scholarly journals Adaptive Control for a Biological Process under Input Saturation and Unknown Control Gain via Dead Zone Lyapunov Functions

2020 ◽  
Vol 11 (1) ◽  
pp. 251
Author(s):  
Alejandro Rincón ◽  
Fredy E. Hoyos ◽  
John E. Candelo-Becerra
Keyword(s):  
Lower Bounds ◽  
Distinctive Feature ◽  
Biological Process ◽  
Dead Zone ◽  
Tracking Error ◽  
Input Saturation ◽  
Auxiliary System ◽  
Upper And Lower Bounds ◽  
Compact Set ◽  
Control Gain

In this work, substrate control of a biological process with unknown varying control gain, input saturation, and uncertain reaction rate is addressed. A novel adaptive controller is proposed, which tackles the combined effect of input saturation and unknown varying control gain with unknown upper and lower bounds. The design is based on dead zone radially unbounded Lyapunov-like functions, with the state backstepping as control framework. The convergence of the modified tracking error and the boundedness of the updated parameters are ensured by means of the Barbalat’s lemma. As the first distinctive feature, a new second-order auxiliary system is proposed that tackles the effect of saturated input and the unknown varying control gain with unknown upper and lower bounds. As the second distinctive feature, the modified tracking error converges to a compact set whose width is user-defined, so that it does not depend on bounds of either external disturbances, model terms, or model coefficients. The convergence region of the current tracking error is determined for the closed loop system subject to the formulated controller and the proposed auxiliary system. Finally, numerical simulation illustrates the performance of the proposed controller.

scholarly journals An Improved Robust Adaptive Controller for a Fed-Batch Bioreactor with Input Saturation and Unknown Varying Control Gain via Dead-Zone Quadratic Forms

Computation ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 100
Author(s):  
Alejandro Rincón ◽  
Gloria María Restrepo ◽  
Óscar J. Sánchez
Keyword(s):  
Distinctive Feature ◽  
Quadratic Forms ◽  
Dead Zone ◽  
Tracking Error ◽  
Input Saturation ◽  
Adaptive Controller ◽  
Fed Batch ◽  
Batch Bioreactor ◽  
Control Gain ◽  
Robust Adaptive

In this work, a new adaptive controller is designed for substrate control of a fed-batch bioreactor in the presence of input saturation and unknown varying control gain with unknown upper and lower bounds. The output measurement noise and the unknown varying nature of reaction rate and biomass concentration and water volume are also handled. The design is based on dead zone quadratic forms. The designed controller ensures the convergence of the modified tracking error and the boundedness of the updated parameters. As the first distinctive feature, a new robust adaptive auxiliary system is proposed in order to tackle input saturation and control gain uncertainty. As the second distinctive feature, the modified tracking error converges to a compact region whose bound is user-defined, in contrast to related studies where the convergence region depends on upper bounds of either external disturbances, system states, model parameters or terms and model parameter values. Simulations confirm the properties of the closed loop behavior.

scholarly journals A Robust Observer—Based Adaptive Control of Second—Order Systems with Input Saturation via Dead-Zone Lyapunov Functions

Computation ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 82
Author(s):  
Alejandro Rincón ◽  
Gloria M. Restrepo ◽  
Fredy E. Hoyos
Keyword(s):  
Lyapunov Functions ◽  
Dead Zone ◽  
Tracking Error ◽  
Input Saturation ◽  
Chemical Reactor ◽  
Second Order ◽  
Control Law ◽  
Compact Set ◽  
State Variables ◽  
Robust Observer

