arXiv subjects

Frank Allgöwer

Publications and source records attributed to Frank Allgöwer.

At least 163 records · Page 9Linked to original sources

arXiv2020

A computationally efficient robust model predictive control framework for uncertain nonlinear systems -- extended version

In this paper, we present a nonlinear robust model predictive control (MPC) framework for general (state and input dependent) disturbances. This approach uses an online constructed tube in order to tighten the nominal (state and input) constraints. To facilitate an efficient online implementation, the shape of the tube is based on an offline computed incremental Lyapunov function with a corresponding (nonlinear) incrementally stabilizing feedback. Crucially, the online optimization only implicitly includes these nonlinear functions in terms of scalar bounds, which enables an efficient implementation. Furthermore, to account for an efficient evaluation of the worst case disturbance, a simple function is constructed offline that upper bounds the possible disturbance realizations in a neighbourhood of a given point of the open-loop trajectory. The resulting MPC scheme ensures robust constraint satisfaction and practical asymptotic stability with a moderate increase in the online computational demand compared to a nominal MPC. We demonstrate the applicability of the proposed framework in comparison to state of the art robust MPC approaches with a nonlinear benchmark example. This paper is an extended version of [1], and contains further details and additional considers: continuous-time systems (App. A), more general nonlinear constraints (App. B) and special cases (Sec. IV).

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arXiv2020

Sampling Strategies for Data-Driven Inference of Input-Output System Properties

Due to their relevance in controller design, we consider the problem of determining the $\mathcal{L}^2$-gain, passivity properties and conic relations of an input-output system. While, in practice, the input-output relation is often undisclosed, input-output data tuples can be sampled by performing (numerical) experiments. Hence, we present sampling strategies for discrete time and continuous time linear time-invariant systems to iteratively determine the $\mathcal{L}^2$-gain, the shortage of passivity and the cone with minimal radius that the input-output relation is confined to. These sampling strategies are based on gradient dynamical systems and saddle point flows to solve the reformulated optimization problems, where the gradients can be evaluated from only input-output data samples. This leads us to evolution equations, whose convergence properties are then discussed in continuous time and discrete time.

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arXiv2020

Economic model predictive control for snake robot locomotion

In this work, the control of snake robot locomotion via economic model predictive control (MPC) is studied. Only very few examples of applications of MPC to snake robots exist and rigorous proofs for recursive feasibility and convergence are missing. We propose an economic MPC algorithm that maximizes the robot's forward velocity and integrates the choice of the gait pattern into the closed loop. We show recursive feasibility of the MPC optimization problem, where some of the developed techniques are also applicable for the analysis of a more general class of system. Besides, we provide performance results and illustrate the achieved performance by numerical simulations. We thereby show that the economic MPC algorithm outperforms a standard lateral undulation controller and achieves constraint satisfaction. Surprisingly, a gait pattern different to lateral undulation results from the optimization.

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arXiv2020

Stability Analysis for Nonlinear Weakly Hard Real-Time Control Systems

This paper considers the stability analysis for nonlinear sampled-data systems with failures in the feedback loop. The failures are caused by shared resources, and modeled by a weakly hard real-time (WHRT) dropout description. The WHRT dropout description restricts the considered dropout sequences with a non-probabilistic, window based constraint, that originates from schedulability analysis. The proposed approach is based on the emulation of a controller for the nonlinear sampled-data system from a continuous-time feedback. The emulation technique is extended and combined with non-monotonic Lyapunov functions and a graph description for the WHRT constraints to guarantee asymptotic stability. The effectiveness of the proposed approach is illustrated with a numerical example from literature. This paper is the accepted version of Hertneck et al. (2020), containing also proofs of the main results.

