Affine Control Research Articles

Surrogate Formulation for Chance-Constrained DC Optimal Power Flow With Affine Control Policy

Surrogate Formulation for Chance-Constrained DC Optimal Power Flow With Affine Control Policy

Enhancing ZnO/Si Heterojunction Solar Cells: A Combined Experimental And Simulation Approach

In this study, we explore the fabrication and optimization of ZnO/Si heterojunction solar cells to enhance their performance through precise control of electron affinity and bandgap properties. ZnO thin films were synthesized using thermal oxidation in a high-vacuum chamber, followed by annealing to improve crystallinity and electrical characteristics. The photovoltaic performance of the ZnO/Si heterojunction solar cells was systematically characterized, and Quantum ESPRESSO simulations were employed to refine the electronic properties of ZnO. Our results show significant improvements in open-circuit voltage, short-circuit current density, and overall conversion efficiency. The optimization of ZnO/Si heterojunction solar cells involves enhancing the electronic properties of ZnO thin films. Quantum ESPRESSO simulations were utilized to optimize the ZnO structure, calculate the band structure and density of states (DOS), and study the effects of Ga and Mg doping on the electronic properties of ZnO. The initial step in our study involved the structural optimization of ZnO to determine its lowest energy configuration. The optimization of the band offset engineering to improve the efficiency of n-ZnO/p-Si photovoltaic cells was found to be critical. Doping ZnO with Ga and Mg improved the band alignment with Si, reduced recombination losses, and enhanced charge carrier mobility. Our findings underscore the potential of optimized ZnO/Si heterojunction solar cells for high-efficiency solar energy conversion, demonstrating their viability as cost-effective and efficient solutions for renewable energy applications. This study highlights the importance of precise material engineering and simulation-driven optimization in developing advanced photovoltaic devices.

Chemosensitive Properties of Electrochemically Synthesized Poly-3-Thienylboronic Acid: Conductometric Detection of Glucose and Other Diol-Containing Compounds under Electrical Affinity Control.

Due to the presence of the boronic acid moieties, poly-3-thienylboronic acid has an affinity for saccharides and other diol-containing compounds. Thin films of this novel chemosensitive polymer were synthesized electrochemically on the gold surface. The adhesion of the polymer was enhanced by the deposition of a monomolecular layer of thiophenol. The technology was used to fabricate conductometric sensors for glucose and other diol-containing compounds. Simultaneous two- and four-electrode conductivity measurements were performed. The chemical sensitivity to sorbitol, fructose, glucose, and ethylene glycol was studied at different pH and electrode potentials, and the corresponding binding constants were obtained. Depending on the electrode potential, the reciprocal values of the binding constants of glucose to poly-3-thienylboronic acid at neutral pH are in the range of 0.2 mM-1.0 mM. The affinity for glucose has been studied in buffer solutions and in solutions containing the major components of human blood. It was shown that the presence of human serum albumin increases the affinity of poly-3-thienylboronic acid for diol-containing compounds.

Approximation of Chattering Arcs in Optimal Control Problems Governed by Mono-Input Affine Control Systems

Approximation of Chattering Arcs in Optimal Control Problems Governed by Mono-Input Affine Control Systems

Tracking optimal feedback control under uncertain parameters

Optimal control problems of tracking type for a class of linear systems with uncertain parameters in the dynamics are investigated. An affine tracking feedback control input is obtained by considering the minimization of an energy-like functional depending on a finite ensemble of training/sample parameters. It is computed from the solution of an associated differential Riccati equation. Simulations are presented showing the tracking performance of the computed input for trained as well as untrained parameters.

Global Stabilization of a Bounded Controlled Lorenz System

In this work, we present a method for the Global Asymptotic Stabilization (GAS) of an affine control chaotic Lorenz system, via admissible (bounded and regular) feedback controls, where the control bounds are given by a class of (convex) polytopes. The proposed control design method is based on the control Lyapunov function (CLF) theory introduced in [Artstein, 1983; Sontag, 1998]. Hence, we first recall, with parameters including those in [Lorenz, 1963], that these equations are point-dissipative, i.e. there is an explicit absorbing ball [Formula: see text] given by the level set of a certain Lyapunov function, [Formula: see text]. However, since the minimum point of [Formula: see text] does not coincide with any rest point of Lorenz system, we apply a modified solution to the “uniting CLF problem” (to unify local (possibly optimal) controls with global ones, proposed in [Andrieu & Prieur, 2010]) in order to obtain a CLF [Formula: see text] for the affine system with minimum at a desired equilibrium point. Finally, we achieve the GAS of “any” rest point of this system via bounded and regular feedback controls by using the proposed CLF method, which also contains the following controllers: (i) damping controls outside [Formula: see text], so they collaborate with the beneficial stable free dynamics, and (ii) (possibly optimal) feedback controls inside [Formula: see text] that stabilize the control system at “any” desired rest point of the (unforced) Lorenz system.

