Parametrized infinite-horizon model predictive control for linear time-invariant systems with input and state constraints

Basis functions design for the approximation of constrained linear quadratic regulator problems encountered in model predictive control

“…Proof The proof is taken from [2] and included for completeness. The following notation is introduced:…”

Application of an approximate model predictive control scheme on an unmanned aerial vehicle

“…Likewise, this paper proposes a continuous time approximation of the control and state trajectory, but over an infinite horizon, as proposed in [15] (see references therein). The quadratic programming solver routine is running purely onboard, on a STM32 Cortex M4 processor (168 MHz) with 192 KB RAM.…”

Approximation of continuous-time infinite-horizon optimal control problems arising in model predictive control

“…We analyze both with respect to convergence of the optimal costs as the number of basis functions is increased. In particular, the optimal cost of the approximation given in [5] decreases monotonically and approaches the cost of underlying infinite dimensional problem from above. It is shown that the corresponding optimal trajectories are guaranteed to converge and that the second approximation approaches the optimal cost of the infinite dimensional problem from below.…”

“…Herein, we compare the approach from [5] to a different finite dimensional approximation. We analyze both with respect to convergence of the optimal costs as the number of basis functions is increased.…”