Matthias Kawski develops, and employs, tools from differential geometry and algebraic combinatorics to study nonlinear control systems.
Controlled dynamical systems are distinguished from classical ones by their input and output channels that allow one to interact with the systems. Prototypical is the difference between planetary motion and motion of a human-made satellite. Classically one asks: Where will the system go? When is the next eclipse? Is the solar system stable? Control theory asks inverse questions: Can I get there, and if so how? How optimally? Is the system stabilizable? Applications are ubiquitous, from mechanical and electrical systems, to finance, biomedicine and beyond.
Kawski employs diverse mathematical tools, from Lie algebras to combinatorial Hopf algebras, to uncover geometric properties of control systems on manifolds, and to design efficient algorithms suiting the inherently nonassociative nature of noncommuting flows (control actions).
J.-P. Gauthier and M. Kawski. Minimal Complexity Sinusoidal Controls for Path Planning. 53rd IEEE Conference on Decision and Control (2014).
Matthias Kawski. Math Circles: Innovative Communities for Doing Mathematics. Universities of Canterbury and Auckland (2011).
Matthias Kawski. Vector field analyzer II and Iterated Integrals. (2011).
Jean-Michel Coron, Matthias Kawski, and Zhiqiang Wang. Analysis of a conservation law modeling a highly re-entrant manufacturing system. Discrete and Continuous Dynamical Systems - Series B (2010).
Kawski, Matthias. Literally Changing the Point of View. Elec. Journal Math. Technology (2010).
Matthias Kawski. Chronological Calculus in Systems and Control Theory. Encyclopedia of Complexity and System Science (2009).
Matthias Kawski. Springer Encyclopedia of Complexity and System Science. Section title: Control and Dynamical Systems. (2009).
Kawski, Matthias. Control interpretations of products in the Hopf algebra. Proceedings 48th IEEE Conference on Decision and Control (2009).
Matthias Kawski. Curvature of optimal control: Deformation of classical planar systems. Journal Control and Cybernetics (2008).
Gehrig, Eric, and Kawski, Matthias. A Hopf-algebraic formula for compositions of noncommuting flows. Proceedings 47th IEEE Conference on Decision and Control (2008).
Matthias Kawski. From f(x) to xf: Using technology to promote advanced modern mathematical thinking. Proceedings 13th Asian Technology Conference Mathematics (2008).
Kawski, Matthias (author) ,Taylor, Thomas J (author) . Canonical operators on graphs. Modeling, Estimation and Control (2007).
Matthias Kawski and Thomas Taylor. Canonical operators on graphs. Modeling, Estimation and Control (2007).
Kawski, Matthias. On the problem whether controllability is finitely determined. Proceedings 17th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2006) (2006).
Kawski, Matthias. On the problem whether controllability is finitely determined. Proceedings 17th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2006) (2006).
Matthias Kawski. Functions and Operators in MAPLE and in MATLAB. Proceedings delta03, 4th Southern Hemisphere Symposium on Undergraduate Mathematics Teaching (2003).
Matthias Kawski. High Order Maximal Principles. New Trends in Nonlinear Dynamic and Control, and their Applications (2003).
Matthias Kawski, R Bianchini. Needle variations that cannot be summed. SIAM Journal of Control & Optimization (2003).
Rosa-Maria Bianchini, Matthias Kawski. Lack of convexity for tangent cones of needle variations. Proc.IEEE Conference on Decision and Control (2003).
Matthias Kawski. The combinatorics of nonlinear controllability and noncommuting flows. Abdus Salam ICTP Lecture Notes series (2002).
Kawski, Matthias. Controllability and coordinates of the first kind. Contemporary Trends in Nonlinear Geometric Control Theory and its Applications (2002).
Kawski, Matthias. Interactive visualization in complex analysis. Proc. 2nd International Conference Mathematics Teaching (2002).
Matthias Kawski. Chronological algebras: combinatorics and control. Itogi Nauki i Techniki (2000).
Kawski, Matthias. Calculating the logarithm of the Chen Fliess series. Proceedings 14th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2000) (2000).
Kawski, Matthias. Calculus of nonlinear interconnections with nonlinear applications. Proc. 39th IEEE Conference Decision and Control (2000).
