Fast Model Predictive Control Using Online Optimization

Abstract

Abstract-A widely recognized shortcoming of model predictive control (MPC) is that it can usually only be used in applications with slow dynamics, where the sample time is measured in seconds or minutes. A well-known technique for implementing fast MPC is to compute the entire control law offline, in which case the online controller can be implemented as a lookup table. This method works well for systems with small state and input dimensions (say, no more than five), few constraints, and short time horizons. In this paper, we describe a collection of methods for improving the speed of MPC, using online optimization. These custom methods, which exploit the particular structure of the MPC problem, can compute the control action on the order of 100 times faster than a method that uses a generic optimizer. As an example, our method computes the control actions for a problem with 12 states, 3 controls, and horizon of 30 time steps (which entails solving a quadratic program with 450 variables and 1284 constraints) in around 5 ms, allowing MPC to be carried out at 200 Hz.Index Terms-Model predictive control (MPC), real-time convex optimization.

On real-time robust model predictive control

“…However, the results on structure exploitation in MPC methods presented in the literature, e.g. Wang and Boyd (2010), Wright (1997), cannot be directly applied in the considered case, due to the fact that the Lyapunov constraint and the cost of the tracking formulation introduce coupling across the horizon and thereby significantly modify the structure of the resulting Newton system. There are two main options to exploit the new structure in the real-time problem:…”

“…Rao, Wright, and Rawling (1998), Wang and Boyd (2010), or the recent results in Domahidi et al (2012) that are tailored to MPC with quadratic constraints. The number of optimization variables can be reduced by employing a parametrization of the steady-state x s = M x θ , u s = M u θ, see Limon et al (2008) for more details.…”

“…Several methods have been proposed in recent years, demonstrating that the computation times can be pushed into a range where online optimization can be used for the control of high-speed systems (Ferreau, Bock, & Diehl, 2008;Wang & Boyd, 2010). Significant reduction of the computational complexity can be achieved by exploiting the particular structure and sparsity inherent in the MPC problem (Axehill & Hansson, 2008;Milman & Davison, 2008;Wang & Boyd, 2010;Wright, 1997). In a real-time environment, all available methods for fast online MPC resort to early termination, sacrificing guarantees on either feasibility or stability of the applied control action.…”

1-Bit processing based model predictive control for fractionated satellite missions

“…Wang and Boyd (2010) combined a series of existing iteration methods to increase the online optimization speed. In addition to the fast primal barrier interior point method, a warm-starting method can be used to reduce the number of Newton steps e.g.…”

Fighter Aircraft Maneuver Limiting Using MPC : Theory and Application

“…For a final implementation off-the-shelf software for solving the QP should not be used but instead tailor made software for fast solution of MPC problems such as, e.g., Wang and Boyd [2010] should be utilized. One could also consider approaches such as those found in Gibbens and Medagoda [2011], Richards et al [2009], Zavala andBiegler [2009] or Hartley et al [2012] to improve the realtime implementation.…”