Aroc

Kochdumper, Niklas; Gruber, Felix; Schürmann, Bastian; Gaßmann, Victor; Klischat, Moritz; Althoff, Matthias

doi:10.1145/3447928.3456703

Cited by 10 publications

(5 citation statements)

References 43 publications

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“…To account for these, one could integrate interval arithmetic as done in [74]. Our proposed algorithm will be implemented in the next release of the automated reachset optimal control (AROC) toolbox 5 [75].…”

Section: Methodsmentioning

confidence: 99%

Polynomial Controller Synthesis of Nonlinear Systems With Continuous State Feedback Using Trust Regions

Gaßmann¹,

Althoff²

2023

IEEE Open J. Control. Syst.

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We present a novel, correct-by-construction control approach for disturbed, nonlinear systems with continuous state feedback under state and input constraints. For the first time, we jointly synthesize a feedforward and feedback controller by solving a single non-convex, continuously differentiable approximation of the original synthesis problem, which we combine with a trust-region approach in an iterative manner to obtain non-conservative results. We ensure the formal correctness of our algorithm through reachability analysis and show that its computational complexity is polynomial in the state dimension for each trust-region iteration. In contrast to previous work, we also avoid the introduction of several algorithm parameters that require expert knowledge to tune, making the proposed synthesis approach easier to use for non-experts while guaranteeing state and input constraint satisfaction. Numerical benchmarks demonstrate the applicability of our novel synthesis approach.INDEX TERMS Correct-by-construction controller synthesis, reachability analysis, trust regions, optimization.

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Section: Methodsmentioning

confidence: 99%

Polynomial Controller Synthesis of Nonlinear Systems With Continuous State Feedback Using Trust Regions

Gaßmann¹,

Althoff²

2023

IEEE Open J. Control. Syst.

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“…Our implementation and the benchmark systems alongside all parameters will be made publicly available with the next release of the AROC 1 toolbox [71]. For reachability analysis, we use our open-source toolbox CORA [72].…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…To obtain a better impression of the scalability of our approach, we consider a chain of n mass nonlinear mass-springdamper systems, where we increased n mass from one (n x = 2) to ten (n x = 20). The dynamics of the j−th mass are governed by the set of differential equations (based on the cart system from [71])…”

Section: A Computation Timesmentioning

confidence: 99%

Scalable Computation of Robust Control Invariant Sets of Nonlinear Systems

Schäfer

Gruber

Althoff

2024

IEEE Trans. Automat. Contr.

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Ensuring robust constraint satisfaction for an infinite time horizon is a challenging, yet crucial task when deploying safety-critical systems. We address this issue by synthesizing robust control invariant sets for perturbed nonlinear sampled-data systems. This task can be encoded as a nonconvex program for which we propose a tailored, computationally efficient successive convexification algorithm. Based on the zonotopic representation of invariant sets, we obtain an updated candidate for the invariant set and the safety-preserving controller by solving a single convex program. To obtain a possibly large region of safe operation, our algorithm is designed so that the sequence of candidate invariant sets has monotonically increasing volume. We demonstrate the efficacy and scalability of our approach by applying it to a broad range of nonlinear control systems from the literature with up to 20 dimensions.

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“…To ensure that the model ( 10) encloses all possible behaviors of the real system, we performed conformance checking using the AROC toolbox [49] to determine the process noise as without safety shield with safety shield To incorporate the size of the car, we use the output function in ( 6) with length 0.51 m and width 0.31 m.…”

Section: A F1tenth Racecarmentioning

confidence: 99%

Provably Safe Reinforcement Learning via Action Projection Using Reachability Analysis and Polynomial Zonotopes

Kochdumper

Krasowski

Wang

et al. 2023

IEEE Open J. Control. Syst.

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While reinforcement learning produces very promising results for many applications, its main disadvantage is the lack of safety guarantees, which prevents its use in safety-critical systems. In this work, we address this issue by a safety shield for nonlinear continuous systems that solve reach-avoid tasks. Our safety shield prevents applying potentially unsafe actions from a reinforcement learning agent by projecting the proposed action to the closest safe action. This approach is called action projection and is implemented via mixed-integer optimization. The safety constraints for action projection are obtained by applying parameterized reachability analysis using polynomial zonotopes, which enables to accurately capture the nonlinear effects of the actions on the system. In contrast to other state-of-the-art approaches for action projection, our safety shield can efficiently handle input constraints and dynamic obstacles, eases incorporation of the spatial robot dimensions into the safety constraints, guarantees robust safety despite process noise and measurement errors, and is well suited for high-dimensional systems, as we demonstrate on several challenging benchmark systems.

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Aroc

Cited by 10 publications

References 43 publications

Polynomial Controller Synthesis of Nonlinear Systems With Continuous State Feedback Using Trust Regions

Polynomial Controller Synthesis of Nonlinear Systems With Continuous State Feedback Using Trust Regions

Scalable Computation of Robust Control Invariant Sets of Nonlinear Systems

Provably Safe Reinforcement Learning via Action Projection Using Reachability Analysis and Polynomial Zonotopes

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