Kawski, Matthias, Holland, S. An interactive JAVA vector field analyzer. (2000).
Research Activity
Kostelich,Eric John*, Armbruster,Hans Dieter, Czygrinow,Andrzej Michal, Fishel,Susanna, Gelb,Anne, Jacobs,Mark, Kawski,Matthias, Kuang,Yang, Mahalov,Alex, Moustaoui,Mohamed, Platte,Rodrigo B, Tang,Wenbo. MCTP: Mathematics Mentoring Partnership Between Arizona State University and the Maricopa County Community College District. NSF-MPS-DMS(7/15/2012 - 6/30/2017).
Kawski,Matthias*. Trimester in Combinatorics and Control COCO 2010. NSF-MPS(4/15/2010 - 3/31/2012).
Kawski,Matthias*. Geometry of Nonlinear Control with Applications. NSF-MPS-DMS(9/15/2009 - 8/31/2013).
Kawski,Matthias*. Chronological Calculus and Nonlinear Control. NSF-MPS(8/1/2005 - 7/31/2009).
Kawski,Matthias*. IGMS: OPTIMIZING SUPPLY NETWORKS AND RE-ENTRANT MANUFACTURING SYSTEMS IN THE SEMICONDUCTOR INDUSTRY. NSF-MPS(3/1/2002 - 8/31/2003).
Kawski,Matthias*. GEOMETRY AND ALGEBRA OF NONLINEAR CONTROL SYSTEMS. NSF-MPS(7/15/2000 - 6/30/2004).
Kawski,Matthias*. VECTOR CALCULUS VIA LINEARIZATION: VISUALIZATION AND MODERN APPLICATIONS. NSF-EHR(1/15/1998 - 12/31/2000).
Evans,Donovan L*, Burrows,Veronica Ann, Doak,R Bruce, Grondin,Robert Oscar, Kawski,Matthias, Moor,William C, Roedel,Ronald J, Spielberg,John Samuel. THE FOUNDATION COALITION (YEAR 5). TEXAS ENGINEER EXPERIMENT STAT(10/1/1997 - 9/30/1998).
Evans,Donovan L*, Carlson,Marilyn P, Craft,Elizabeth Ann, Hestenes,David Orlin, Kawski,Matthias, Linder,Darwyn E, Mckelvy,Michael J, Rockwood,Alyn Paul, Spanias,Andreas Savva, Uttal,William R, Watson,George L. PLANNING GRANT FOR CENTER FOR COLLABORATIVE RESEARCH IN LEARNING TECHNOLOGIES BASED AT ASU. NSF-CISE(10/1/1996 - 10/31/1997).
Evans,Donovan L*, Aberle,James T, Burrows,Veronica Ann, Doak,R Bruce, Grondin,Robert Oscar, Kawski,Matthias, Mccarter,Joan Hosdowich, Roedel,Ronald J. THE FOUNDATION COALITION (YEAR 4). TEXAS ENGINEER EXPERIMENT STAT(10/1/1996 - 9/30/1997).
Evans,Donovan L*, Burrows,Veronica Ann, Doak,R Bruce, Grondin,Robert Oscar, Kawski,Matthias, Roedel,Ronald J. THE FOUNDATION COALITION (YEAR 3). TEXAS ENGINEER EXPERIMENT STAT(10/1/1995 - 9/30/1996).
Rodriguez,Armando A*, Kawski,Matthias. MODELING & ROBUST CONTROL OF RE-ENTRANT. INTEL CORP(1/1/1995 - 12/31/1998).
Kawski,Matthias*. GEOMETRY OF HIGHLY NONLINEAR MULTI-INPUT SYSTEMS. NSF-MPS(6/1/1993 - 11/30/1997).
Kawski,Matthias*. IMPLEMENTAT & DISSEMIN OF HARVARD CONSORTIUM MAT IN AZ,OK,UT. UNIV OF AZ(10/1/1992 - 3/31/1997).
Matthias Kawski. Minimal Complexity Sinusoidal Controls for Path Planning. 53rd IEEE Conf. Decision & Control (Dec 2014).