Design stabilisers for multi-input affine control stochastic systems via stochastic control Lyapunov functions

This paper studies the problem of state feedback stabilisation, in the sense of a weak solution, for a class of multi-input affine control stochastic systems whose drift and diffusion terms are dependent on the control and for which classical methods are not applicable. Based on the generalised stochastic Lyapunov theorem and on the technique of stochastic control Lyapunov functions, sufficient conditions for the existence of a continuous stabilising feedback control are proposed, and a state feedback controller can be developed to guarantee the closed-loop system globally asymptotically stable in probability. This work generalises previous results on the stabilisation of single-input affine control stochastic systems. The obtained results are illustrated by a numerical example.

An LMI-based robust state-feedback controller design for the position control of a knee rehabilitation exoskeleton robot: Comparative analysis

Rehabilitation exoskeleton robots play a crucial role in restoring functional lower limb movements for individuals with locomotor disorders. Numerous research studies have concentrated on adapting the control of these rehabilitation robotic systems. In this study, we investigate an affine state-feedback control law for robust position control of a knee exoskeleton robot, taking into account its nonlinear dynamic model that includes solid and viscous frictions. To ensure robust stabilization, we employ the Lyapunov approach and propose three methods to establish stability conditions using the Schur complement, the Young inequality, the matrix inversion lemma, and the S-procedure lemma. These conditions are formulated as Linear Matrix Inequalities (LMIs). Furthermore, we conduct a comprehensive comparison among these methods to determine the most efficient approach. At the end of this work, we present simulation results to validate the developed LMI conditions and demonstrate the effectiveness of the adopted control law in achieving robust position control of the knee exoskeleton robot.

Chain Recurrence and Selgrade’s Theorem for Affine Flows

AbstractAffine flows on vector bundles with chain transitive base flow are lifted to linear flows and the decomposition into exponentially separated subbundles provided by Selgrade’s theorem is determined. The results are illustrated by an application to affine control systems with bounded control range.

Existence results and stabilization of homogeneous conformable fractional order systems

In this paper, we give results on the stability of homogeneous conformable fractional order systems using assumptions on a family of compact sets and provide the stabilization of an affine control system and given an explicit homogeneous feedback control with the requirement that a control Lyapunov function exists and satisfying a homogeneous condition and we present existence and uniqueness theorems for sequential linear conformable fractional differential equations.

Global stabilization of a bounded controlled system based on the Rössler system

In this work we present a method for the global asymptotic stabilization of an affine control system based on a Rössler system (which is well known by its chaotic behavior), through regular feedback controls constrained to control value sets given by (convex) polytopes U. The proposed method for control designing is based on the control Lyapunov function (clf) theory due to Artstein and Sontag. To this aim, we construct first an explicit absorbing ballB to “trap” the global attractor of Rössler system: we show that the affine system is the feedback interconnection of two subsystems, that leads to obtain B as the level set of a Lyapunov function, V∞(x). However, since the minimum point of V∞(x) is not a rest point of Rössler system, we apply a modified solution to the “uniting clf problem” (to unite local (possibly optimal) controls with global ones, proposed in Andrieu and Prieur (2010)) in order to obtain a clfV(x) for the affine system with minimum at a desired rest point. Finally, we achieve the global asymptotic stabilization of “any” rest point of this system via bounded and regular feedback controls by using the proposed clf method, also obtaining that controls are: (i) damping controls outside B, so they collaborate with the beneficial stable free dynamics, and (ii) (possibly optimal) feedback controls inside B that stabilize the control system at “any” desired equilibrium point of the (unforced) Rössler system.

