VirtualArena package for the design of MPC controllers with closed-loop guarantees.
Consider the dynamical system
\dot{x}=f(t,x,u) (1)
and a control law k_aux : R x R^n -> R^n that stabilizes the origin exponentially quickly, with Lyapunov Certificated of exponential stability esLyapCertificate (see help ESLyapunovCertificate).
Moreover, let the stage cost function l: R x R^n x R^m -> R satisfies
l(t,x,k_aux(t,x))<= \sum_{i=1}^{length(a)} a(i) ||x||^i
for a vector a = [a1,a2,...,am]. Then, along the closed-loop (1) with u = k_aux (t,x), the function
m(t,x) = @(t,x) terminalCostES(t,x,esLyapCertificate,a)
satisfies
\dot{m}(t,x) <= -l(t,x, k_aux(t,x)).
Reference:
Alessandretti A., Aguiar P. A., Jones C.. "On Convergence and Performance Certification of a Continuous-Time Economic Model Predictive Control Scheme with Time-Varying Performance Index." Automatica (in Press), 2016.