Active-Set based Inexact Interior Point QP Solver for Model Predictive Control

Frey, Jonathan; Cairano, Stefano Di; Quirynen, Rien

doi:10.1016/j.ifacol.2020.12.067

Cited by 5 publications

(12 citation statements)

References 17 publications

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“…In the inexact Newton-type algorithm of ASIPM, 46 we solve the linearized KKT system in Equation ( 6) approximately by solving the following reduced block-tridiagonal linear system…”

Section: Active-set Based Inexact Newton Methodsmentioning

confidence: 99%

“…The optimization algorithm should be relatively simple to code with a moderate use of resources, while the software implementation is preferably compact and library independent. In the present paper, we will use a tailored active‐set based interior point method (ASIPM) that was presented in Reference 46 to solve the block‐sparse convex QP relaxations in the B&B method, resulting in an MIQP solver that will further be referred to as BB‐ASIPM. The recent work in Reference 47 showed how infeasibility detection and early termination based on duality can be implemented efficiently for an infeasible primal‐dual interior point method (IPM) based on a computationally efficient projection strategy that will be used within our BB‐ASIPM solver.…”

Section: Introductionmentioning

confidence: 99%

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Tailored presolve techniques in branch‐and‐bound method for fast mixed‐integer optimal control applications

Quirynen

Cairano

2023

Optim Control Appl Methods

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Mixed‐integer model predictive control (MI‐MPC) can be a powerful tool for controlling hybrid systems. In case of a linear‐quadratic objective in combination with linear or piecewise‐linear system dynamics and inequality constraints, MI‐MPC needs to solve a mixed‐integer quadratic program (MIQP) at each sampling time step. This paper presents a collection of exact block‐sparse presolve techniques to efficiently remove decision variables, and to remove or tighten inequality constraints, tailored to mixed‐integer optimal control problems. In addition, we describe a novel approach based on a heuristic presolve algorithm to compute a feasible but possibly suboptimal MIQP solution. We present benchmarking results for a C code implementation of the proposed BB‐ASIPM solver, including a branch‐and‐bound (B&B) method with the proposed tailored presolve techniques and an active‐set based interior point method (ASIPM), compared against multiple state‐of‐the‐art MIQP solvers on a case study of motion planning with obstacle avoidance constraints. Finally, we demonstrate the feasibility and computational performance of the BB‐ASIPM solver in embedded system on a dSPACE Scalexio real‐time rapid prototyping unit for a second case study of stabilization for an underactuated cart‐pole with soft contacts.

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“…In the inexact Newton-type algorithm of ASIPM, 46 we solve the linearized KKT system in Equation ( 6) approximately by solving the following reduced block-tridiagonal linear system…”

Section: Active-set Based Inexact Newton Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Tailored presolve techniques in branch‐and‐bound method for fast mixed‐integer optimal control applications

Quirynen

Cairano

2023

Optim Control Appl Methods

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“…A primal-dual interior point method (IPM) uses a Newtontype algorithm to solve a sequence of relaxed Karush-Kuhn-Tucker (KKT) conditions for the convex QP. We use the activeset based inexact Newton implementation of ASIPM [18], which exploits the block-sparse structure in the linear system, with improved numerical conditioning, reduced matrix factorization updates, warm starting, early termination and infeasibility detection [17]. If the convex QP relaxation…”

Section: Block-sparse Qp Solver For Convex Relaxationsmentioning

confidence: 99%

“…method with reliability branching and warm starting [16], block-sparse presolve techniques [13], early termination and infeasibility detection [17] within a fast convex QP solver [18].…”

Section: Embedded Miqp Solver For Mixed-integer Model Predictive Controlmentioning

confidence: 99%

“…Recent work [13] indicates that, by exploiting the particular structure of the MIOCPs, real-time solvers can achieve performance comparable to commercial tools, e.g., GUROBI [14] and MOSEK [15], especially for small to medium-scale problems. Therefore, we use the tailored BB-ASIPM solver [13], using a branch-and-bound (B&B) method with reliability branching and warm starting [16], block-sparse presolve techniques [13], early termination and infeasibility detection [17] within a fast convex quadratic programming (QP) solver based on an active-set interior point method (ASIPM) [18].…”

Section: Introductionmentioning

confidence: 99%

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Sequential Quadratic Programming Algorithm for Real-Time Mixed-Integer Nonlinear MPC

Quirynen

Cairano

2021

2021 60th IEEE Conference on Decision and Control (CDC)

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We develop a real-time feasible mixed-integer programming-based decision making (MIP-DM) system for automated driving. Using a linear vehicle model in a roadaligned coordinate frame, the lane change constraints, collision avoidance and traffic rules can be formulated as mixed-integer inequalities, resulting in a mixed-integer quadratic program (MIQP). The proposed MIP-DM simultaneously performs maneuver selection and trajectory generation by solving the MIQP at each sampling time instant. While solving MIQPs in real time has been considered intractable in the past, we show that our recently developed solver BB-ASIPM is capable of solving MIP-DM problems on embedded hardware in real time. The performance of this approach is illustrated in simulations in various scenarios including merging points and traffic intersections, and hardware-in-the-loop simulations on dSPACE Scalexio and MicroAutoBox-III. Finally, we present results from hardware experiments on small-scale automated vehicles.

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