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arXiv2020

A Resource-Aware Approach to Self-Triggered Model Predictive Control: Extended Version

In this paper, we consider a self-triggered formulation of model predictive control. In this variant, the controller decides at the current sampling instant itself when the next sample should be taken and the optimization problem be solved anew. We incorporate a pointwise-in-time resource constraint into the optimization problem, whose exact form can be chosen by the user. Thereby, the proposed scheme is made resource-aware with respect to a universal resource, which may pertain in practice for instance to communication, computation, energy or financial resources. We show that by virtue of the pointwise-in-time constraints, also a transient and an asymptotic average constraint on the resource usage are guaranteed. Furthermore, we derive conditions on the resource under which the proposed scheme achieves recursive feasibility and convergence. Finally, we demonstrate our theoretical results in a numerical example.

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arXiv2020

Saving Tokens in Rollout Control with Token Bucket Specification

We consider a communication network over which transmissions must fulfill the so-called token bucket traffic specification, with a rollout (i.e., predictive) controller that both schedules transmissions and computes the corresponding control values. In the token bucket specification, a transmission is allowed if the current level of tokens is above a certain threshold. Recently, it has been shown that having a full bucket at the time of a set point change significantly improves the control performance as compared to when the bucket level is low. In this work, we develop mechanisms that guarantee that the bucket fills up after the controlled plant has converged to a set point. To do this, we consider two different setups. First, we consider that all transmissions over the network must fulfill the token bucket specification and show convergence to the upper sector of the bucket by adding a slight terminal cost on the bucket level. Afterwards, we consider a modified network which additionally features a direct link over which transmissions need not fulfill the token bucket specification. In this setup, we prove convergence of the bucket level exactly to the upper rim. These mechanisms enable a similar level of flexibility as event-triggered control: In converged state, little communication is used while in precarious operating conditions, a burst of transmissions is possible. Other than event-triggered approaches, the proposed methods allow to specify the network traffic beforehand by means of the token bucket. Lastly, we validate the proposed approaches in a numerical example.

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arXiv2020

Verifying dissipativity properties from noise-corrupted input-state data

There exists a vast amount of literature how dissipativity properties can be exploited to design controllers for stability and performance guarantees for the closed loop. With the rising availability of data, there has therefore been an increasing interest in determining dissipativity properties from data as a means for data-driven systems analysis and control with rigorous guarantees. Most existing approaches, however, consider dissipativity properties that hold only over a finite horizon and mostly only qualitative statements can be made in the presence of noisy data. In this work, we present a novel approach to determine dissipativity of linear time-invariant systems from data where we inherently consider properties that hold over the infinite horizon. Furthermore, we provide rigorous guarantees in the case of noisy state measurements.

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arXiv2020

Linear robust adaptive model predictive control: Computational complexity and conservatism -- extended version

In this paper, we present a robust adaptive model predictive control (MPC) scheme for linear systems subject to parametric uncertainty and additive disturbances. The proposed approach provides a computationally efficient formulation with theoretical guarantees (constraint satisfaction and stability), while allowing for reduced conservatism and improved performance due to online parameter adaptation. A moving window parameter set identification is used to compute a fixed complexity parameter set based on past data. Robust constraint satisfaction is achieved by using a computationally efficient tube based robust MPC method. The predicted cost function is based on a least mean squares point estimate, which ensures finite-gain $\mathcal{L}_2$ stability of the closed loop. The overall algorithm has a fixed (user specified) computational complexity. We illustrate the applicability of the approach and the trade-off between conservatism and computational complexity using a numerical example. This paper is an extended version of~[1], and contains additional details regarding the theoretical proof of Theorem~1, the numerical example, and the offline computations in Appendix~A--B.

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arXiv2020

A nonlinear model predictive control framework using reference generic terminal ingredients -- extended version

In this paper, we present a quasi infinite horizon nonlinear model predictive control (MPC) scheme for tracking of generic reference trajectories. This scheme is applicable to nonlinear systems, which are locally incrementally stabilizable. For such systems, we provide a reference generic offline procedure to compute an incrementally stabilizing feedback with a continuously parameterized quadratic quasi infinite horizon terminal cost. As a result we get a nonlinear reference tracking MPC scheme with a valid terminal cost for general reachable reference trajectories without increasing the online computational complexity. As a corollary, the terminal cost can also be used to design nonlinear MPC schemes that reliably operate under online changing conditions, including unreachable reference signals. The practicality of this approach is demonstrated with a benchmark example. This paper is an extended version of the accepted paper [1], and contains additional details regarding \textit{robust} trajectory tracking (App.~B), continuous-time dynamics (App.~C), output tracking stage costs (App.~D) and the connection to incremental system properties (App.~A).

