RECENT RESEARCH PAPERS

CONSENSUS AT COMPETITIVE EQUILIBRIUM: DYNAMIC FLOW OF AUTONOMOUS CARS IN TRAFFIC NETWORKS 

ACC 2016 Paper

STRUCTURAL ANALYSIS AND DESIGN OF DYNAMIC-FLOW NETWORKS: IMPLICATIONS IN THE BRAIN DYNAMICS 

Plenary Talk
The International Conference on Hybrid Systems and Applications
University of Louisiana, Lafayette, LA, May 22-26, 2006

DYNAMIC GRAPHS 

Plenary Talk
The 10th IFAC Symposium on Large Scale Systems
Osaka, Japan, July 26-28, 2004


CONTROL OF LARGE-SCALE SYSTEMS:
BEYOND DECENTRALIZED FEEDBACK

 

INCLUSION PRINCIPLE FOR DESCRIPTOR SYSTEMS, IEEE Transactions on Automatic Control, , 2009.

ROBUST STABILIZATION OF NONLINEAR INTERCONNECTED SYSTEMS BY DECENTRALIZED DYNAMIC OUTPUT FEEDBACK, Systems & Control Letters, 2009.

CONTROL DESIGN WITH ARBITRARY INFORMATION STRUCTURE CONSTRAINTS, Automatica, 2008.

STABILIZATION OF FIXED MODES IN EXPANSIONS OF LTI SYSTEMS, Systems & Control Letters, 2008.

COOPERATIVE AVOIDANCE CONTROL FOR MULTIAGENT SYSTEMS, Journal of Dynamic Systems, Measurement, and Control, 2007.

DECENTRALIZED DYNAMIC OUTPUT FEEDBACK FOR ROBUST STABILIZATION OF A CLASS OF NONLINEAR INTERCONNECTED SYSTEMS, Automatica, 2007.

A CANONICAL FORM FOR THE INCLUSION PRINCIPLE OF DYNAMIC SYSTEMS, SIAM Journal of Control and Optimizations, 2006.

STABILITY OF INTERVAL TWO-VARIABLE POLYNOMIALS AND QUASIPOLYNOMIALS VIA POSITIVITYSpringer-Verlag, 2005.

GLOBAL LOW-RANK ENHANCEMENT OF DECENTRALIZED CONTROL FOR LARGE-SCALE SYSTEMS, IEEE Transactions of Automatic Control, 2005.

A DECOPMPOSITION-BASED CONTROL STRATEGY FOR LARGE, SPARSE DYNAMIC SYSTEMS, Mathematical Problems in Engineering, 2005.

A NEW APPROACH TO CONTROL DESIGN WITH OVERLAPPING INFORMATION STRUCTURE CONSTRAINTS, Automatica, 2005.

CONTROL OF LARGE-SCALE SYSTEMS IN A MULTIPROCESSOR ENVIRONMENT, Applied Mathematics and Computation, 2005.

DESIGN OF ROBUST STATIC OUTPUT FEEDBACK FOR LARGE-SCALE SYSTEMS, IEEE Transactions of Automatic Control, 2004.

ROBUST DECENTRALIZED EXCITER CONTROL WITH LINEAR FEEDBACK, IEEE Transactions on Power Systems, 2004.

STABILIZATION OF NONLINEAR SYSTEMS WITH MOVING EQUILIBRIA, IEEE Transactions on Automatic Control, 2003.

CONNECTIVE STABILITY OF DISCONTINUOUS DYNAMIC SYSTEMS, Journal of Optimization Theory and Applications, 2002.

STABILITY OF POLYTOPIC SYSTEMS VIA CONVEX M-MATRICES AND PARAMETER-DEPENDENT LIAPUNOV FUNCTIONS, Nonlinear Analysis, 2000.

JACOBI AND GAUSS-SEIDEL ITERATIONS FOR POLYTOPIC SYSTEMS: CONVERGENCE VIA CONVEX M-MATRICES, Reliable Computing, 2000

 

 

 

 

 

INCLUSION PRINCIPLE FOR TIME-VARYING SYSTEMS

40th Conference on Decision and Control, Orlando, Florida, December 4-7, 2001.

Co-author  S. S. Stankovic

 

In this paper the inclusion concept is applied to time-varying linear continuous-time dynamic systems.  Starting from general definitions, which contain restriction and aggregation as special cases, inclusion

conditions are derived.  Properties of different inclusion types are discussed.  It is proved that any inclusion can be considered as a composition of one restriction and one aggregation.

