Slovakia

Stabilizing conditions for nonlinear predictive control typically rely on standard Lyapunov functions and thus require a monotonically decreasing cost function. These conditions cannot certify stability of predictive controllers in the presence of non-monotonic cost functions. In this paper we develop new dissipativity-based stabilizing conditions for nonlinear predictive control that allow for non-monotonic cost functions. Firstly, we establish that dissipation inequalities with a cyclically negative supply imply asymptotic stability. Secondly, we show that closed-loop trajectories generated by predictive control satisfy a fundamental dissipation inequality. This enables dissipativity-based stabilizing conditions that do not require a special terminal cost and apply to both model-based and data-driven predictive control algorithms.

Nonlinear Model Predictive Control Conference 2021

A Dissipativity-Based Framework for Analyzing Stability of Predictive Controllers

data-enabled predictive control

lyapunov functions

dissipation inequalities

nonlinear predictive control

nominal stability of predictive control

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.

technical paper

Trajectory planning with the consideration of obstacles is a classical task in

Mixed-Integer optimization-based planning for autonomous racing with obstacles and rewards

We propose the design of a nonlinear model predictive controller (NMPC) for the

Control of Fixed-Wing UAV Attitude and Speed Based on Embedded Nonlinear Model Predictive Control

We consider an input-constrained differential-drive robot with actuator dynamics.

On MPC without terminal conditions for dynamic non-holonomic robots

This paper highlights the benefits of a feedback linearization local controller and the associated terminal bound constraints (box-type inequalities) in an NMPC (Nonlinear Model Predictive Control) design for a multicopter system. We replace the standard invariant construction for the terminal region of the NMPC design with two sets: i) a $\delta$-invariant set (with $\delta$ the sampling time) which constrains the trajectories to re-enter it periodically, at pre-defined moments of time; ii) a constraint admissible safe set in which the trajectories lie in the remaining time instants. We show that this alternative construction verifies the recursive feasibility and asymptotic stability. Moreover, the additional degrees of freedom and simpler construction show advantages over similar NMPC designs with standard ellipsoidal terminal region.

Stabilizing a multicopter using an NMPC design with a relaxed terminal region

Brushless DC (BLDC) motor is the rst choice for lightweight electric vehicles

Nonlinear Model Predictive Control of BLDC Motor with State Estimation

We investigate the rendezvous problem for the

Aperiodic Communication for MPC in Autonomous Cooperative Landing

In this talk, we discuss an NMPC design using a finite-tail cost.

Stability and Performance in MPC Using a Finite-Tail Cost

The analysis of convergence and stability conditions for Non-linear Model Predictive

Towards Necessary and Sufficient Stability Conditions for NMPC

The stability analysis of NMPC schemes has seen significant progress in recent years, which includes schemes with and without terminal ingredients such as penalties and constraints. In the context of economic MPC, turnpike properties, which are closely related to dissipativity properties of the underlying optimal control problem, have enabled novel insights on stability conditions. In this talk, we show that turnpike properties naturally enable to bound the required stabilizing horizon length in MPC. The main idea is to define the turnpike with respect to a level-set of the terminal penalty. This way we derive a bound on the stabilizing horizon which guarantees that a terminal constraint is satisfied without being explicitly stated in the underlying optimal control problem. A numerical example indicates that if the terminal set is not too small, the horizon bound is not overly conservative.

First Results on Turnpike Bounds for Stabilizing Horizons in NMPC

Predictive functional control (PFC) is the simplest model-based algorithm, equipped with the attributes of a fully fledged predictive controller but at the cost and complexity threshold of a standard PID regulator. It has proven benefits in controlling stable SISO dynamic systems, but similarly to its competitor PID, it loses efficacy when a challenging application is introduced. In this paper, we present a modified PFC approach, especially tailored for open-loop unstable processes, using pre-stabilisation to efficiently control the undesirable dynamics at hand. This is essentially a two-stage design scheme with implications for PFC tuning and constraint handling. The proposal, nevertheless, is straightforward and intuitive, and provides improved closed-loop control in the presence of external perturbations against the standard PFC, and significantly better performance overall compared to the common PID algorithm, as demonstrated in a numerical case-study.

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Towards Necessary and Sufficient Stability Conditions for NMPC