In this study, a novel robust observer-based adaptive controller was formulated for systems represented by second-order input–output dynamics with unknown second state, and it was applied to concentration tracking in a chemical reactor. By using dead-zone Lyapunov functions and adaptive backstepping method, an improved control law was derived, exhibiting faster response to changes in the output tracking error while avoiding input chattering and providing robustness to uncertain model terms. Moreover, a state observer was formulated for estimating the unknown state. The main contributions with respect to closely related designs are (i) the control law, the update law and the observer equations involve no discontinuous signals; (ii) it is guaranteed that the developed controller leads to the convergence of the tracking error to a compact set whose width is user-defined, and it does not depend on upper bounds of model terms, state variables or disturbances; and (iii) the control law exhibits a fast response to changes in the tracking error, whereas the control effort can be reduced through the controller parameters. Finally, the effectiveness of the developed controller is illustrated by the simulation of concentration tracking in a stirred chemical reactor.

scholarly journals On the Generalized Distance Energy of Graphs

Mathematics ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 17 ◽  
Author(s):  
Abdollah Alhevaz ◽  
Maryam Baghipur ◽  
Hilal A. Ganie ◽  
Yilun Shang
Keyword(s):  
Lower Bounds ◽  
Complete Graph ◽  
Connected Graph ◽  
Distance Matrix ◽  
Wiener Index ◽  
Diagonal Matrix ◽  
Upper And Lower Bounds ◽  
Star Graph ◽  
Extremal Graphs ◽  
Generalized Distance

The generalized distance matrix D α ( G ) of a connected graph G is defined as D α ( G ) = α T r ( G ) + ( 1 − α ) D ( G ) , where 0 ≤ α ≤ 1 , D ( G ) is the distance matrix and T r ( G ) is the diagonal matrix of the node transmissions. In this paper, we extend the concept of energy to the generalized distance matrix and define the generalized distance energy E D α ( G ) . Some new upper and lower bounds for the generalized distance energy E D α ( G ) of G are established based on parameters including the Wiener index W ( G ) and the transmission degrees. Extremal graphs attaining these bounds are identified. It is found that the complete graph has the minimum generalized distance energy among all connected graphs, while the minimum is attained by the star graph among trees of order n.

scholarly journals Hadamard k-fractional inequalities of Fejér type for GA-s-convex mappings and applications

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Hui Lei ◽  
Gou Hu ◽  
Zhi-Jie Cao ◽  
Ting-Song Du
Keyword(s):  
Lower Bounds ◽  
Hypergeometric Functions ◽  
Upper And Lower Bounds ◽  
Weighted Inequalities ◽  
Convex Mappings ◽  
Special Means

Abstract The main aim of this paper is to establish some Fejér-type inequalities involving hypergeometric functions in terms of GA-s-convexity. For this purpose, we construct a Hadamard k-fractional identity related to geometrically symmetric mappings. Moreover, we give the upper and lower bounds for the weighted inequalities via products of two different mappings. Some applications of the presented results to special means are also provided.

Uniformly ultimately bounded tracking control of sandwich systems with nonsymmetric sandwiched dead-zone nonlinearity and input saturation constraint

2021 ◽  
pp. 107754632098794
Author(s):  
Meysam Azhdari ◽  
Tahereh Binazadeh
Keyword(s):  
Dead Zone ◽  
Input Saturation ◽  
Closed Loop System ◽  
Unknown Parameters ◽  
External Disturbances ◽  
Uniformly Ultimately Bounded ◽  
Output Tracking ◽  
Saturation Constraint ◽  
Two Phases ◽  
Practical Constraints

This article studies the uniformly ultimately bounded output tracking problem of uncertain nonlinear sandwich systems with sandwiched dead-zone nonlinearity in the presence of some practical constraints such as nonsymmetric input saturation, model uncertainties, time-varying external disturbances, and unknown parameters. Due to the existence of both dead-zone and saturation nonlinearities, the design process is more complicated; therefore, to solve the design complexities, the designing process is divided into two phases. The proposed method leads to output tracking with acceptable accuracy. Moreover, all signals in the closed-loop system are ultimately bounded. Simulation results illustrate the applicability and effectiveness of the proposed method by its application on two practical sandwich systems (robotic system and electrohydraulic servo press system).

scholarly journals On the Second-Largest Reciprocal Distance Signless Laplacian Eigenvalue

