Practical Sample-and-Hold Stabilization of Nonlinear Systems Under Approximate Optimizers

Osinenko, Pavel; Beckenbach, Lukas; Streif, Stefan

doi:10.1109/lcsys.2018.2845130

Cited by 12 publications

(16 citation statements)

References 13 publications

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“…Remark 2. The first part in Assumption 2 contains a local homogeneity condition for all pointsỹ ∈Ỹ, i. e., V is globally lower Dini differentiable and the lim inf in (6) is locally uniform, as stated in [31]. The second part in Assumption 2 covers all points in Y, which do not satisfy (17).…”

Section: Robust Practical Stabilization Under Computational Uncementioning

confidence: 99%

“…and A ≤ 1 δ ∆t 2 L ff , whereq is bounded later. Under Lemma 1, equation (39), inequality (31) and the definition ofζ…”

Section: Part 3: Deriving Decay Along System Trajectoriesmentioning

confidence: 99%

“…This works starts with a nominal system under the InfC feedback κ in the SH mode. The transition from a system ẋ = f (x, κ(x)) to the one ẋ = f (x, κ(x)), where κ denotes the InfC feedback in the SH mode under non-exact computation, was addressed in [31]. The goal of this work is to fuse the result of [31] with robustness w. r. t. measurement noise and system disturbance, which is a challenging task.…”

Section: Introductionmentioning

confidence: 99%

“…The transition from a system ẋ = f (x, κ(x)) to the one ẋ = f (x, κ(x)), where κ denotes the InfC feedback in the SH mode under non-exact computation, was addressed in [31]. The goal of this work is to fuse the result of [31] with robustness w. r. t. measurement noise and system disturbance, which is a challenging task. Furthermore, the aim of the paper is a verified analysis of nonlinear systems extended by a measurement error and system disturbance.…”

Section: Introductionmentioning

confidence: 99%

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On Inf-Convolution-Based Robust Practical Stabilization Under Computational Uncertainty

Schmidt

Osinenko

Streif

2021

IEEE Trans. Automat. Contr.

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This work is concerned with practical stabilization of nonlinear systems by means of inf-convolution-based sample-and-hold control. It is a fairly general stabilization technique based on a generic non-smooth control Lyapunov function (CLF) and robust to actuator uncertainty, measurement noise, etc. The stabilization technique itself involves computation of descent directions of the CLF. It turns out that non-exact realization of this computation leads not just to a quantitative, but also qualitative obstruction in the sense that the result of the computation might fail to be a descent direction altogether and there is also no straightforward way to relate it to a descent direction. Disturbance, primarily measurement noise, complicate the described issue even more. This work suggests a modified inf-convolution-based control that is robust w. r. t. system and measurement noise, as well as computational uncertainty. The assumptions on the CLF are mild, as, e. g., any piece-wise smooth function, which often results from a numerical LF/CLF construction, satisfies them. A computational study with a three-wheel robot with dynamical steering and throttle under various tolerances w. r. t. computational uncertainty demonstrates the relevance of the addressed issue and the necessity of modifying the used stabilization technique. Similar analyses may be extended to other methods which involve optimization, such as Dini aiming or steepest descent.

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Section: Robust Practical Stabilization Under Computational Uncementioning

confidence: 99%

“…and A ≤ 1 δ ∆t 2 L ff , whereq is bounded later. Under Lemma 1, equation (39), inequality (31) and the definition ofζ…”

Section: Part 3: Deriving Decay Along System Trajectoriesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On Inf-Convolution-Based Robust Practical Stabilization Under Computational Uncertainty

Schmidt

Osinenko

Streif

2021

IEEE Trans. Automat. Contr.

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“…All these methods require performing optimization at each time step. In fact, a generalization of Theorem 1 for systems of the kind (sys-aug) applies also in the case when the said optimization is non-exact [24], [25]. A final comment should be made about the generator A.…”

Section: Generalizations and Applicationsmentioning

confidence: 99%

On stochastic stabilization of sampled systems

Osinenko¹

2021

Preprint

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Sample-and-hold refers to implementation of control policies in a digital mode, in which the dynamical system is treated continuous, whereas the control actions are held constant in predefined time steps. In such a setup, special attention should be paid to the sample-to-sample behavior of the involved Lyapunov function. This paper extends on the stochastic stability results specifically to address for the sampleand-hold mode. We show that if a Markov policy stabilizes the system in a suitable sense, then it also practically stabilizes it in the sample-and-hold sense. This establishes a bridge from an idealized continuous application of the policy to its digital implementation. The central results applies to dynamical systems described by stochastic differential equations driven by the standard Brownian motion. Some generalizations are discussed, including the case of non-smooth Lyapunov functions, given that the controls are bounded or, alternatively, the driving noise possesses bounded realizations. A brief overview of models of such processes is given.

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A stabilizing reinforcement learning approach for sampled systems with partially unknown models

Beckenbach,

Osinenko,

Streif

2024

Intl J Robust & Nonlinear

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Reinforcement learning is commonly associated with training of reward‐maximizing (or cost‐minimizing) agents, in other words, controllers. It can be applied in model‐free or model‐based fashion, using a priori or online collected system data to train involved parametric architectures. In general, online reinforcement learning does not guarantee closed loop stability unless special measures are taken, for instance, through learning constraints or tailored training rules. Particularly promising are hybrids of reinforcement learning with classical control approaches. In this work, we suggest a method to guarantee practical stability of the system‐controller closed loop in a purely online learning setting, in other words, without offline training. Moreover, we assume only partial knowledge of the system model. To achieve the claimed results, we employ techniques of classical adaptive control. The implementation of the overall control scheme is provided explicitly in a digital, sampled setting. That is, the controller receives the state of the system and computes the control action at discrete, specifically, equidistant moments in time. The method is tested in adaptive traction control and cruise control where it proved to significantly reduce the cost.

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Practical Sample-and-Hold Stabilization of Nonlinear Systems Under Approximate Optimizers

Cited by 12 publications

References 13 publications

On Inf-Convolution-Based Robust Practical Stabilization Under Computational Uncertainty

On Inf-Convolution-Based Robust Practical Stabilization Under Computational Uncertainty

On stochastic stabilization of sampled systems

A stabilizing reinforcement learning approach for sampled systems with partially unknown models

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