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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…
We investigate finite-dimensional constrained structured optimization problems, featuring composite objective functions and set-membership constraints. Offering an expressive yet simple language, this problem class provides a modeling…
Binary optimization is a central problem in mathematical optimization and its applications are abundant. To solve this problem, we propose a new class of continuous optimization techniques which is based on Mathematical Programming with…
We propose a method of bi-coordinate variations for non-stationary and non-smooth optimization problems, which involve a single linear equality and box constraints. Here only approximation sequences are known instead of exact values of the…
The min-knapsack problem with compactness constraints extends the classical knapsack problem, in the case of ordered items, by introducing a restriction ensuring that they cannot be too far apart. This problem has applications in…
We present necessary and sufficient optimality conditions for finite time optimal control problems for a class of hybrid systems described by linear complementarity models. Although these optimal control problems are difficult in general…
Optimal control for switch-based dynamical systems is a challenging problem in the process control literature. In this study, we model these systems as hybrid dynamical systems with finite number of unknown switching points and reformulate…
Linear Model Predictive Control (MPC) has been successfully used for generating feasible walking motions for humanoid robots. However, the effect of uncertainties on constraints satisfaction has only been studied using Robust MPC (RMPC)…
Model Predictive Control (MPC) for tracking formulation presents numerous advantages compared to standard MPC, such as a larger domain of attraction and recursive feasibility even when abrupt changes in the reference are produced. As a…
In this paper, we study a class of optimization problems, called Mathematical Programs with Cardinality Constraints (MPCaC). This kind of problem is generally difficult to deal with, because it involves a constraint that is not continuous…
This paper proposes a new sampling-based nonlinear model predictive control (MPC) algorithm, with a bound on complexity quadratic in the prediction horizon N and linear in the number of samples. The idea of the proposed algorithm is to use…
In this paper we propose an Approximate Weak stationarity ($AW$-stationarity) concept designed to deal with {\em Mathematical Programs with Cardinality Constraints} (MPCaC), and we proved that it is a legitimate optimality condition…
Computing the receding horizon optimal control of nonlinear hybrid systems is typically prohibitively slow, limiting real-time implementation. To address this challenge, we propose a layered Model Predictive Control (MPC) architecture for…
A system of N points, each having mass m, and a central mass M forming a planar central configuration, is considered. The equations of motion of a test particle are given and compared using different coordinates. For large values of N, even…
Reducing the computation time of model predictive control (MPC) is important, especially for systems constrained by many state constraints. In this paper, we propose a new online constraint removal framework for linear systems, for which we…
Mathematical programs with disjunctive constraints (MPDCs for short) cover several different problem classes from nonlinear optimization including complementarity-, vanishing-, cardinality-, and switching-constrained optimization problems.…
A common problem affecting neural network (NN) approximations of model predictive control (MPC) policies is the lack of analytical tools to assess the stability of the closed-loop system under the action of the NN-based controller. We…
Coordinate descent algorithms are widely used in machine learning and large-scale data analysis due to their strong optimality guarantees and impressive empirical performance in solving non-convex problems. In this work, we introduce Block…
The Model Predictive Control (MPC) scheme Funnel MPC enables output tracking of smooth reference signals with prescribed error bounds for nonlinear multi-input multi-output systems with stable internal dynamics. Earlier works achieved the…
Efficient methods to provide sub-optimal solutions to non-convex optimization problems with knowledge of the solution's sub-optimality would facilitate the widespread application of nonlinear optimal control algorithms. To that end,…