**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**

**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.

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

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

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

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

**INCLUSION PRINCIPLE FOR TIME-VARYING SYSTEMS**

*40 ^{th} 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.