arXiv subjects

Pavel Osinenko

Publications and source records attributed to Pavel Osinenko.

46 records · Page 3Linked to original sources

arXiv2021

A method of online traction parameter identification and mapping

Fuel consumption of heavy-duty vehicles such as tractors, bulldozers etc. is comparably high due to their scope of operation. The operation settings are usually fixed and not tuned to the environmental factors, such as ground conditions. Yet exactly the ground-to-propelling-unit properties are decisive in energy efficiency. Optimizing the latter would require a means of identifying those properties. This is the central matter of the current study. More specifically, the goal is to estimate the ground conditions from the available measurements, such as drive train signals, and to establish a map of those. The ground condition parameters are estimated using an adaptive unscented Kalman filter. A case study is provided with the actual and estimated ground condition maps. Such a mapping can be seen as a crucial milestone in optimal operation control of heavy-duty vehicles.

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arXiv2021

On inf-convolution-based robust practical stabilization under computational uncertainty

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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arXiv2020

Stacked adaptive dynamic programming with unknown system model

Adaptive dynamic programming is a collective term for a variety of approaches to infinite-horizon optimal control. Common to all approaches is approximation of the infinite-horizon cost function based on dynamic programming philosophy. Typically, they also require knowledge of a dynamical model of the system. In the current work, application of adaptive dynamic programming to a system whose dynamical model is unknown to the controller is addressed. In order to realize the control algorithm, a model of the system dynamics is estimated with a Kalman filter. A stacked control scheme to boost the controller performance is suggested. The functioning of the new approach was verified in simulation and compared to the baseline represented by gradient descent on the running cost.

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arXiv2020

Nonsmooth stabilization and its computational aspects

This work has the goal of briefly surveying some key stabilization techniques for general nonlinear systems, for which, as it is well known, a smooth control Lyapunov function may fail to exist. A general overview of the situation with smooth and nonsmooth stabilization is provided, followed by a concise summary of basic tools and techniques, including general stabilization, sliding-mode control and nonsmooth backstepping. Their presentation is accompanied with examples. The survey is concluded with some remarks on computational aspects related to determination of sampling times and control actions.

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arXiv2020

A reinforcement learning method with closed-loop stability guarantee

Reinforcement learning (RL) in the context of control systems offers wide possibilities of controller adaptation. Given an infinite-horizon cost function, the so-called critic of RL approximates it with a neural net and sends this information to the controller (called "actor"). However, the issue of closed-loop stability under an RL-method is still not fully addressed. Since the critic delivers merely an approximation to the value function of the corresponding infinite-horizon problem, no guarantee can be given in general as to whether the actor's actions stabilize the system. Different approaches to this issue exist. The current work offers a particular one, which, starting with a (not necessarily smooth) control Lyapunov function (CLF), derives an online RL-scheme in such a way that practical semi-global stability property of the closed-loop can be established. The approach logically continues the work of the authors on parameterized controllers and Lyapunov-like constraints for RL, whereas the CLF now appears merely in one of the constraints of the control scheme. The analysis of the closed-loop behavior is done in a sample-and-hold (SH) manner thus offering a certain insight into the digital realization. The case study with a non-holonomic integrator shows the capabilities of the derived method to optimize the given cost function compared to a nominal stabilizing controller.

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arXiv2020

Model predictive control with stage cost shaping inspired by reinforcement learning

This work presents a suboptimality study of a particular model predictive control with a stage cost shaping based on the ideas of reinforcement learning. The focus of the suboptimality study is to derive quantities relating the infinite-horizon cost function under the said variant of model predictive control to the respective infinite-horizon value function. The basis control scheme involves usual stabilizing constraints comprising of a terminal set and a terminal cost in the form of a local Lyapunov function. The stage cost is adapted using the principles of Q-learning, a particular approach to reinforcement learning. The work is concluded by case studies with two systems for wide ranges of initial conditions.

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arXiv2018

Analysis of extremum value theorems for function spaces in optimal control under numerical uncertainty

The extremum value theorem for function spaces plays the central role in optimal control. It is known that computation of optimal control actions and policies is often prone to numerical errors which may be related to computability issues. The current work addresses a version of the extremum value theorem for function spaces under explicit consideration of numerical uncertainties. It is shown that certain function spaces are bounded in a suitable sense i.e. they admit finite approximations up to an arbitrary precision. The proof of this fact is constructive in the sense that it explicitly builds the approximating functions. Consequently, existence of approximate extremal functions is shown. Applicability of the theorem is investigated for finite--horizon optimal control, dynamic programming and adaptive dynamic programming. Some possible computability issues of the extremum value theorem in optimal control are shown on counterexamples

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arXiv2018

Practical sample-and-hold stabilization of nonlinear systems under approximate optimizers

It is a known fact that not all controllable systems can be asymptotically stabilized by a continuous static feedback. Several approaches have been developed throughout the last decades, including time-varying, dynamical and even discontinuous feedbacks. In the latter case, the sample-and-hold framework is widely used, in which the control input is held constant during sampling periods. Consequently, only practical stability can be achieved at best. Existing approaches often require solving optimization problems for finding stabilizing control actions exactly. In practice, each optimization routine has a finite accuracy which might influence the state convergence. This work shows, what bounds on optimization accuracy are required to achieve prescribed stability margins. Simulation studies support the claim that optimization accuracy has high influence on the state convergence.

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arXiv2016

A note on Brehm's extension theorem

Brehm's extension theorem states that a non-expansive map on a finite subset of a Euclidean space can be extended to a piecewise-linear map on the entire space. In this note, it is verified that the proof of the theorem is constructive provided that the finite subset consists of points with rational coordinates. Additionally, the initial non-expansive map needs to send points with rational coordinates to points with rational coordinates. The two-dimensional case is considered.

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arXiv2016

A note on constructive treatment of eigenvectors

The eigenvalue problem plays a central role in linear algebra and its applications in control and optimization methods. In particular, many matrix decompositions rely upon computation of eigenvalue-eigenvector pairs, such as diagonal or Jordan normal forms. Unfortunately, numerical algorithms computing eigenvectors are prone to errors. Due to uncomputability of eigenpairs, perturbation theory and various regularization techniques only help if the matrix at hand possesses certain properties such as the absence of non-zero singular values, or the presence of a distinguishable gap between the large and small singular values. Posing such a requirement might be restrictive in some practical applications. In this note, we propose an alternative treatment of eigenvectors which is approximate and constructive. In comparison to classical eigenvectors whose computation is often prone to numerical instability, a constructive treatment allows addressing the computational uncertainty in a controlled way.

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