 

 

CONTRACTIBILITY OF OVERLAPPING DECENTRALIZED CONTROL

Systems & Control Letters, vol. 44, 2001, pp. 189-200.

Co-author  S. S. Stankovic

 

The purpose of this paper is to generalize the concept of contractibility of decentralized control laws in the Inclusion Principle.  After a system with overlapping subsystems is expanded into a larger space, and decentralized control laws are formulated for the disjoint subsystems, the laws need to be contracted for implementation in the original space.  We proposed broader definitions of restriction and aggregation in the framework of inclusion, which provide more flexibility in the contraction phase of the expansion-contraction process.  In particular, we discuss contractibility conditions for dynamic output controllers including state observers, which have been of special interest in applications.

 

 

ORGANICALLY-STRUCTURED CONTROL

Proceedings of the 2001 Automatic Control Conference, Arlington, VA, June 25-27, 2001, pp. 2736-2742.  Co-author  D. M. Stipanovic

 

The purpose of this paper is to propose a study of the following control problem:  Given a complex interconnected system, determine autonomous decentralized control laws which stabilize the system despite structural perturbations whereby subsystems are disconnected and again connected in various ways during its lifetime.  The underlying assumption is that subsystems (overlapping or disjoint) are made of structural elements connected to at least one intelligent element (controller); they are either multiple controller or multiple plant configurations.   A distributed intelligence over interconnected complex structures imitates what goes on in the biological world, and we initiate a systematic investigation of the problem of Organically-Structured Control (OS-control), which can stabilize the system uder structural perturbations and, ultimately, prevent a system breakdown.

 

 

CONNECTIVE STABILITY OF DISCONTINUOUS INTERCONNECTED SYSTEMS VIA PARAMETER-DEPENDENT LIAPUNOV FUNCTIONS

Proceedings of the 2001 American Control Conference, Arlington, VA, June 25-27, 2001, pp. 4189-4196.  Co-author  D. M. Stipanovic

 

Connective stability is defined for discontinuous interconnected systems under structural perturbations.  Stability conditions are obtained using both Lipschitz and - type vector Liapunov functions.  The functions are chosen to be parameter-dependent in order to handle uncertainties in the interconnections.  Connective stability conditions are converted to convex optimization problems via theory of M-matrices.  As an illustration of the obtained results it is shown that generalized matching conditions apply to stabilization of systems with piecewise-continuous interconnections.

 

ROBUST STABILITY AND STABILIZATION OF DISCRETE-TIME NON-LINEAR SYSTEMS:  THE LMI APPROACH

International Journal of Control, vol. 74, No. 9, 2001, pp. 873-879. 

Co-author  D. M. Stipanovic

 

The purpose of this paper is to convert the problem of robust stability of a discrete-time system under non-linear perturbation to a constrained convex optimization problem involving linear matrix inequalities (LMI).  The nominal system is linear and time-invariant, while the perturbation is an uncertain non-linear time-varying function, which satisfies a quadratic constraint.  We show how the proposed LMI framework can be used to select a quadratic Lyapunov function, which allows for the least restrictive nonlinear constraints.  When the nominal system is unstable the framework can be used to design a linear state feedback which stabilizes the system with the same maximal results regarding the class of non-linear perturbations.  Of particular interest in this context is our ability to use the LMI formulation for stabilization of interconnected systems composed of linear subsystems with uncertain non-linear and time-varying coupling.  By assuming stabilizability of the subsystems we can produce local control laws under decentralized information structure constraints dictated by the subsystems.  Again, the stabilizing feedback laws produce a closed-loop system that is maximally robust with respect to the size of the uncertain interconnection terms.

 

 

ROBUST STABILIZATION OF NONLINEAR SYSTEMS:  THE LMI APPROACH

Mathematical Problems in Engineering , vol. 6, 2000, pp. 461-493.

Co-author D. M. Stipanovic

 

This paper presents a new approach to robust quadratic stabilization of nonlinear system within the framework of Linear Matrix Inequalities (LMI).  The systems are composed of a linear constant part perturbed by an additive nonlinearity, which depends discontinuously on both time and state.  The only information about the nonlinearity is that it satisfies a quadratic constraint.  Our major objective is to show how linear constant feedback laws can be formulated to stabilize this type of systems and, at the same time, maximize the bounds on the nonlinearity, which the system can tolerate without going unstable.

