Data driven stability analysis of black-box switched linear systems

Kenanian, Joris; Balkan, Ayça; Jungers, Raphaël M.; Tabuada, Paulo

doi:10.1016/j.automatica.2019.108533

Cited by 59 publications

(75 citation statements)

References 20 publications

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“…Once Algorithm 1 is stopped, the stability of the resulting controller can be checked by resorting to its nonminimal state-space representation. 28 Accordingly, the model-based approach proposed in 57 or the data-driven method presented in 58,59 can be exploited to study the stability of  ⋆ s . However, provided that only input/output data are available in closed-loop, to the best of the authors knowledge, no input/output criterion exists to check the stability of the closed-loop system once  ⋆ s has been learned.…”

Section: The Design Methodsmentioning

confidence: 99%

“…For the piecewise constant reference, the RMSE attained with the learned PWA controller is equal to 0.606. Instead, RMSE=0.614 is achieved with a single controller with the same structure described in (59), trained by running Step 1.1 with the same regularization parameters. When the sinusoidal reference is considered, the RMSEs attained with the PWA and LTI controllers are equal to 0.726 and 0.929, respectively.…”

Section: Numerical Example: Lti Reference Modelmentioning

confidence: 99%

“…Nonetheless, we still design  s so that it is composed by K c first-order linear local controllers with the structure in (59) for all i = 1, … , K c . Note that, since  s is forced to behave as a PWL system with partition induced by the conditions in (61c), the number of submodels cannot be easily fixed even if K is known.…”

Section: Numerical Example: Pwl Reference Modelmentioning

confidence: 99%

See 2 more Smart Citations

Direct data‐driven design of switching controllers

Breschi

Formentin

2019

Intl J Robust & Nonlinear

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Switching linear models can be used to represent the behavior of hybrid, time-varying, and nonlinear systems, while generally providing a satisfactory trade-off between accuracy and complexity. Although several control design techniques are available for such models, the effect of modeling errors on the closed-loop performance has not been formally evaluated yet. In this paper, a data-driven synthesis scheme is thus introduced to design optimal switching controllers directly from data, without needing a model of the plant. In particular, the theory will be developed for piecewise affine controllers, which have proven to be effective in many real-world engineering applications. The performance of the proposed approach is illustrated on some benchmark simulation case studies.

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Section: The Design Methodsmentioning

confidence: 99%

Section: Numerical Example: Lti Reference Modelmentioning

confidence: 99%

Section: Numerical Example: Pwl Reference Modelmentioning

confidence: 99%

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Direct data‐driven design of switching controllers

Breschi

Formentin

2019

Intl J Robust & Nonlinear

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“…The latter article proposes an identification method that uses mixed-integer programming to identify a piecewise linear model with a bound on the disturbance for formal synthesis. The works in [31] and [32] discuss data-driven stability analysis centered around Lyapunov functions but without any consideration for control synthesis. What is clear, in all of the abovementioned articles, however, is that system identification and control synthesis are undertaken separately, and the identified model is not necessarily "optimal" for control synthesis.…”

Section: A Background and Literature Reviewmentioning

confidence: 99%

Data-Driven Computation of Robust Control Invariant Sets With Concurrent Model Selection

Chen

Özay

2022

IEEE Trans. Contr. Syst. Technol.

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Set invariance in the presence of uncertainty and disturbance is of central importance for the safety of control systems. This article proposes a data-driven method to compute an approximation of a minimal robust control invariant set (mRCI) from experimental data. For a given dynamical model with additive and multiplicative uncertainty, the proposed method is able to compute a polytopic mRCI with fixed complexity via linear programming (LP). Moreover, the method can be combined with model selection to enable mRCI computation directly from experiment data when the system dynamics are unknown. Specifically, given a model structure, our algorithm begins by identifying the set of admissible models with constraints extracted from the experimental data. Each model in the set of admissible models contains information about the nominal model and the characterization of the model uncertainties. Then, two iterative algorithms based on robust optimization are proposed to compute an mRCI while simultaneously searching for a model "optimal" with regard to the mRCI computation and the corresponding invariance-inducing controller. Finally, the method is demonstrated in an experiment with an autonomous vehicle lane-keeping control example.

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“…The proposed approaches are based on data-driven methods and assume some knowledge on the system. Work [16,20] impose a strong assumption that the underlying system is linear. Then, they employ techniques such as Bayesian inference and chance-constrained optimization to provide probabilistic guarantees for the unknown system from a finite set of data.…”

Section: Introductionmentioning

confidence: 99%

Strategy synthesis for partially-known switched stochastic systems

Jackson

Laurenti

Frew

et al. 2021

Proceedings of the 24th International Conference on Hybrid Systems: Computation and Control

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We present a data-driven framework for strategy synthesis for partially-known switched stochastic systems. The properties of the system are specified using linear temporal logic (LTL) over finite traces (LTL f ), which is as expressive as LTL and enables interpretations over finite behaviors. The framework first learns the unknown dynamics via Gaussian process regression. Then, it builds a formal abstraction of the switched system in terms of an uncertain Markov model, namely an Interval Markov Decision Process (IMDP), by accounting for both the stochastic behavior of the system and the uncertainty in the learning step. Then, we synthesize a strategy on the resulting IMDP that maximizes the satisfaction probability of the LTL f specification and is robust against all the uncertainties in the abstraction. This strategy is then refined into a switching strategy for the original stochastic system. We show that this strategy is near-optimal and provide a bound on its distance (error) to the optimal strategy. We experimentally validate our framework on various case studies, including both linear and non-linear switched stochastic systems. CCS CONCEPTS• Theory of computation → Abstraction; Logic and verification; • Computing methodologies → Gaussian processes; • Mathematics of computing → Stochastic processes; • Computer systems organization → Robotic autonomy.

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Data driven stability analysis of black-box switched linear systems

Cited by 59 publications

References 20 publications

Direct data‐driven design of switching controllers

Direct data‐driven design of switching controllers

Data-Driven Computation of Robust Control Invariant Sets With Concurrent Model Selection

Strategy synthesis for partially-known switched stochastic systems

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