem.  
• M. V. Salapaka, M. Dahleh, and P. Voulgaris. Mixed objective control synthesis: Optimal l1/H2 control SIAM Journal on Control and Optimization, V35 no. 5:pp. 1672--1689, 1997.
  • In this paper we consider the problem of minimizing the l1 norm of the transfer function from the exogenous input to the regulated output over all internally stabilizing controllers while keeping its H2 norm under a specified level. The problem is analysed for the discrete-time, single-input single-output (SISO), linear time invariant case. It is shown that an optimal solution always exists. Duality theory is employed to show that any optimal solution is a finite impulse response sequence and an a priori bound is given on its length. Thus, the problem can be reduced to a finite dimensional convex optimization problem with an a priori determined dimension. Finally it is shown that, in the region of interest of the H2 constraint level the optimal is unique and continuous with respect to changes in the constraint level.
• M. V. Salapaka, P. Voulgaris, and M. Dahleh, "SISO controller design to minimize a positive combination of the l1 and the H2 norm",  Automatica, V33, no. 3:pp. 387--391, March 1997. 
  • In this paper we consider the problem of minimizing a given positive linear combination of the l1 norm and the square of the H2 norm of the closed loop over all internally stabilizing controllers. The problem is analysed for the discrete-time, SISO, linear time invariant case. It is shown that a unique optimal solution always exists which can be obtained by solving a finite dimensional convex optimization problem with an a priori determined dimension. It is also established that the solution is continuous with respect to changes in the coefficients of the linear combination.
• M. V. Salapaka, P. Voulgaris, and M. Dahleh, "Controller design to optimize a composite performance measure", Journal of Optimization Theory and Applications, V91, no. 1:pp. 91-113, 1996. 
  • This paper studies a ``mixed'' objective problem of minimizing a composite measure of the l1, H2, and l\infty norms together with the l\infty norm of the step response of the closed loop . This performance index can be used to generate Pareto optimal solutions with respect to the individual measures. The problem is analysed for the discrete time, single-input single-output (SISO), linear time invariant systems. It is shown via the Lagrange duality theory that the problem can be reduced to a convex optimization problem with a priori known dimension. In addition, continuity of the unique optimal solution with respect to changes in the coefficients of the linear combination is established.
• Qi, Xin, M. Khammash, M. V. Salapaka, “Integrated Parameter and Control Design”, Proceedings of the American Control Conference, 2002.
• Qi, X., M. H. Khammash, and M. V. Salapaka, "A Matlab Package for Multiobjective Control Synthesis", IEEE conference on Decision and Control, 2001, Volume: 4 , 2001 Page(s): 3991 -3996.
• Qi, X., M. H. Khammash, and M. V. Salapaka, “Optimal controller synthesis with multiple objectives”, Proceedings of the 2001 American Control Conference, Arlington VA, 2001, pp: 2730-2735.
• Qi, X., M. H. Khammash, and M. V. Salapaka, “A new approach to multiple-objective controller synthesis”, Proceedings of the 38th annual allerton conference on communication, control and computing, Allerton, Urbana, Illinois, 2000.
• M. Khammash, M. V. Salapaka, T. Vanvoorhis, “Synthesis of globally optimal controllers in l1 sing linear relaxation,” Proceedings of the 37th IEEE Conference on Decision and Control, Tampa, Florida, December 1998, pp. 3315-3320.
• M. V. Salapaka, M. Khammash, “Multi-objective MIMO optimal control design without zero interpolation”, Proceedings of the 1998 American Control Conference, Philadelphia, Pennsylvania, June 1998, Vol. 1, pp.660-664.
• M. V. Salapaka, M. Khammash, and M. Dahleh, “Recent progress in mixed objective control synthesis with l1 and H2 norms”, Proceedings of the ASME conference, 1998.
• M. V. Salapaka, M. Khammash, and M. Dahleh, “Solution of MIMO H2/l1 problem without zero interpolation”, Proceedings of the 36th IEEE Conference on Decision and Control, San-Diego, CA, 1997, pp. 1546-1551.
• M. V. Salapaka, M. Dahleh, A. Vicino, and A. Tesi, “Nominal H2 performance and l1 robust performance,” Proceedings of the IEEE Conference on Decision and Control. pp. 4034-4039, Kobe, Japan, December 1996.
• M. V. Salapaka and M. Dahleh, “l1/H2 control”, Proceedings of the Allerton Conference, Urbana, Illinois, 1997.
• M. V. Salapaka, M. Dahleh and P. Voulgaris, “MIMO optimal control design: the interplay of the H2 and the l1 norms,” Proceedings of the IEEE Conference on Decision and Control, Vol. 1, pp: 3682-3687, New Orleans, La., December 1995.
• M. V. Salapaka, P. Voulgaris and M. Dahleh, “Controller design to minimize a composite measure of the l1 and the H2 norms”, Proceedings of the third Mediterranean Symposium on New Directions in Control and Automation”, Vol. 2 pp: 93-100, Cyprus, 1995.
• M. V. Salapaka, P. Voulgaris and M. Dahleh, “ Controller design to optimize a composite performance measure”, Proceedings of the IEEE Conference on Decision and Control, Vol.1, pp: 817-22, New Orleans, La. December 1995.
• M. V. Salapaka, M. Dahleh and P. Voulgaris, “Mixed objective control synthesis: optimal l1/H2 control”, Proceedings of the American Control Conference, Vol. 2, pp. 1438-1442, Seattle, Washington, June 1995.