Stabilizing GNEP-Based Model Predictive Control: Quasi-GNEPs and End Constraints

We present a feedback scheme for non-cooperative dynamic games and investigate its stabilizing properties. The dynamic games are modeled as generalized Nash equilibrium problems (GNEP), in which the shared constraint consists of linear time-discrete dynamic equations (e.g., sampled from a partial or ordinary differential equation), which are jointly controlled by the players’ actions. Further, the … Read more

Sample Average Approximation and Model Predictive Control for Multistage Stochastic Optimization

Sample average approximation-based stochastic dynamic programming and model predictive control are two different methods of approaching multistage stochastic optimization. Model predictive control—despite a lack of theoretical backing—is often used instead of stochastic dynamic programming due to computational necessity. For settings where the stage reward is a convex function of the random terms, the stage dynamics … Read more

Optimization and Simulation for the Daily Operation of Renewable Energy Communities

Renewable Energy Communities (RECs) are an important building block for the decarbonization of the energy sector. The concept of RECs allows individual consumers to join together in local communities to generate, store, consume and sell renewable energy. A major benefit of this collective approach is a better match between supply and demand profiles, and thus, … Read more

Sample average approximation and model predictive control for inventory optimization

We study multistage stochastic optimization problems using sample average approximation (SAA) and model predictive control (MPC) as solution approaches. MPC is frequently employed when the size of the problem renders stochastic dynamic programming intractable, but it is unclear how this choice affects out-of-sample performance. To compare SAA and MPC out-of-sample, we formulate and solve an … Read more

Experimental operation of a solar-driven climate system with thermal energy storages using mixed-integer nonlinear MPC

This work presents the results of experimental operation of a solar-driven climate system using mixed-integer nonlinear Model Predictive Control (MPC). The system is installed in a university building and consists of two solar thermal collector fields, an adsorption cooling machine with different operation modes, a stratified hot water storage with multiple inlets and outlets as … Read more

Design, Implementation and Simulation of an MPC algorithm for Switched Nonlinear Systems under Combinatorial Constraints

Within this work, we present a warm-started algorithm for Model Predictive Control (MPC) of switched nonlinear systems under combinatorial constraints based on Combinatorial Integral Approximation (CIA). To facilitate high-speed solutions, we introduce a preprocessing step for complexity reduction of CIA problems, and include this approach within a new toolbox for solution of CIA problems with … Read more

Efficient Convex Optimization for Linear MPC

Model predictive control (MPC) formulations with linear dynamics and quadratic objectives can be solved efficiently by using a primal-dual interior-point framework, with complexity proportional to the length of the horizon. An alternative, which is more able to exploit the similarity of the problems that are solved at each decision point of linear MPC, is to … Read more

A Condensing Algorithm for Nonlinear MPC with a Quadratic Runtime in Horizon Length

A large number of practical algorithms for Optimal Control Problems (OCP) relies on a so-called condensing procedure to exploit the given structure in the quadratic programming (QP) subproblems. While the established structure-exploiting condensing algorithm is of cubic complexity in the horizon length, in this technical note we propose a novel algorithm that is only of … Read more

SQP Methods for Parametric Nonlinear Optimization

Sequential quadratic programming (SQP) methods are known to be effi- cient for solving a series of related nonlinear optimization problems because of desirable hot and warm start properties–a solution for one problem is a good estimate of the solution of the next. However, standard SQP solvers contain elements to enforce global convergence that can interfere … Read more

A Parallel Quadratic Programming Method for Dynamic Optimization Problems

Quadratic programming problems (QPs) that arise from dynamic optimization problems typically exhibit a very particular structure. We address the ubiquitous case where these QPs are strictly convex and propose a dual Newton strategy that exploits the block-bandedness similarly to an interior-point method. Still, the proposed method features warmstarting capabilities of active-set methods. We give details … Read more