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Small-scale Mixed-Integer Quadratic Programming (MIQP) problems often arise in embedded control and estimation applications. Driven by the need for algorithmic simplicity to target computing platforms with limited memory and computing…
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…
Hybrid model predictive control with both continuous and discrete variables is widely applicable to robotic control tasks, especially those involving contacts with the environment. Due to combinatorial complexity, the solving speed of…
Iteration limited model predictive control (MPC) can stabilize a feedback control system under sufficient conditions; this work explores combining a low iteration limit MPC with a high iteration limit MPC for mixed-integer quadratic…
This work solves suboptimal mixed-integer quadratic programs recursively for feedback control of dynamical systems. The proposed framework leverages parametric mixed-integer quadratic programming (MIQP) and hybrid systems theory to model a…
Mixed Integer Linear Programs (MILP) are well known to be NP-hard (Non-deterministic Polynomial-time hard) problems in general. Even though pure optimization-based methods, such as constraint generation, are guaranteed to provide an optimal…
Today's fast linear algebra and numerical optimization tools have pushed the frontier of model predictive control (MPC) forward, to the efficient control of highly nonlinear and hybrid systems. The field of hybrid MPC has demonstrated that…
The alternating-current unit commitment problem provides a realistic representation of power system operations, which is a nonconvex mixed-integer nonlinear programming problem and hence is computationally intractable. A common relaxation…
We propose a dual dynamic integer programming (DDIP) framework for solving multi-scale mixed-integer model predictive control (MPC) problems. Such problems arise in applications that involve long horizons and/or fine temporal…
Mixed Integer Linear Programming (MILP) can be considered the backbone of the modern power system optimization process, with a large application spectrum, from Unit Commitment and Optimal Transmission Switching to verifying Neural Networks…
This paper describes the computational challenge developed for a computational competition held in 2023 for the $20^{\textrm{th}}$ anniversary of the Mixed Integer Programming Workshop. The topic of this competition was reoptimization, also…
Maintaining instantaneous balance between electricity supply and demand is critical for reliability and grid instability. System operators achieve this through solving the task of Unit Commitment (UC),ca high dimensional large-scale…
This paper presents a method to certify the computational complexity of a standard Branch and Bound method for solving Mixed-Integer Quadratic Programming (MIQP) problems defined as instances of a multi-parametric MIQP. Beyond previous…
Mixed integer Model Predictive Control (MPC) problems arise in the operation of systems where discrete and continuous decisions must be taken simultaneously to compensate for disturbances. The efficient solution of mixed integer MPC…
Model Predictive Control (MPC) is widely used in robot control by optimizing a sequence of control outputs over a finite-horizon. Computational approaches for MPC include deterministic methods (e.g., iLQR and COBYLA), as well as…
Global optimization of decision trees is a long-standing challenge in combinatorial optimization, yet such models play an important role in interpretable machine learning. Although the problem has been investigated for several decades, only…
Mixed-integer quadratic programs (MIQPs) are a versatile way of formulating vehicle decision making and motion planning problems, where the prediction model is a hybrid dynamical system that involves both discrete and continuous decision…
We present a computationally tractable framework for real-time predictive control of multi-chiller plants that involve both discrete and continuous control decisions coupled through nonlinear dynamics, resulting in a mixed-integer optimal…
Model predictive control (MPC) is of increasing interest in applications for constrained control of multivariable systems. However, one of the major obstacles to its broader use is the computation time and effort required to solve a…
This work proposes an approach that integrates reinforcement learning and model predictive control (MPC) to solve finite-horizon optimal control problems in mixed-logical dynamical systems efficiently. Optimization-based control of such…