Model Predictive Control

Contents xi
Set Operators and Functions
∅ The empty set
|P| The cardinality of P, i.e., the number of elements in P
P ∩ Q Set intersection P ∩ Q = {x : x ∈ P and x ∈ Q}
P ∪ Q
r∈{1,...,R}
Set union P ∪ Q = {x : x ∈ P or x ∈ Q}
Pr Union of R sets Pr, i.e.
r∈{1,...,R} Pr
P
= {x : x ∈ P0 or . . . or x ∈ PR}
c Complement of the set P, Pc = {x : x /∈ P}
P \ Q Set difference P \ Q = {x : x ∈ P and x /∈ Q}
P ⊆ Q The set P is a subset of Q, x ∈ P ⇒ x ∈ Q
P ⊂ Q The set P is a strict subset of Q, x ∈ P ⇒ x ∈ Q and ∃x ∈ (Q \ P)
P ⊇ Q The set P is a superset of Q
P ⊃ Q The set P is a strict superset of Q
P ⊖ Q Pontryagin difference P ⊖ Q = {x : x + q ∈ P, ∀q ∈ Q}
P ⊕ Q Minkowski sum P ⊕ Q = {x + q : x ∈ P, q ∈ Q}
∂P The boundary of P
int(P) The interior of P, i.e. int(P) = P \ ∂P
f(x) with abuse of notation denotes the value of the function f in x or the function f, f : x → f(x). T
: “such that”
Acronyms
ARE Algebraic Riccati Equation
BMI Bilinear Matrix Inequality
CLQR Constrained Linear Quadratic Regulator
CFTOC Constrained Finite Time Optimal Control
CITOC Constrained Infinite Time Optimal Control
DP Dynamic Program(ming)
LMI Linear Matrix Inequality
LP Linear Program(ming)
LQR Linear Quadratic Regulator
LTI Linear Time Invariant
MILP Mixed Integer Linear Program
MIQP Mixed Integer Quadratic Program
MPC Model Predictive Control
mp-LP multi-parametric Linear Program
mp-QP multi-parametric Quadratic Program
PWA Piecewise Affine (See Definition 3.7)
PPWA Piecewise Affine on Polyhedra (See Definition 3.8)
PWP Piecewise Polynomial
PWQ Piecewise Quadratic
QP Quadratic Program(ming)
RHC Receding Horizon Control
rhs right-hand side
SDP Semi Definite Program(ming)