We shall broaden the new setting to include design of decentralized control laws for robust stabilization of interconnected systems.  Again, the LMI methods will be used to maximize the class of uncertain interconnections , which leave the overall system connectively  stable.  it is useful to learn that the proposed LMI formulation “recognizes” the matching conditions by returning a feedback gain matrix for any prescribed bound on the interconnection terms.  More importantly, the new formulation provides a suitable setting for robust stabilization of nonlinear systems where the nonlinear perturbations satsfy the generalized matching conditions.

 

 

DECENTRALIZED OVERLAPPING CONTROL OF A PLATOON OF VEHICLES

IEEE Transactions on Control Systems Technology, vol. 8, no. 5, 2000, pp. 816-832. 

Co-authors  S. S. Stankovic and M. J. Stanojevic

 

In this paper a novel methodology is proposed for longitudinal control design of platoons of automotive vehicles within intelligent vehicle/highway systems (IVHSs).  The proposed decentralized overlapping control law is obtained by using the inclusion principle, i.e., by decomposing the original system model by an appropriate input/state expansion, and by applying the Linear Quadratic (LQ) optimization to the locally extracted subsystems.  The local quadratic criteria directly reflect the desired system performance.  Optimization is carried out by using a sequential algorithms adapted to the lower block triangular (LBT) structure of the closed-loop system model.  Contraction to the original space provides a decentralized platoon controller, which preserves the asymptotic stability and the steady-state behavior of the controller obtained in the expanded space.  Conditions for eliminating the “slinky effect” and obtaining the strict string stability are defined; it is shown that the corresponding constraints on the controller parameters are not too restrictive.  A new dynamic platoon controller structure, consisting of a reduced order observer and a static feedback map, is obtained by applying the inclusion principle to the decentralized overlapping platoon control design in the case when the information from the preceding vehicle is missing.  Numerous simulation results show that the proposed methodology provides a reliable tool for a systematic and efficient design of platoon controllers within IVHS.

 

 

STOCHASTIC INCLUSION PRINCIPLE APPLIED TO DECENTRALIZED AUTOMATIC GENERATION CONTROL

International Journal of Control, vol. 72, no. 5, 1999, pp. 276-288.

Co-authors S. S. Stankovic, X. B. Chen and M. R. Matausek

 

An input-state-output inclusion principle is formulated for stochastic system and applied to Automatic Generation Control (AGC) for large power systems.  Three types of overlapping decentralized and fully decentralized dynamic controllers, which incorporate the state estimators, are proposed for the cases of full and reduced measurement sets.  An extensive analysis of both steady-state and transient regimes under a wide variety of operating conditions shows superiority of the proposed AGC scheme when compared to standard AGC designs.

 

 

 

Robust Stability and Polynomial Positivity

 

 

SPR CRITERIA FOR UNCERTAIN RATIONAL MATRICES VIA POLYNOMIAL POSITIVITY AND BERNSTEIN’S EXPANSIONS

IEEE Transactions of Circuits and Systems, vol. 48, no. 11, 2001, pp. 1366-1369.

Co-author D. M. Stipanovic

 

The main purpose of this paper is to convert the Strict Positive Real (SPR) conditions for rational matrices to conditions involving only positivity of polynomials.  The polynomial formulation provides efficient SPR criteria for matrices with uncertain interval parameters.  To establish the robust SPR property it suffices to test positivity of only three uncertain polynomials regardless of the order of the matrix.  The most interesting feature of the proposed polynomial formulation is that the coefficients of uncertain matrices are allowed to have polynomial uncertainty structure.  This generality is easily handled by using the Bernstein expansion algorithm.  The efficiency of the proposed polynomial approach is illustrated by testing absolute stability of a MIMO Lur’e-Postnikov system having interval parameters.

 

 

ROBUST D-STABILITY VIA POSITIVITY

Automatica, vol. 35, no. 8, 1999, pp. 1477-1484.

Co-author D. M. Stipanovic

 

The main objective of the paper is to convert the general problem of robust D-stability of a complex polynomial to positivity in the real domain of the corresponding magnitude function.  In particular, the obtained criterion for Hurwitz stability is applied to polynomials with interval parameters and polynomic uncertainty structures.  The robust stability is verified by testing positivity of a real polynomial using the Bernstein subdivision algorithm.  A new feature in this context is the stopping criterion, which is applied whenever the algorithm is inconclusive after a large number of iterations, but we can show that at least one zero of the polynomial is closer to the imaginary axis than a prescribed limit.