Complex Couplings - A Universal, Adaptive, and Bilinear Formulation of Power Grid Dynamics

The energy transition introduces new classes of dynamical actors into the power grid. There is, in particular, a growing need for so-called grid-forming inverters (GFIs) that can contribute to dynamic grid stability as the share of synchronous generators decreases. Understanding the collective behavior and stability of future grids, featuring a heterogeneous mix of dynamics, remains an urgent and challenging task. Two recent advances in describing such modern power grid dynamics have made this problem more tractable. First, the normal form for grid-forming actors provides a uniform technology-neutral description of plausible grid dynamics, including grid-forming inverters and synchronous machines. Second, the notion of the complex frequency has been introduced to effortlessly describe how the nodal dynamics influence the power flows in the grid. The major contribution of this paper is to show how the normal-form approach and the complex-frequency dynamics of power grids combine and how they relate naturally to adaptive dynamical networks and control-affine systems. Using the normal form and the complex frequency, we derive a remarkably elementary and universal equation for the collective grid dynamics. Notably, we obtain an elegant equation entirely in terms of a matrix of complex couplings, in which the network topology does not appear explicitly. These complex couplings give rise to new adaptive network formulations of future power grid dynamics. We give a new formulation of the Kuramoto model, with inertia as a special case. Starting from this formulation of the grid dynamics, the question of the optimal design of future grid-forming actors becomes treatable by methods from affine and bilinear control theory. We demonstrate the power of this perspective by deriving a quasilocal control dynamics that can stabilize arbitrary power flows, even if the effective network Laplacian is not positive definite. Published by the American Physical Society 2024

Decomposition of Equations of Nonlinear Affine Control Systems and its Application to the Synthesis of Regulators

The article deals with the decomposition of nonlinear differential equations based on the group-theoretic approach. At the beginning, the decomposition of differential equations of linear systems using a transition matrix of state is presented, and then, based on the theory of continuous groups (Lie groups), the process of decomposition of differential equations of nonlinear systems is shown. The decomposition approach is based on the isomorphism theorem of the space of vector fields and Lie derivatives, which allows us to consider vector fields as differential operators of smooth functions. A formula is derived about the adjoin representation of a Lie group in its Lie algebra, which actually determines the finding of a vector field that characterizes the interaction of two or more vector fields. The Lie algebra of derivatives makes it possible to determine the infinitesimal action of the Lie group, i.e. the linearization of this action is carried out (transformation of the points of the trajectory space of the original system in a small neighborhood). Decomposition allows, as in the linear case, to separate the finding of an action (only locally) of a group of transformations from the transformed points themselves. For linear systems, this separation is global. It is also shown that the decomposition of linear equations is a particular case of the decomposition of nonlinear equations. An algorithm of the method of model predictive control with Gramian weighting using this decomposition is presented. A practical example of decomposition and application of the model predictive control for stabilization of a nonstationary nonlinear system is considered.

Time optimal problems on Lie groups and applications to quantum control

<abstract><p>In this paper we introduce a natural compactification of a left (right) invariant affine control system on a semi-simple Lie group $ G $ in which the control functions belong to the Lie algebra of a compact Lie subgroup $ K $ of $ G $ and we investigate conditions under which the time optimal solutions of this compactified system are "approximately" time optimal for the original system. The basic ideas go back to the papers of R.W. Brockett and his collaborators in their studies of time optimal transfer in quantum control (<sup>[<xref ref-type="bibr" rid="b1">1</xref>]</sup>, <sup>[<xref ref-type="bibr" rid="b2">2</xref>]</sup>). We showed that every affine system can be decomposed into two natural systems that we call horizontal and vertical. The horizontal system admits a convex extension whose reachable sets are compact and hence posess time-optimal solutions. We then obtained an explicit formula for the time-optimal solutions of this convexified system defined by the symmetric Riemannian pair $ (G, K) $ under the assumption that the Lie algebra generated by the control vector fields is equal to the Lie algebra of $ K $.</p> <p>In the second part of the paper we applied our results to the quantum systems known as Icing $ n $-chains (introduced in <sup>[<xref ref-type="bibr" rid="b2">2</xref>]</sup>). We showed that the two-spin chains conform to the theory in the first part of the paper but that the three-spin chains show new phenomena that take it outside of the above theory. In particular, we showed that the solutions for the symmetric three-spin chains studied by (<sup>[<xref ref-type="bibr" rid="b3">3</xref>]</sup>, <sup>[<xref ref-type="bibr" rid="b4">4</xref>]</sup>) are solvable in terms of elliptic functions with the solutions completely different from the ones encountered in the two-spin chains.</p></abstract>

