arXiv subjects

Sameer Pokhrel

Publications and source records attributed to Sameer Pokhrel.

4 recordsLinked to original sources

arXiv2023

Higher-order Lie bracket approximation and averaging of control-affine systems with application to extremum seeking

This paper provides a rigorous derivation for what is known in the literature as the Lie bracket approximation of control-affine systems in a more general and sequential framework for higher-orders. In fact, by using chronological calculus, we show that said Lie bracket approximations can be derived, and considered, as higher-order averaging terms. Hence, the theory provided in this paper unifies both averaging and approximation theories of control-affine systems. In particular, the Lie bracket approximation of order ($n$) turns out to be a higher-order averaging of order ($n+1$). The derivation and formulation provided in this paper can be directly reduced to the first and second-order Lie bracket approximations available in the literature. However, we do not need to make many of the assumptions that were needed/provided in the literature and show that they are in fact natural corollaries from our work. Moreover, we use our results to show that important and useful information about control-affine extremum seeking systems can be obtained and used for significant performance improvement, including a faster convergence rate influenced by higher-order derivatives. We provide multiple numerical simulations to demonstrate both the conceptual elements of this work as well as the significance of our results on extremum seeking with comparison against the literature.

math.OC↗

arXiv2023

Analyzing and Mimicking the Optimized Flight Physics of Soaring Birds: A Differential Geometric Control and Extremum Seeking System Approach with Real Time Implementation

For centuries, soaring birds -- such as albatrosses and eagles -- have been mysterious and intriguing for biologists, physicists, aeronautical/control engineers, and applied mathematicians. These fascinating biological organisms have the ability to fly for long-duration while spending little to no energy. This flight technique/maneuver is called dynamic soaring (DS). For biologists and physicists, the DS phenomenon is nothing but a wonder of the very elegant ability of the bird's interaction with nature and using its physical ether in an optimal way for better survival and energy efficiency. For the engineering community, it is a source of inspiration and an unequivocal promising chance for bio-mimicking. In literature, significant work has been done on modeling and constructing control systems that allow the DS maneuver to be mimicked. However, mathematical characterization of the DS phenomenon in literature has been limited to optimal control configurations that utilized developments in numerical optimization algorithms along with control methods to identify the optimal DS trajectory taken (or to be taken) by the bird/mimicking system. In this paper, we provide a novel two-layered mathematical approach to characterize, model, mimic, and control DS in a simple and real-time implementation. The first layer will be a differential geometric control formulation and analysis of the DS problem. The second layer will be a linkage between the DS philosophy and a class of dynamical control systems known as extremum seeking systems. We believe our framework captures more of the biological behavior of soaring birds and opens the door for geometric control theory and extremum seeking systems to be utilized in systems biology and natural phenomena. Simulation results are provided along with comparisons with powerful optimal control solvers to illustrate the advantages of the introduced method.

math.OC↗

arXiv2023

Control-Affine Extremum Seeking Control with Attenuating Oscillations: A Lie Bracket Estimation Approach

Control-affine Extremum Seeking Control (ESC) systems have been increasingly studied and applied in the last decade. In a recent effort, many control-affine ESC structures have been generalized in a unifying class and their stability was analyzed. However, guaranteeing vanishing oscillations at the extremum point for said class requires strong conditions that may not be feasible or easy to check/design by the user, especially when the gradient of the objective function is unknown. In this paper, we introduce a control-affine ESC structure that remedies this problem such that: (i) its oscillations attenuate structurally via a novel application of a geometric-based Kalman filter and a Lie bracket estimation approach; and (ii) its stability is characterized by a time-dependent (one-bound) condition that is easier to check and relaxed when compared to the generalized approach mentioned earlier. We provide numerical simulations of three problems to demonstrate the effectiveness of our proposed ESC; these problems cannot be solved with vanishing oscillations using the generalized approach in the literature.

math.OC↗

arXiv2023

A novel hypothesis for how albatrosses optimize their flight physics in real-time: an extremum seeking model and control for dynamic soaring

The albatross optimized flight maneuver -- known as dynamic soaring -- is nothing but a wonder of biology, physics, and engineering. By utilizing dynamic soaring, the bird can travel in the desired flight direction almost for free by harvesting energy from the wind. Dynamic soaring biological inspiration has triggered a momentous interest among many communities of science and engineering. Studying, modeling, and simulating dynamic soaring have been conducted in literature by mostly configuring dynamic soaring as an optimal control problem. Said configuration requires accurate dynamic system modeling of the albatross/mimicking-object, accurate wind profile models, and a defined mathematical formula of an objective function that aims at conserving energy and minimizing its dissipation. However, the experimental observations of albatrosses indicate their ability to conduct dynamic soaring in real time. Indeed, a functioning modeling and control framework for dynamic soaring that allows for a meaningful bio-mimicry of the albatross needs to be autonomous, real-time, stable, and capable of tolerating the absence of mathematical expressions of the wind profiles and the objective function, hypothetically similar to what the bird does. The qualifications of such modeling and control framework are the very same characteristics of the so-called extremum seeking systems. In this paper, we propose an extremum seeking modeling and control framework for the dynamic soaring problem. We provide and discuss the problem setup, design, and stability of the introduced framework. Our results, supported by simulations and comparison with optimal control methods of the literature, provide a proof of concept that the dynamic soaring phenomenon can be a natural expression of extremum seeking. Hence, dynamic soaring has the potential to be performed autonomously and in real-time with stability guarantees.

math.OC↗