Set-based control for disturbed piecewise affine systems with state and actuation constraints

Schürmann, Bastian; Vignali, Riccardo; Prandini, Maria; Althoff, Matthias

doi:10.1016/j.nahs.2019.100826

Cited by 12 publications

(3 citation statements)

References 78 publications

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“…The first zonotope containment approach transforms Z 2 from generator to halfspace representation [44], which is usually a computationally complex task [43]. According to [45],…”

Section: B Zonotope Containmentmentioning

confidence: 99%

Scalable Robust Safety Filter With Unknown Disturbance Set

Gruber

Althoff

2023

IEEE Trans. Automat. Contr.

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Equipping any controller with formal safety guarantees can be achieved by using safety filters. These filters modify the desired control input in the least restrictive way to guarantee safety. However, it is an unresolved issue to construct scalable safety filters without assuming the availability of the disturbance set. We address this issue by proposing an efficient approach to implementing safety filters. In particular, we perform offline set membership identification to obtain a linear model that is conformant to a finite set of training data. Based on this conformant model, we compute a set-based safe backup controller with a corresponding safe set. Because a new measurement obtained online might invalidate the model conformance, we update the model, the safe backup controller, and the safe set online to restore formal safety guarantees. We use scalable reachability analysis and convex optimization algorithms to perform these updates as quickly as possible. We demonstrate the usefulness and scalability of our safety filter approach using four numerical examples from the literature.

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“…The first zonotope containment approach transforms Z 2 from generator to halfspace representation [44], which is usually a computationally complex task [43]. According to [45],…”

Section: B Zonotope Containmentmentioning

confidence: 99%

Scalable Robust Safety Filter With Unknown Disturbance Set

Gruber

Althoff

2023

IEEE Trans. Automat. Contr.

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“…In this paper, we further develop the AG theory and computational approaches to enable AG design based on PWA models with both parametric and additive uncertainties. More specifically, this paper differentiates itself from our previous work in [33] and the work of [49] by considering both parametric and additive uncertainties in the PWA model, while [33] and [49] only consider additive disturbances. On the one hand, incorporating both parametric and additive uncertainties significantly enlarges the class of systems to which the RAG can be applied.…”

Section: Introductionmentioning

confidence: 99%

Robust Action Governor for Uncertain Piecewise Affine Systems with Non-convex Constraints and Safe Reinforcement Learning

Li¹,

Li²,

Tseng³

et al. 2022

Preprint

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The action governor is an add-on scheme to a nominal control loop that monitors and adjusts the control actions to enforce safety specifications expressed as pointwise-in-time state and control constraints. In this paper, we introduce the Robust Action Governor (RAG) for systems the dynamics of which can be represented using discrete-time Piecewise Affine (PWA) models with both parametric and additive uncertainties and subject to non-convex constraints. We develop the theoretical properties and computational approaches for the RAG. After that, we introduce the use of the RAG for realizing safe Reinforcement Learning (RL), i.e., ensuring all-time constraint satisfaction during online RL exploration-and-exploitation process. This development enables safe real-time evolution of the control policy and adaptation to changes in the operating environment and system parameters (due to aging, damage, etc.). We illustrate the effectiveness of the RAG in constraint enforcement and safe RL using the RAG by considering their applications to a soft-landing problem of a mass-spring-damper system.

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“…Genetic programming has been used for formal synthesis for reach-avoid problems in [28,29], in which controllers and Lyapunov-like functions are automatically synthesized for nonlinear and hybrid systems. Also, reachability analysis has been used in formal controller synthesis for reach-avoid problems, e.g., in [25], MPC is combined with reachability analysis, whereas in [30][31][32] synthesizes a sequence of optimal control inputs [32] or linear controllers [30,31] for a sequence of time intervals.…”

Section: Introductionmentioning

confidence: 99%

Formal synthesis of closed-form sampled-data controllers for nonlinear continuous-time systems under STL specifications

Verdier¹,

Kochdumper²,

Althoff³

et al. 2020

Preprint

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We propose a counterexample-guided inductive synthesis framework for the formal synthesis of closed-form sampled-data controllers for nonlinear systems to meet general STL specifications. Rather than stating the STL specification for a single initial condition, we consider an (infinite) set of initial conditions. Candidate solutions are proposed using genetic programming, which evolves controllers based on a finite number of simulations. Subsequently, the best candidate is verified using reachability analysis; if the candidate solution does not satisfy the specification, an initial condition violating the specification is extracted as a counterexample. Based on this counterexample, candidate solutions are refined until eventually a solution is found. The resulting sampled-data controller is expressed as a closed-form expression, enabling the implementation in embedded hardware with limited memory and computation power. The effectiveness of our approach is demonstrated for multiple systems.

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Set-based control for disturbed piecewise affine systems with state and actuation constraints

Cited by 12 publications

References 78 publications

Scalable Robust Safety Filter With Unknown Disturbance Set

Scalable Robust Safety Filter With Unknown Disturbance Set

Robust Action Governor for Uncertain Piecewise Affine Systems with Non-convex Constraints and Safe Reinforcement Learning

Formal synthesis of closed-form sampled-data controllers for nonlinear continuous-time systems under STL specifications

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