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arXiv2020

Safe and Fast Tracking on a Robot Manipulator: Robust MPC and Neural Network Control

Fast feedback control and safety guarantees are essential in modern robotics. We present an approach that achieves both by combining novel robust model predictive control (MPC) with function approximation via (deep) neural networks (NNs). The result is a new approach for complex tasks with nonlinear, uncertain, and constrained dynamics as are common in robotics. Specifically, we leverage recent results in MPC research to propose a new robust setpoint tracking MPC algorithm, which achieves reliable and safe tracking of a dynamic setpoint while guaranteeing stability and constraint satisfaction. The presented robust MPC scheme constitutes a one-layer approach that unifies the often separated planning and control layers, by directly computing the control command based on a reference and possibly obstacle positions. As a separate contribution, we show how the computation time of the MPC can be drastically reduced by approximating the MPC law with a NN controller. The NN is trained and validated from offline samples of the MPC, yielding statistical guarantees, and used in lieu thereof at run time. Our experiments on a state-of-the-art robot manipulator are the first to show that both the proposed robust and approximate MPC schemes scale to real-world robotic systems.

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arXiv2020

Scheduling and control over networks using MPC with time-varying terminal ingredients: extended version

Rollout approaches are an effective tool to address the problem of co-designing the transmission schedule and the corresponding input values, when the controller is connected to the plant via a resource-constrained communication network. These approaches typically employ an MPC, activated at multiples of the period length of a base transmission schedule. Using multi-step invariant terminal regions and a prediction horizon longer than the base period, stability can be ensured. This strategy, however, suffers from intrinsic shortcomings, such as a high computational complexity and low robustness. We aim to resolve these drawbacks by proposing an MPC with periodically time-varying terminal region and cost for the rollout setup, where the controller is activated at each time instant and features an arbitrary but fixed prediction horizon. We consider in more detail two specific setups from the literature on Networked Control Systems, namely the token bucket network and actuator scheduling. For both setups, we provide conditions for which convergence under application of the time-varying MPC can be guaranteed. In two numerical examples, we demonstrate the benefits of the proposed method.

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arXiv2020

Determining optimal input-output properties: A data-driven approach

Due to their relevance in systems analysis and (robust) controller design, we consider the problem of determining control-theoretic system properties of an a priori unknown system from data only. More specifically, we introduce a necessary and sufficient condition for a discrete-time linear time-invariant system to satisfy a given integral quadratic constraint (IQC) over a finite time horizon using only one input-output trajectory of finite length. Furthermore, for certain classes of IQCs, we provide convex optimization problems in form of semidefinite programs (SDPs) to retrieve the optimal, i.e. the tightest, system property description that is satisfied by the unknown system. Finally, we provide bounds on the difference between finite and infinite horizon IQCs and illustrate the effectiveness of the proposed scheme in a variety of simulation studies including noisy measurements and a high dimensional system.

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arXiv2020

Model-Based Nonlinear Periodic Event-Triggered Control for Continuous-Time Systems with Sampled-Data Prediction

In this paper, we present a model-based periodic event-triggered control mechanism for nonlinear continuous-time Networked Control Systems. A sampled-data prediction of the system behavior is used at the actuator to reduce the amount of required communication while maintaining a user-defined performance level. This prediction is based on a possibly inaccurate discretization of the nonlinear system dynamics and can be implemented on simple hardware. Nevertheless, guarantees for asymptotic stability and a user-defined performance level are given for the periodic event-triggered control (PETC) mechanism, whilst the reduction of the required amount of transmissions of state information depends on the quality of the prediction. We discuss furthermore how the prediction can be implemented. The performance of the proposed PETC mechanism is illustrated with a numerical example. This paper is the accepted version of [1], containing also the proofs of the main results.