Matthias Kawski. Approximating subRiemannian Geodesics by highly oscillatory controls. Institute Henri Poincare, Paris (Nov 2014).
Matthias Kawski. IBL experiments in the MathCircle at ASU Tempe. 17th Annual Legacy of R.L. Moore - IBL Conference (Jun 2014).
Matthias Kawski. Hopf algebras and linear functionals in nonlinear control. AMS Spring Central Sectional Meeting. Lubbock (Apr 2014).
Matthias Kawski. Control and interactive visualization in DE courses. AMS Western Fall Sectional Meeting. Riverside (Nov 2013).
Matthias Kawski. Control and Mathematics Curricula. IFAC ACE 10th IFAC Symposium on Advances in Control Education (Aug 2013).
Matthias Kawski. Tiling, parity, and induction and Catalan numbers. Math Camp at Dine College, Tsaille, Navajo Nation (Jul 2013).
Matthias Kawski. Noncommuting Flows and Combinatorial Hopf Algebra. Seminar, Laboratoire des Sciences de l'Information et des Systems (LSIS), Universite de Toulon (Jun 2013).
Matthias Kawski. Workshop on Stochastic Systems Simulation and Control (SSSC 2012). Workshop on Stochastic Systems Simulation and Control (SSSC 2012) (Nov 2012).
Matthias Kawski. Derivative or derivation?. 12th Internat. Congress Mathematical Education (ICME 12), Seou South Korea (Jul 2012).
Matthias Kawski. Optimal control of re-entrant manufacturing systems. 14th Internat. Conf. Theory, Numerics & Applications of Hyperbolic Problems (Universita di Padova) (Jun 2012).
Matthias Kawski. Discrete Games. Circle on the Road Spring 2012, Smithsonian, Washington DC (Apr 2012).
Matthias Kawski. A conservation law modeling a highly re-entrant manufacturing system. Penn State University, Computational and Applied Mathematics Colloquium (Feb 2012).
Matthias Kawski. Geometry and algebra of noncommuting flows. 50th IEEE Conf. Decision & Control and European Control Conference. Orlando, FL (Dec 2011).
Matthias Kawski. Math Circles: Innovative Communities for Doing Mathematics. 8th Southern Hemisphere Symposium on Undergraduate Mathematics Teaching. New Zealand (Nov 2011).
Matthias Kawski. Math Circles: Doing math after school because it is fun. aatm (Arizona Assoc. of Teachers of Mathematics) Fall Conference, Tempe, AZ, October 2011 (Oct 2011).
Matthias Kawski. Chronological Calculus and Hopf Algebras in Control. 7th Internat. Congress Industrial & Applied Mathematics (ICIAM). Vancouver, BC (Jul 2011).
Matthias Kawski. Rough Paths and Combinatorics in Control Theory (RPCCT2011). Rough Paths and Combinatorics in Control Theory (RPCCT2011). La Jolla, CA (Jul 2011).
Matthias Kawski. Challenges in applications and education. DIMACS Workshop Perspectives & Future Directions Systems & Control Theory (SontagFest 2011) (May 2011).
Matthias Kawski. Tiling and induction. Circle on the Road, 2nd Annual meeting of the National Association of Math Circles. Houston, TX (Mar 2011).
Matthias Kawski. Adapted bases in geometric control. Trimester Madrid 2010 COMBINATORICS and CONTROL Workshop April 6-9, 2010 (Apr 2010).
Matthias Kawski. Combinatorial Aspects in Control. WorksTrimester Benasque 2010 COMBINATORICS and CONTROL School April 12-16, 2010 (Apr 2010).
Matthias Kawski. Combinatorics in control and the role of nilpotency. Trimester Madrid 2010 COMBINATORICS and CONTROL Conference June 21-25, 2010 (Apr 2010).
Kawski, Matthias. Control interpretations of the two convolution products in the Hopf algebra. 48th IEEE Conference Decision and Control (Dec 2009).
Kawski, Matthias. Elementary Partial Differential Equations with CAS technology. 14th atcm Asian Technology Conference Mathematics, (Dec 2009).
Kawski, Matthias. Interactive visualization tools for div, curl, Stokes theorem and differential equations. 14th atcm Asian Technology Conference Mathematics, (Dec 2009).
