  Model predictive control (MPC) is an effective method for control of
constrained systems but is susceptible to the external disturbances and
modeling error often encountered in real-world applications. To address these
issues, techniques such as Tube MPC (TMPC) utilize an ancillary
offline-generated robust controller to ensure that the system remains within an
invariant set, referred to as a tube, around an online-generated trajectory.
However, TMPC is unable to modify its tube and ancillary controller in response
to changing state-dependent uncertainty, often resulting in overly-conservative
solutions. Dynamic Tube MPC (DTMPC) addresses these problems by simultaneously
optimizing the desired trajectory and tube geometry online. Building upon this
framework, Adaptive DTMPC (ADTMPC) produces better model approximations by
reducing model uncertainty, resulting in more accurate control policies. This
work presents an experimental analysis and performance evaluation of TMPC,
DTMPC, and ADTMPC for an uncertain nonlinear system. In particular, DTMPC is
shown to outperform TMPC because it is able to dynamically adjust to changing
environments, limiting aggressive control and conservative behavior to only the
cases when the constraints and uncertainty require it. Applied to a pendulum
testbed, this enables DTMPC to use up to 30% less control effort while
achieving up to 80% higher speeds. This performance is further improved by
ADTMPC, which reduces the feedback control effort by up to another 35%, while
delivering up to 34% better trajectory tracking. This analysis establishes that
the DTMPC and ADTMPC frameworks yield significantly more effective robust
control policies for systems with changing uncertainty, goals, and operating
conditions.