 

 

Parametric Stability

 

PARAMETRIC ABSOLUTE STABILITY OF MULTIVARIABLE LUR’E SYSTEMS

Automatica, vol. 36, no. 9, 2000, pp. 1365-1372.

Co-authors T. Wada, M. Ikeda, Y. Ohta

 

The objective of this paper is to consider parametric absolute stability of multivariable Lur’e systems with uncertain parameters and constant reference inputs.  Both state-space and frequency-domain conditions are formulated to guarantee that the system remains stable despite shifts of the equilibrium location caused by changes of uncertain parameters and reference inputs.  The state-space condition can be tested using existing software tools for solving linear matrix inequalities.  For testing Popov-type frequency-domain condition, the value set software tool for the Interval Arithmetic can be used.

 

 

PARAMETRIC ABSOLUTE STABILITY OF MULTIVARIABLE LUR’E SYSTEMS

IEEE Transactions on Automatic Control, vol. 43, no. 11, 1999, pp. 1649-1653.

Co-authors T. Wada, M. Ikeda and Y. Ohta

 

The concept of absolute stability is extended to include Lur’e-type nonlinear control systems with uncertain parameetrs and constant reference inputs.  Conditions for parametric absolute stability are derived, which guarantee the the system remains stable despite uncertainty of equilibrium location caused by parametric uncertainties and values of the reference input.  The conditions can be tested by computing value sets using Polygon Interval Arithmetic.

 

 

Numerical Methods and Algorithms

 

 

STABILITY ANALYSIS OF DISCONTINUOUS NONLINEAR SYSTEMS VIA PIECEWISE LINEAR LYAPUNOV FUNCTIONS

Proceedings of the 2001 American Automatic Control Conference, Arlington, VA, June 25-27, 2001, pp. 4852-4857.

C0-authors Y. Ohta, and T. Wada

 

The purpose of this paper is to present a stability analysis of discontinuous nonlinear systems using Piecewise Linear Lyapunov Functions (PWLLFs).  The functions are parametrized by hyperplanes which intersect the stability region, and stability conditions are formulated as Linear Programming Problems (LPs) in terms of the parameters inserted by the hyperplanes.  An interesting feature of the analysis is that it can include the uncertainty caused by time delays which are inherent in switching devises controlling the system.  A few examples are used to illustrate the obtained results.

 

 

A PARALLEL KRYLOV-NEWTON ALGORITHM FOR ACCURATE SOLUTION OF LARGE, SPARSE RICCATI EQUATIONS

Advances in Computation: Theory and Practice (to appear).

Co-author A. I. Zecevic

 

In this paper we present a new parallel algorithm which is designed to accurately solve large sparse Riccati equations.  The algorithm utilizes epsilon decompositions to obtain a good initial approximation for the solution, and subsequently combines the Arnoldi-Krylov subspace method with Newton’s iterative process to refine this approximation.  The results indicate that in a parallel environment this approach can produce accurate solutions with only modest demands on the execution time.

 

 

JACOBI AND GAUSS-SEIDEL ITERATIONS FOR POLYTOPIC SYSTEMS: CONVERGENCE VIA CONVEX M-MATRICES

Reliable Computing, vol. 6, no. 2, 2000, pp. 123-137.

Co-author D. M. Stipanovic

 

A natural generalization of Jacobi and Gauss-Seidel iterations for interval systems is to allow the matrices to reside in convex polytopes.  In order to apply the standard convergence criteria involving M-matrices to iterations for polytopic systems, we derive conditions for convex polytope of M-matrices in terms of vertices.  We show how the conditions are used in the convergence analysis of iterations for block and nonlinear polytopic systems

 

 

PARALLEL SOLUTIONS OF VERY LARGE SPARSE LYAPUNOV EQUATIONS BY BALANCED BBD DECOMPOSITIONS

IEEE Transactions on Automatic Control, vol. 44, no. 3, 1999, pp. 612-

Co-author A. I. Zecevic

 

In this paper, a method for parallel solution of large sparse matrix equations is presented.  The method is based on the balanced Bordered Block Diagonal (BBD) decompositions which is applied in conjunction with the SOR iterative method to solve large Lyapunov equations in the Kronecker sum representation.  A variety of experimental results will be presented, including solutions of Lyapunov equations with matrices as large as 1993 x 1993.