A simple and efficient algorithm for nonlinear model predictive control

Abstract

We present PANOC, a new algorithm for solving optimal control problems arising in nonlinear model predictive control (NMPC). A usual approach to this type of problems is sequential quadratic programming (SQP), which requires the solution of a quadratic program at every iteration and, consequently, inner iterative procedures. As a result, when the problem is ill-conditioned or the prediction horizon is large, each outer iteration becomes computationally very expensive. We propose a line-search algorithm that combines forwardbackward iterations (FB) and Newton-type steps over the recently introduced forward-backward envelope (FBE), a continuous, real-valued, exact merit function for the original problem. The curvature information of Newton-type methods enables asymptotic superlinear rates under mild assumptions at the limit point, and the proposed algorithm is based on very simple operations: access to first-order information of the cost and dynamics and low-cost direct linear algebra. No inner iterative procedure nor Hessian evaluation is required, making our approach computationally simpler than SQP methods. The lowmemory requirements and simple implementation make our method particularly suited for embedded NMPC applications.

Microsecond nonlinear model predictive control for DC‐DC converters

“…The proposed NMPC problem is solved at every time step using PANOC, a recently introduced optimization algorithm. 23,26 This algorithm combines proximal gradient steps and limited memory BFGS steps to efficiently iterate towards an optimal solution. It can thus deal with an optimization problem consisting of an objective function and a set of easy to project upon constraints.…”

“…The simulator, which can be found in repository, 25 gives the possibility of MPC, PID control, and open-loop simulation of the two switch PWM DC-DC converters. The MPC controller relies on the PANOC algorithm developed in Stella et al, 26 tailored for NMPC problems. PANOC is implemented in the C programming language 23 using the CasADi package 27 for automatic differentiation.…”

Embedded nonlinear model predictive control for obstacle avoidance using PANOC

“…The resulting problems are solved using PANOC, a proximal averaged Newton-type method for optimal control, which was recently proposed in [16]. Gradients of the cost function can be efficiently computed using automatic differentiation toolboxes such as CasADi.…”

“…The gradient of function in (16) can be computed by means of the reverse mode of automatic differentiation (also known as adjoint method or backpropagation) as shown in Alg. 1 [20].…”

“…We employ the proximal averaged Newton-type method for optimal control, for short PANOC, which was recently proposed in [16]. PANOC performs fast Newton-type updates while an FBE-based linesearch endows it with global convergence properties while it uses the same oracle as the projected gradient method.…”