Finite element error analysis of affine optimal control problems

This paper is concerned with error estimates for the numerical approximation for affine optimal control problems subject to semilinear elliptic PDEs. To investigate the error estimates, we focus on local minimizers that satisfy certain local growth conditions. The local growth conditions we consider in this paper appeared recently in the context of solution stability and contain the joint growth of the first and second variation of the objective functional. These growth conditions are especially meaningful for affine control constrained optimal control problems because the first variation can satisfy a local growth, which is not the case for unconstrained problems. The main results of this paper are the achievement of error estimates for the numerical approximations generated by a finite element scheme with piecewise constant controls or a variational discretization scheme. Even though the growth conditions considered are weaker than those appearing in the recent literature on finite element error estimates for affine problems, this paper substantially improves the existing error estimates for both the optimal controls and the states when a Hölder-type growth is assumed.

Necessary conditions for local controllability of a particular class of systems with two scalar controls

We consider control-afflne systems with two scalar controls, such that one control vector field vanishes at an equilibrium state. We state two necessary conditions for local controllability around this equilibrium, involving the iterated Lie brackets of the system vector fields, with controls that are either bounded, small in L∞ or small in W1,∞. These results are illustrated with several examples.

Admissible Control Laws for Constrained Linear Power Flow: The General Case

Linearized power flow with line flow and voltage constraints can be modeled as a system of linear inequalities depending on the power injections. When some injections are controlled by the grid operator while others are determined exogenously, robust control aims at determining grid operator's actions under imperfect system observability such that the grid state is feasible for all possible realizations of the exogenous actions. It was shown how to design and analyze such admissible control policies efficiently for the subclass of affine control laws, but this paper shows that there are important cases that require more general control policies. We show that, for the constrained linear power flow setting, general admissible control policies can always be chosen as piecewise affine (PWA) mappings. The PWA mapping can be explicitly characterized offline or control actions can be computed online by solving an optimization problem given a current observation. For the latter setup, we provide an algorithm that verifies offline that the online control scheme is admissible. This verification step is a crucial precondition to apply the online control scheme in real, safety-critical power grids. The proposed framework is demonstrated with applications to voltage regulation in active distribution grids subject to uncertain prosumers and low observability.

Event-triggered finite-time admissibilization of bio-economic singular semi-Markovian jump fuzzy systems

An event-triggered scheme-based admissibilization problem of bio-economic singular semi-Markovian jump systems over a finite-time interval is investigated in this study, where the commodity price is assumed to follow a semi-Markov process. To facilitate analysis, the addressed system is expressed using Takagi-Sugeno fuzzy modeling with two fuzzy rules, which is then generalized to a finite number of fuzzy rules. Following that, an affine membership-based event-triggered controller is proposed for the system under consideration to ensure the desired admissibility within a given finite-time interval. A new set of conditions that adequately guarantees the aforementioned problem is derived using the Lyapunov-Krasovskii stability theory, parameterized linear matrix inequality technique and dissipative theory. A numerical example based on the eel seedling harvesting model is considered to validate the developed theoretical findings, where the significance of the proposed control design method is clearly demonstrated.

A new theorem on finite‐time stability of stochastic homogeneous systems and its application

AbstractThis paper provides a novel Lyapunov theorem on finite‐time stability of stochastic homogeneous systems. Different from the existing results, the differential operator in this paper is not required to be negative definite and could be negative semidefinite. The obtained condition is somehow similar to the LaSalle's condition. Moreover, the existing theorem of finite‐time stability for stochastic homogeneous systems is a special case of our result. As an application of the obtained theorem, stochastic finite‐time stabilization is considered for stochastic homogeneous affine control systems. Some examples and simulations are provided to show the effectiveness of the results.

Data-driven control for discrete-time piecewise affine systems

This paper studies the problem of data-driven control for discrete-time piecewise affine (PWA) systems. Based on a sequel of sampled control inputs and states with satisfactory rank conditions, the closed loop dynamics of PWA systems can be represented and therefore the explicit information of system matrices is not needed in system stability analysis and controller synthesis processes. First, via S-procedure, system stability analysis results have been obtained, and then, two novel data-driven controller design methods in the form of linear matrix inequalities and equations have been proposed such that the resulting closed loop system is asymptotically stable. For PWA systems with unknown state space partition information, an online data-driven control method has been further proposed to guarantee the asymptotic stability of the resulting closed loop systems. Finally, simulation studies of two examples have been given to validate the effectiveness of the proposed data-driven controller design approaches.