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 512
Author(s):  
Maryam Baghipur ◽  
Modjtaba Ghorbani ◽  
Hilal A. Ganie ◽  
Yilun Shang
Keyword(s):  
Lower Bounds ◽  
Complete Graph ◽  
Distance Matrix ◽  
Upper And Lower Bounds ◽  
Laplacian Eigenvalue ◽  
Signless Laplacian ◽  
Graph Parameters ◽  
Simple Connected Graph ◽  
Second Largest Eigenvalue ◽  
Reciprocal Distance Matrix

The signless Laplacian reciprocal distance matrix for a simple connected graph G is defined as RQ(G)=diag(RH(G))+RD(G). Here, RD(G) is the Harary matrix (also called reciprocal distance matrix) while diag(RH(G)) represents the diagonal matrix of the total reciprocal distance vertices. In the present work, some upper and lower bounds for the second-largest eigenvalue of the signless Laplacian reciprocal distance matrix of graphs in terms of various graph parameters are investigated. Besides, all graphs attaining these new bounds are characterized. Additionally, it is inferred that among all connected graphs with n vertices, the complete graph Kn and the graph Kn−e obtained from Kn by deleting an edge e have the maximum second-largest signless Laplacian reciprocal distance eigenvalue.

scholarly journals Multilevel Monte Carlo methods and lower–upper bounds in initial margin computations

2020 ◽  
Vol 26 (2) ◽  
pp. 131-161
Author(s):  
Florian Bourgey ◽  
Stefano De Marco ◽  
Emmanuel Gobet ◽  
Alexandre Zhou
Keyword(s):  
Monte Carlo ◽  
Lower Bounds ◽  
Asymptotic Optimality ◽  
Upper Bounds ◽  
Upper And Lower Bounds ◽  
Independent Random Variables ◽  
Outer Function ◽  
Control Problems ◽  
Multilevel Monte Carlo ◽  
Primal Dual

AbstractThe multilevel Monte Carlo (MLMC) method developed by M. B. Giles [Multilevel Monte Carlo path simulation, Oper. Res. 56 2008, 3, 607–617] has a natural application to the evaluation of nested expectations {\mathbb{E}[g(\mathbb{E}[f(X,Y)|X])]}, where {f,g} are functions and {(X,Y)} a couple of independent random variables. Apart from the pricing of American-type derivatives, such computations arise in a large variety of risk valuations (VaR or CVaR of a portfolio, CVA), and in the assessment of margin costs for centrally cleared portfolios. In this work, we focus on the computation of initial margin. We analyze the properties of corresponding MLMC estimators, for which we provide results of asymptotic optimality; at the technical level, we have to deal with limited regularity of the outer function g (which might fail to be everywhere differentiable). Parallel to this, we investigate upper and lower bounds for nested expectations as above, in the spirit of primal-dual algorithms for stochastic control problems.

scholarly journals A Lower Bound for the Query Phase of Contraction Hierarchies and Hub Labels and a Provably Optimal Instance-Based Schema

Algorithms ◽  
2021 ◽  
Vol 14 (6) ◽  
pp. 164
Author(s):  
Tobias Rupp ◽  
Stefan Funke
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Real World ◽  
Road Network ◽  
Upper And Lower Bounds ◽  
Bounded Degree ◽  
Shortest Path Routing ◽  
Graph Classes ◽  
Speed Up ◽  
To Come

We prove a Ω(n) lower bound on the query time for contraction hierarchies (CH) as well as hub labels, two popular speed-up techniques for shortest path routing. Our construction is based on a graph family not too far from subgraphs that occur in real-world road networks, in particular, it is planar and has a bounded degree. Additionally, we borrow ideas from our lower bound proof to come up with instance-based lower bounds for concrete road network instances of moderate size, reaching up to 96% of an upper bound given by a constructed CH. For a variant of our instance-based schema applied to some special graph classes, we can even show matching upper and lower bounds.

Sign in / Sign up

Export Citation Format

Share Document