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Model Predictive Control (MPC) is a popular control approach due to its ability to consider constraints, including input and state restrictions, while minimizing a cost function. However, in practice, these constraints can result in…

Model predictive control (MPC) is an optimal control strategy where control input calculation is based on minimizing the predicted tracking error over a finite horizon that moves with time. This strategy has an advantage over conventional…

Mixed-integer model predictive control (MI-MPC) requires the solution of a mixed-integer quadratic program (MIQP) at each sampling instant under strict timing constraints, where part of the state and control variables can only assume a…

We tackle the problem of flying time-optimal trajectories through multiple waypoints with quadrotors. State-of-the-art solutions split the problem into a planning task - where a global, time-optimal trajectory is generated - and a control…

In this paper we propose a parallel coordinate descent algorithm for solving smooth convex optimization problems with separable constraints that may arise e.g. in distributed model predictive control (MPC) for linear network systems. Our…

Quadratic programming is a workhorse of modern nonlinear optimization, control, and data science. Although regularized methods offer convergence guarantees under minimal assumptions on the problem data, they can exhibit the slow…

Sampling-based Model Predictive Control (MPC) is a flexible control framework that can reason about non-smooth dynamics and cost functions. Recently, significant work has focused on the use of machine learning to improve the performance of…

Despite decades of research, existing navigation systems still face real-world challenges when deployed in the wild, e.g., in cluttered home environments or in human-occupied public spaces. To address this, we present a new class of…

Safety is one of the fundamental challenges in control theory. Recently, multi-step optimal control problems for discrete-time dynamical systems were formulated to enforce stability, while subject to input constraints as well as…

This tutorial consists of a brief introduction to the modern control approach called model predictive control (MPC) and its numerical implementation using MATLAB. We discuss the basic concepts and numerical implementation of the two major…

In this work we adapt a prediction-correction algorithm for continuous time-varying convex optimization problems to solve dynamic programs arising from Model Predictive Control. In particular, the prediction step tracks the evolution of the…

This article presents a sparse, low-memory footprint optimization algorithm for the implementation of the model predictive control (MPC) for tracking formulation in embedded systems. This MPC formulation has several advantages over standard…

The closed-loop performance of model predictive controllers (MPCs) is sensitive to the choice of prediction models, controller formulation, and tuning parameters. However, prediction models are typically optimized for prediction accuracy…

This article investigates synthetic model-predictive control (MPC) problems to demonstrate that an increased precision of the internal prediction model (PM) automatially entails an improvement of the controller as a whole. In contrast to…

This paper proposes a novel real-time affordable solution to the trajectory tracking control problem for self-driving cars subject to longitudinal and steering angular velocity constraints. To this end, we develop a dual-mode Model…

This article introduces a numerical algorithm that serves as a preliminary step toward solving continuous-time model predictive control (MPC) problems directly without explicit time-discretization. The chief ingredients of the underlying…

In hybrid Model Predictive Control (MPC), a Mixed-Integer Quadratic Program (MIQP) is solved at each sampling time to compute the optimal control action. Although these optimizations are generally very demanding, in MPC we expect…

Model predictive control (MPC) is a de facto standard control algorithm across the process industries. There remain, however, applications where MPC is impractical because an optimization problem is solved at each time step. We present a…

Equilibrium equations in the form of complementarity conditions often appear as constraints in optimization problems. Problems of this type are commonly referred to as mathematical programs with complementarity constraints (MPCCs). A…

This paper presents a time-optimal Model Predictive Control (MPC) scheme for linear discrete-time systems subject to multiplicative uncertainties represented by interval matrices. To render the uncertainty propagation computationally…