Kawski, Matthias. Control interpretations of the two convolution products in the Hopf algebra. SIAM Conf. Control and Applics (Jul 2009).
Kawski, Matthias. Minisymposium: Algebraic Tools for Nonlinear Control. SIAM Conf. Control and Applics (Jul 2009).
Kawski, Matthias. Applications of Hopf Algebras and Chronological Calculus to Controllability. 7th Int. Conf. Large-Scale Scient. Computations (Jun 2009).
Kawski, Matthias, Gehrig, Eric. A Hopf-algebraic formula for compositions of noncommuting flows. 47th IEEE Conference Decision and Control (Dec 2008).
Matthias Kawski. From f(x) to xf: Using technology to promote advanced modern mathematical thinking. 13th Asian Technology Mathematics Conference (Dec 2008).
Matthias Kawski. Computing compositions of noncommuting flows: geometry and algebra. Laboratoire Jacques-Louis Lions at Universite Pierre et Marie Curie Paris VI (Nov 2008).
Matthias Kawski. Hopf algebra structures in nonlinear control systems . American Mathematical Society (May 2008).
Kawski, Matthias. Chronological calculus and nonlinear feedback loops. American Math. Society Joint Internat. Meeting with the NewZealand Math. Society (Dec 2007).
Kawski, Matthias. Interactive visualization in advanced university mathematics. American Math. Society Joint Internat. Meeting with the NewZealand Math. Society (Dec 2007).
Kawski, Matthias. Modeling oxygen uptake dynamics during exercise. Workshop Applications Math to Biomedical Problems (Dec 2007).
Kawski, Matthias. Dynamic visualization in advanced undergraduate courses. 6th Southern Hemisphere Symposium on Undergraduate Mathematics Teaching (Nov 2007).
Kawski, Matthias. Teaching university mathematics and coaching youth soccer: problem solving. 6th Southern Hemisphere Symposium on Undergraduate Mathematics Teaching (Nov 2007).
Kawski, Matthias. Simplifying series expressions in optimal control. American Math. Society Joint Internat. Meeting with the Polish Math. Society (Aug 2007).
Kawski, Matthias. Curvature of optimal control: Deformation of classical planar systems. 23rd IFIP Conference on System Modelling and Optimization (Jul 2007).
Kawski, Matthias, Gehrig, Eric. Bases for the Shuffle Algebra. SIAM Conference on Control Theory and its Applications (Jun 2007).
Kawski, Matthias, Maxwell, Parnell. Curvature of Optimal Control: Deformation of Planar Systems. SIAM Conference on Control Theory and its Applications (Jun 2007).
Kawski, Matthias. Continuous stabilization of low-dimensional nonlinear systems. Emerging Frontiers in Control Theory: Research and Innovative Applications (Dayawansa Memorial) (Apr 2007).
Kawski, Matthias. Zermelo's Navigation Problem: Optimal Control, Geometry, and Computer Algebra. 11th Asian Tech in Math Conf Hongkong, China (Dec 2006).
Kawski, Matthias, Sanyal, Amit. Using bases to simplify asymptotic expansions. 3rd IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control (Jul 2006).
Kawski, Matthias. On the problem whether controllability is finitely determined. MTNS 2006 (Jul 2006).
Kawski, Matthias, Sanyal, Amit. Using bases to simplify asymptotic expansions. IFAC 3rd Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control (Jul 2006).
Kawski, Matthias. Symmetries in Feedback Stabilization: Combining Dilations with the Hopf Map. Geometric Control and Nonsmooth Analysis (Jun 2006).
Kawski, Matthias, Roberts, Tony. Round Table / Panel on Teaching of Linear Algebra. 5th Southern Hemisphere Symposium on Undergraduate Mathematics Teaching (Nov 2005).
Kawski, Matthias. Functions: Looking ahead beyond calculus. delta05 5th Southern Hemisphere Symposium on Undergraduate Mathematics Teaching, Australia (Nov 2005).
Kawski, Matthias. Combinatorics and algebra of series expansions in nonlinear control. 9th Int. Conf. Stability, Control & Rigid Bodies Dynamics Donetsk, Ukraine, September 2005 (Sep 2005).
