Florian A. Bayer

Discrete-time Incremental ISS: A framework for Robust NMPC

In this paper, Incremental Input-to-State Stability is studied as a system theoretic framework to address the challenges of robust nonlinear model predictive control. In the first part of the paper, a Lyapunov framework for Incremental Input-to-State Stability of nonlinear discrete-time dynamical systems is established. In the second part, Incremental Input-to-State Stability is shown to lead to an efficient MPC method for disturbed nonlinear systems. Based on the Incremental Input-to-State Stability Lyapunov function, a tightening of the constraints is proposed. Satisfaction of the tightened constraints can be guaranteed under the disturbances. By this concept, a robust nonlinear model predictive control problem is handled and the effectiveness is shown through an example from the literature.

Trajectory optimization for vehicles in a constrained environment

An approach for trajectory optimization for vehicles maneuvering in a constrained environment is developed. Within this framework, a benchmark problem, the minimimzation of the transit time of a point mass vehicle through a chicane is proposed. This problem is solved using the projection operator Newton method with barrier functions to manage the acceleration and roadwidth constraints. The numerical solution of the benchmark problem is analyzed in detail as is the characteristics of the solution itself.

Robust economic Model Predictive Control using stochastic information

In this paper, we develop a new tube-based robust economic MPC scheme for linear time-invariant systems subject to bounded disturbances with given distributions. By using the error distribution in the predictions of the finite horizon optimal control problem, we can incorporate stochastic information in order to improve the expected performance while being able to guarantee strict feasibility. For this new framework, we can provide bounds on the asymptotic average performance of the closed-loop system. Moreover, a constructive approach is presented in order to find an appropriate terminal cost leading to a slight degradation of the bound on the guaranteed average performance.

On State-Constrained Control of a CSTR*

Abstract In this note, we study the problem of multiple hard output constraints imposed on a continuous stirred tank reactor (CSTR) subject to external disturbances. Constraints on the concentration and on the temperature are considered. We show, analytically and with simulations, that there are critical combinations of constraints, where robust constraint satisfaction cannot be guaranteed. As a consequence violation of at least one constraint has to be allowed.

A projected SQP method for nonlinear optimal control with quadratic convergence

In this paper, we propose a discrete-time Sequential Quadratic Programming (SQP) algorithm for nonlinear optimal control problems. Using the idea by Hauser of projecting curves onto the trajectory space, the introduced algorithm has guaranteed recursive feasibility of the dynamic constraints. The second essential feature of the algorithm is a specific choice of the Lagrange multiplier update. Due to this ad hoc choice of the multiplier, the algorithm converges locally quadratically. Finally, we show how the proposed algorithm connects standard SQP methods for nonlinear optimal control with the Projection Operator Newton method by Hauser.

Constrained optimal motion planning for autonomous vehicles using PRONTO

This chapter provides an overview of the authors’ efforts in vehicle trajectory exploration and motion planning based on PRONTO , a numerical method for solving optimal control problems developed over the last two decades. The chapter reviews the basics of PRONTO, providing the appropriate references to get further details on the method. The applications of the method to the constrained optimal motion planning of single and multiple vehicles is presented. Interesting applications that have been tackled with this method include, e.g., computing minimum-time trajectories for a race car, exploiting the energy from the surrounding environment for long endurance missions of unmanned aerial vehicles (UAVs) , and cooperative motion planning of autonomous underwater vehicles (AUVs) for environmental surveying.

Final-state constrained optimal control via a projection operator approach

In this paper we develop a numerical method to solve nonlinear optimal control problems with final-state constraints. Specifically, we extend the PRojection Operator based Netwons method for Trajectory Optimization (PRONTO), which was proposed by Hauser for unconstrained optimal control problems. While in the standard method final-state constraints can be only approximately handled by means of a terminal penalty, in this work we propose a methodology to meet the constraints exactly. Moreover, our method guarantees recursive feasibility of the final-state constraint. This is an appealing property especially in realtime applications in which one would like to be able to stop the computation even if the desired tolerance has not been reached, but still satisfy the constraints. Following the same conceptual idea of PRONTO, the proposed strategy is based on two main steps which (differently from the standard scheme) preserve the feasibility of the final-state constraints: (i) solve a quadratic approximation of the nonlinear problem to find a descent direction, and (ii) get a (feasible) trajectory by means of a feedback law (which turns out to be a nonlinear projection operator). To find the (feasible) descent direction we take advantage of final-state constrained Linear Quadratic optimal control methods, while the second step is performed by suitably designing a constrained version of the trajectory tracking projection operator. The effectiveness of the proposed strategy is tested on the optimal state transfer of an inverted pendulum.

Min-max economic model predictive control approaches with guaranteed performance

In this paper, we present two approaches for min-max economic model predictive control (MPC). The first is based on the standard approach for robust min-max stabilizing MPC which is well known from literature and transferred to the case of non-definite cost functions. The second is based on ideas from robust tube-based MPC. In contrast to an exact prediction of the error, invariant error sets are considered in the optimization. While this setup is in general more conservative, it can lead to optimization problems which are computationally more appealing. We provide a priori bounds on the asymptotic average performance for both approaches and discuss and compare them in detail.

Robust economic model predictive control with linear average constraints

In this paper, we extend the idea of a tube-based economic MPC framework for linear systems by taking linear average constraints into account. Using a specifically defined integral stage cost, we can explicitly consider the influence of the disturbance. The satisfaction of the average constraints is guaranteed despite the disturbances acting on the system, and we show results on optimal steady-state operation. Moreover, we make use of two algorithmic approaches from tube-based MPC which provide differences in the closed-loop behavior and in the average performance.

Set-based Disturbance Attenuation in Economic Model Predictive Control

Abstract In this paper, we develop a tube-based economic MPC framework for nonlinear systems subject to unknown but bounded disturbances. We show that just transferring the design procedure of tube-based stabilizing MPC to an economic MPC framework might not be the optimal choice in terms of the achievable asymptotic average performance. Instead, the asymptotic average performance can possibly be improved by considering the influence of the disturbance explicitly within the design of the control input. This will be done by using a specifically defined integral stage cost, which is the key feature of our proposed robust economic MPC algorithm. Furthermore, we show that for this algorithm, similar results as in nominal economic MPC (i.e., without disturbances) can be established, in particular with respect to bounds on the asymptotic average performance of the resulting closed-loop system as well as stability.