1. Systems and Control in the Department of Mathematics and in the College of Engineering Department of Mathematics and Statistics New graduate student orientation Fall 2003 1 It is the objectives, the questions we ask, that distinguishes “control(led dynamical systems) theory” controlled dynamical system e.g multi-body spacecraft, pond w/ “harvesting” (open-loop) controllability u(t) (get from one state to another) observability: recover state x(t) from measured/observed output y(t) state-feedback u(x), output-fdbk u(y) e.g. stabilization e.g. disturbance rejection e.g. optimal control uncontrolled dynamics e.g. solar system, ecosystem in pond existence and uniqueness of solutions prediction of long-term solution behavior e.g. stability, e.g. chaos

2. Systems and Control in the Department of Mathematics and in the College of Engineering Department of Mathematics and Statistics New graduate student orientation Fall 2003 2 Diverse models, diverse mathematics tools Continuous time (DEs)  discrete time (difference eqns) Finite state-space (automata)   finite dimensional (systems of ODEs)  infinite dimensional (systems of PDEs) Deterministic  stochastic Linear  nonlinear  nonsmooth.... Common themes / questions / objectives, but diverse mathematics tools  flexible coursework (incl. many options in CEAS)

3. Systems and Control in the Department of Mathematics and in the College of Engineering Department of Mathematics and Statistics New graduate student orientation Fall 2003 3 Faculty Tom Taylor (Harvard, ASU since 1983) Peter Crouch (Harvard, ASU since 1984, dean CEAS) Matt Kawski (Colorado, ASU since 1987) Sergei Nikitin (Moscow, ASU since 1994) Collaboration in math. w/ e.g.dynamical systems Dieter Armbruster, Eric Kostelich, Hal Smith, … Collaboration w/ many engineering departments Dan Riviera (ChemE), Gary Yamaguchi (BioMedE) Toni Rodriguez (EE), Kostas Tsakalis (EE), … …

4. Systems and Control in the Department of Mathematics and in the College of Engineering Department of Mathematics and Statistics New graduate student orientation Fall 2003 4 Traditional strengths, current initiatives at ASU “differential geometric” (TT, PC, MK, SN) finite dimensional / deterministic / continuous time / nonlinear  seminar “Geometry and Dynamical Systems” (PC,MK) “modeling” (TT) of group-behavior and decision making: w/ biologists, psychologists and computer scientists; long range goals include the control of crowd behavior in panic situations “stochastic” (TT) Bayesian estimation; model construction and validation for nonlinear dynamical systems. Goals include effective prediction of future based on learning from past, e.g. climate, markets “manufacturing systems and supply chains” (DA, CR, DR, MK, Intel) modeling, analysis, control – “competition of models and approaches”

5. Systems and Control in the Department of Mathematics and in the College of Engineering Department of Mathematics and Statistics New graduate student orientation Fall 2003 5 Why study control ? Intellectual challenge: –inverse questions, “don’t just watch & predict, but instead take planned action so that … happens” Very lively area at the intersection of pure math with many engineering applications Active and well-supported at ASU; by NSF, DoD, DoE, … Meshes w/ interest in diverse mathematical areas Keep your options open!!! –career in academia, pure sciences, or –“real job” in industrial, business, governmental… applications