Kawski, Matthias. Control for Mathematical Biology. Mathematicsal and Theoretical Biology Institute Summer Program (Los Alamos) (Jun 2005).
Kawski, Matthias. On Agrachev's curvature of optimal control. AMS Regional meeting (Apr 2005).
Kawski, Matthias. Calculus of Vector Fields using JAVA. II Bienal da Sociedade Brasileira de Matemática, Bahia = San Salvador, Brazil (Oct 2004).
Kawski, Matthias. Computer Algebra for Visualizing Curvature. II Bienal da Sociedade Brasileira de Matemática, Bahia = San Salvador, Brazil (Oct 2004).
Kawski, Matthias. Combinatorics and Geometry for Nonlinear Control. 1st Control Training Site Workshop, Istituto de Sistemas e Robotica (Jul 2004).
Kawski, Matthias, Bianchini, Rosa-Maria. Lack of convexity for tangent cones of needle variations. 41th IEEE CDC (Conf. Decision and Control) (Dec 2002).
Kawski, Matthias. On high-order maximum principles. Symp. New Trends Nonlinear Dynamics and Control and their Applications (Oct 2002).
Kawski, Matthias, Hermes, H. Nilpotent bases of distribution. MTNS 2002 (Aug 2002).
Kawski, Matthias. Bases for Lie algebras and a continuous CBH formula. MTNS 2002 (Aug 2002).
Kawski, Matthias. Interactive visualization in complex analysis. 2nd Internat. Conf. Math Teaching (Jul 2002).
Kawski, Matthias. Model software tools for inquiry based learning. 6th Asian Technology Conference Mathematics (Dec 2001).
Kawski, Matthias. A central role for interactive visualization in advanced courses. 3rd Southern Hemisphere Symp Undergrad Math Teaching (Jul 2001).
Kawski, Matthias. Interactive visualization across the curriculum. 5th atcm (Asian Technology Conference Math) (Dec 2000).
Kawski, Matthias. A new era of interactive visualization. AMS Scand 2000 (1st AMS-Scandinavian Joint Mtg. / XXIII Scandinavian Congress of Math) (Jun 2000).
Dray, Tevian, Kawski, Matthias. Visualizing Vector Derivatives: The Vector Field Analyzer. American Mathematical Society and Mathematical AssocAnnual Joint Meetings Joint Mathematics Meetings
Kawski, Matthias. CAS or MATLAB in first year collegiate math?. ICTME 2 Int. Conf. Trends in Math. Education
Kawski, Matthias. Functions and Operators in MAPLE and in MATLAB. Delta 03 (4th Southern Hemisphere Symposium on Undergraduate Mathematics Teaching)
Kawski, Matthias. Optimal control of supply chains with variable product mixes. INFORMS
Dray, Tevian, Hallett, Deborah, Kawski, Matthias, McCallum, William, Manogue, Corinne, Roedel, Ron, Zeilik, Michael. MAA panel: Voices of the partner disciplines: Building on the MAA curriculum foundations project.(co-organizer). AMS-MAA Joint meetings
Kawski, Matthias. Geometry and Algebra of Noncommuting Flows. Los Alamos Days - Arizona
Referee for Grant Proposals (NSF 41, NRF of RSA 1)
Professional Associations
AMS: American Mathematical Society SIAM: Society of Industrial and Applied Mathematics SIAG Control and Systems Theory MAA: Mathematical Association of America
Service
General Studies Council, Member (2009 - Present)
Journal of Mathematical Physics, referee (2007 - Present)
European Control Conference, referee (2014 - 2014)
Girl Scouts: STEM Innovation Circles, member of advisory board (2014 - 2014)
IEEE Conference on Decision and Control, referee (2014 - 2014)
Mathematical Reviews, Reviewer (2014 - 2014)
Systems and Control Letters, referee (2014 - 2014)
Math Circle at ASU Tempe, Founder and Director (2010 - 2014)
Math Camp at Dine College (Tsaile), Session leader (2014 - 2014)
Math Festival at Dine College (Tsaile), Session leader (2014 - 2014)