Slovakia

In this talk, we propose a suboptimal moving horizon estimator for nonlinear systems. For the stability analysis we transfer the “feasibility-implies-stability/robustness” paradigm from model predictive control to the context of moving horizon estimation in the following sense: Using a suitably defined, feasible candidate solution based on the trajectory of an auxiliary observer, robust stability of the proposed suboptimal estimator is inherited independently of the horizon length and even if no optimization is performed.

Nonlinear Model Predictive Control Conference 2021

Robust Stability of Suboptimal Moving Horizon Estimation Using an Observer-Based Candidate Solution

The IFAC Conference on Nonlinear Model Predictive Control (NMPC 2021) aims to bring together researchers interested in and work in the MPC field from both academia and industry. This allows us to reflect and establish the current state-of-the-art and focus on the future development of the MPC field towards relevant directions.

Model predictive control (MPC) is indisputably one of the advanced control techniques that have significantly affected control engineering practice with thousands of controllers implemented in various fields, spanning from the process industry to automotive and robotics. This is due to its unique ability to handle constraints, take preview information about disturbances and setpoint changes into account, and optimize performance. Furthermore, MPC allows the consideration of various types of dynamics, from linear to nonlinear, discrete to continuous, as well as an online adaptation of models and parameters. The research community on MPC is very active, with hundreds of papers published every year. Over the past decades, many theoretical, as well as implementation results, have been achieved.

### **All content presented at NMPC2021, including videos, papers and slides will be available only to registered (regular/student) participants. The content can be accessed until August 31st, 2021.**



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The IFAC Conference on Nonlinear Model Predictive Control (NMPC 2021) aims to bring together researchers interested in and work in the MPC field from both academia and industry. This allows us to reflect and establish the current state-of-the-art and focus on the future development of the MPC field towards relevant directions.

keynote

Recently, a regional MPC approach has been proposed that exploits the piecewise affine structure of the optimal solution (without computing the entire explicit solution before). Here, regional refers to the idea of using the affine feedback law that is optimal in a vicinity of the current state of operation, and therefore provides the optimal input signal without requiring to solve a QP. In the present paper, we apply the idea of regional MPC to min-max MPC problems. We show that the new robust approach can significantly reduce the number of QPs to be solved within min-max MPC resulting in a reduced overall computational effort. Moreover, we compare the performance of the new approach to an existing robust regional MPC approach using a numerical example with varying horizon. Finally, we provide a rule for choosing a suitable robust regional MPC approach based on the horizon.

Reducing the computational effort of min-max model predictive control with regional feedback laws

A new polynomial systems method is defined for the restricted structure nonlinear predictive controllers design. The control algorithm is established for a discrete-time nonlinear system, described in the polynomial matrix linear parameter varying form. The low-order restricted structure controller is parameterized in terms of discrete transfer operators set that the designer chooses multiplied by a set of optimized gains. The controller within the feedback loop can have a general linear parameter varying form or something as simple as a PI structure. The predictive control multi-step cost-index, which is minimized, comprises weighted error, control signal costing, and gain magnitude terms. A simulation of an automotive example is used to evaluate the nonlinear restricted structure controller performance.

Restricted Structure Polynomial Systems Approach to LPV Generalized Predictive Control

In this presentation, we present transient performance guarantees for recently developed, tube-based robust economic model predictive control (MPC) schemes. In particular, we consider both tube-based MPC schemes with and without terminal conditions. We show that the closed-loop performance obtained by applying such MPC schemes is approximately optimal when evaluated on finite time horizons. These performance bounds are similar to those derived previously for nominal economic MPC. The theoretical results are discussed in a numerical example.

Transient Performance of Tube-Based Robust Economic Model Predictive Control

Stochastic Model Predictive Control (MPC) has established itself as a simple method to approximate stochastically disturbed optimal control problems, yet it comes with significant computational effort. In particular, taking into account all information of stochastic disturbances—if at all possible—can be expensive. However, due to the continuous re- optimization, MPC schemes also have a certain inherent robustness. Hence, we ask the question, which part of the perturbation is absorbed by the MPC-inherent robustness, and which needs to be explicitly taken into account in the optimization.

Does the Effort of Monte Carlo Pay Off? a Case Study on Stochastic MPC

In this paper, we propose an efficient zero-order algorithm that can be used to compute an approximate solution to robust optimal control problems (OCP) and robustified nonconvex programs in general. In particular, we focus on robustified OCPs that make use of ellipsoidal uncertainty sets and show that, with the proposed zero-order method, we can efficiently obtain suboptimal, but robustly feasible solutions. The main idea lies in leveraging an inexact sequential quadratic programming (SQP) algorithm in which an advantageous sparsity structure is enforced. The obtained sparsity allows one to eliminate the variables associated

Zero-Order Robust Nonlinear Model Predictive Control with Ellipsoidal Uncertainty Sets

We consider the control of constrained, uncertain systems over wireless communication networks with varying capabilities. We focus on the case that a radio resource manager, which manages the wireless network, provides guaranteed minimum communication at fixed time instants while offering more frequent communication depending on the current load of the shared network, available network capacity or other conditions. To exploit the additionally available

Robust MPC for Networks with Varying Communication Capabilities

We present a feedback-optimizing model predictive

Feedback-Optimizing Model Predictive Control for Constrained Linear Systems

In this presentation, I cover the basic concepts used in our paper which enables real-time MPC for large scale system. To this end, the contraint selection/removal procedure is detailed and the requirements for recursive feasbility and constraint satisfaction are explained. Last, a simulation study is presented to visualize the ca-MPC scheme.

Constraint-Adaptive MPC for Large-Scale Systems: Satisfying State Constraints without Imposing Them

This talk presents recently developed methods for non-standard NMPC problems which cannot directly be formulated and solved in the form of smooth nonlinear programs (NLP).

NMPC with state dependent discontinuities, and homotopy based active set solution methods tailored to mathematical programs with complementarity constraints (MPCC). NMPC with state dependent jumps, and their reformulation to case 1) via “time freezing”. NMPC with discrete actuators, and a Gauss-Newton inspired heuristic. Throughout the talk, the focus will be on the exploitation of convex structure in these strongly non-convex problems The algorithms and methods will be illustrated by tutorial and some real-world examples.

The talk presents joint work with Armin Nurkanovic, Sebastian Albrecht, Jonas Hall, Florian Messerer, Sebastian Sager, Clemens Zeile, and Adrian Bürger.

Related Papers:
• [Time-Freezing for State Dependent Jumps](https://syscop.de/files/users/Moritz.diehl/Nurkanovic2021Freezing.pdf)

• [LCQP Algorithm for Quadratic Programs with Complementarity Contstraints](https://syscop.de/files/users/Moritz.diehl/Hall2022LCQP.pdf)

• [Survey of Sequential Convex Programming (SCP) and GGN](https://syscop.de/files/users/Moritz.diehl/Messerer2022-SCP-GGN.pdf)

• [Software pycombina for CIA MILP arising in MIOCP](https://cdn.syscop.de/publications/Buerger2020a.pdf)

Robust Stability of Suboptimal Moving Horizon Estimation Using an Observer-Based Candidate Solution

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