Ensemble controllability by Lie algebraic methods

Controllability of Nonlinear Discrete Time Systems: a Lie-algebraic Approach

for which the control variables u and state variables x take continuous values. Systems of the type (1) but with discrete-valued states and controls have long been studied in automata and sequential machine theory, but the continuous case has only recently become the subject of serious investigation as far as controllability properties are concerned. Our objective here is to survey a number of ...

Solving Partial Differential Equations by Lie Algebraic Methods

Solution of linear partial differential equations by Lie algebraic methods

A new algorithm is proposed for obtaining explicit solutions of the Cauchy problem defined by a certain class of partial differential equations (PDE) of parabolic type. The algorithm exploits the algebraic structure of the problem to transform the PDE into an ordinary matrix differential equation, which is then solved by Lie algebraic techniques.

Algebraic methods: Lie groups, quantum groups

These notes concentrate on the paradigm of spherical functions on Riemannian symmetric spaces. This paradigm has led to the notion of special functions associated with root systems. The first sections deal with older work on the interaction between spherical functions on rank one symmetric spaces and special functions (q=1) in one variable. The (spectacular) developments in the higher rank case...

Lie Algebraic Methods in Nonlinear Control

Lie algebraic method generalize matrix methods and algebraic rank conditions to smooth nonlinear systems. They capture the essence of noncommuting flows and give rise to noncommutative analogues of Taylor expansions. Lie algebraic rank conditions determine controllability, observability, and optimality. Lie algebraic methods are also employed for statespace realization, control design, and path...