Discrete-Time Inverse Optimal Control for Nonlinear Systems

Notations and Acronyms

NOTATIONS

∀	for all
∈	belonging to
⇒	implies
⊂	contained in
⊆	contained in or equal to
∪	union
∩	intersection
:=	equal by definition
λmin(Q)	the minimum eigenvalue of matrix Q
λmax(Q)	the maximum eigenvalue of matrix Q
P > 0	a positive definite matrix P
P ≥ 0	a positive semidefinite matrix P
ΔV	Lyapunov difference
≥	larger than or equal to
≤	less than or equal to
$\underset{\_}{\succ }$	larger than or equal to, component wise
$\underset{\_}{\prec }$	less than or equal to, component wise
$\mathcal{A}$	set or vector space
$\mathcal{K}$	a class $\mathcal{K}$ function
${\mathcal{K}}_{\infty }$	a class ${\mathcal{K}}_{\infty }$ function
$\mathcal{K}\mathcal{L}$	a class $\mathcal{K}\mathcal{L}$ function
ℕ	the set of all natural numbers
ℤ+	the set of nonnegative integers
ℝ	the set of all real numbers
ℝ+	the set of positive real numbers
ℝ