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arXiv2019

A Constraint-Tightening Approach to Nonlinear Stochastic Model Predictive Control for Systems under General Disturbances

This paper presents a nonlinear model predictive control strategy for stochastic systems with general (state and input dependent) disturbances subject to chance constraints. Our approach uses an online computed stochastic tube to ensure stability, constraint satisfaction and recursive feasibility in the presence of stochastic uncertainties. The shape of the tube and the constraint backoff is based on an offline computed incremental Lyapunov function.

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arXiv2019

Nonlinear Dynamic Periodic Event-Triggered Control with Robustness to Packet Loss Based on Non-Monotonic Lyapunov Functions

This paper considers the stabilization of nonlinear continuous-time dynamical systems employing periodic event-triggered control (PETC). Assuming knowledge of a stabilizing feedback law for the continuous-time system with a certain convergence rate, a dynamic, state dependent PETC mechanism is designed. The proposed mechanism guarantees on average the same worst case convergence behavior except for tunable deviations. Furthermore, a new approach to determine the sampling period for the proposed PETC mechanism is presented. This approach as well as the actual trigger rule exploit the theory of non-monotonic Lyapunov functions. An additional feature of the proposed PETC mechanism is the possibility to integrate knowledge about packet losses in the PETC design. The proposed PETC mechanism is illustrated with a nonlinear numerical example from literature. This paper is the accepted version of [1], containing also the proofs of the main results.

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arXiv2019

Economic MPC using a Cyclic Horizon with Application to Networked Control Systems

In this paper, we analyze an economic model predictive control scheme with terminal region and cost, where the system is optimally operated in a certain subset of the state space. The predictive controller operates with a cyclic horizon, which means that starting from an initial length, the horizon is reduced by one at each time step before it is restored to its maximum length again after one cycle. We give performance guarantees for the closed loop, and under a suitable dissipativity condition, establish convergence to the optimal subset. Moreover, we present conditions under which asymptotic stability of the optimal subset can be guaranteed. The results are illustrated in a practical example from the context of Networked Control Systems, which initially motivated the development of the theory presented in this paper.

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arXiv2018

Learning an Approximate Model Predictive Controller with Guarantees

A supervised learning framework is proposed to approximate a model predictive controller (MPC) with reduced computational complexity and guarantees on stability and constraint satisfaction. The framework can be used for a wide class of nonlinear systems. Any standard supervised learning technique (e.g. neural networks) can be employed to approximate the MPC from samples. In order to obtain closed-loop guarantees for the learned MPC, a robust MPC design is combined with statistical learning bounds. The MPC design ensures robustness to inaccurate inputs within given bounds, and Hoeffding's Inequality is used to validate that the learned MPC satisfies these bounds with high confidence. The result is a closed-loop statistical guarantee on stability and constraint satisfaction for the learned MPC. The proposed learning-based MPC framework is illustrated on a nonlinear benchmark problem, for which we learn a neural network controller with guarantees.

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arXiv2017

Iterative Learning and Extremum Seeking for Repetitive Time-Varying Mappings

In this paper, we develop an extremum seeking control method integrated with iterative learning control to track a time-varying optimizer within finite time. The behavior of the extremum seeking system is analyzed via an approximating system - the modified Lie bracket system. The modified Lie bracket system is essentially an online integral-type iterative learning control law. The paper contributes to two fields, namely, iterative learning control and extremum seeking. First, an online integral type iterative learning control with a forgetting factor is proposed. Its convergence is analyzed via $k$-dependent (iteration- dependent) contraction mapping in a Banach space equipped with $λ$-norm. Second, the iterative learning extremum seeking system can be regarded as an iterative learning control with "control input disturbance." The tracking error of its modified Lie bracket system can be shown uniformly bounded in terms of iterations by selecting a sufficiently large frequency. Furthermore, it is shown that the tracking error will finally converge to a set, which is a $λ$-norm ball. Its center is the same with the limit solution of its corresponding "disturbance-free" system (the iterative learning control law); and its radius can be controlled by the frequency.

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