Jongrae Kim

Backstepping Control Design with Actuator Torque Bound for Spacecraft Attitude Maneuver

BACKSTEPPING is a popular nonlinear control design technique [1,2]. It hinges on using a part of the system states as virtual controls to control the other states. Generating a family of globally asymptotically stabilizing control laws is the main advantage of this method that can be exploited for addressing robustness issues and solving adaptive problems. The term backstepping refers to the recursive nature of the control design procedure in which a control law and a control Lyapunov function are recursively constructed to guarantee stability. Backstepping has been considered for the spacecraft slew maneuvers [3,4]. The cascaded structure of spacecraft kinematics and dynamics makes the integrator backstepping a preferred approach for the spacecraft attitude maneuver problem, resulting in smooth feedback controls [5]. However, the typical control actuators used for this problem (such as reaction wheels, control moment gyros, or thrusters) have an upper bound on the control torque they can exert onto the system and the simple or conventional backstepping control method may result in excessive control input beyond that saturation bound. The issue has been addressed in the literature using other control methodologies such as nonlinear proportional–integral–derivative control [6], Lyapunovoptimal control [7] and variable structure control [8–11]. In this work, we design a nonlinear backstepping attitude controller using the inverse tangent-based tracking function [4] and a family of augmented Lyapunov functions [12]. Using this control law, we derive an analytical upper bound of the control torque norm. The bound is effectively used to tune the control parameters so that, for the given settling time specification, the upper bound of the control input is minimized. The performance of the proposed controller has shown improvements in minimizing the peak control torque and the settling time. The rest of the Note is organized as follows: First, the kinematics and dynamics of rigid spacecraft are summarized. Second, the details of the design procedure for the proposed controller and the analytical bounds for the control torque components are given. Third, the efficacy of the proposed scheme is demonstrated by the numerical simulations for the cases of attitude stabilization and tracking both. Finally, the conclusions are presented.

Aggregation Algorithm Towards Large-Scale Boolean Network Analysis

The analysis of large-scale Boolean network dynamics is of great importance in understanding complex phenomena where systems are characterized by a large number of components. The computational cost to reveal the number of attractors and the period of each attractor increases exponentially as the number of nodes in the networks increases. This paper presents an efficient algorithm to find attractors for medium to large-scale networks. This is achieved by analyzing subnetworks within the network in a way that allows to reveal the attractors of the full network with little computational cost. In particular, for each subnetwork modeled as a Boolean control network, the input-state cycles are found and they are composed to reveal the attractors of the full network. The proposed algorithm reduces the computational cost significantly, especially in finding attractors of short period, or any periods if the aggregation network is acyclic. Also, this paper shows that finding the best acyclic aggregation is equivalent to finding the strongly connected components of the network graph. Finally, the efficiency of the algorithm is demonstrated on two biological systems, namely a T-cell receptor network and an early flower development network.

Clearance of Nonlinear Flight Control Laws Using Hybrid Evolutionary Optimization

The application of two evolutionary optimization methods, namely, differential evolution and genetic algorithms, to the clearance of nonlinear flight control laws for highly augmented aircraft is described. The algorithms are applied to the problem of evaluating a nonlinear handling quality clearance criterion for a simulation model of a high-performance aircraft with a delta canard configuration and a full-authority flight control law. Hybrid versions of both algorithms, incorporating local gradient-based optimization, are also developed and evaluated. Statistical comparisons of computational cost and global convergence properties reveal the benefits of hybridization for both algorithms. The differential evolution approach in particular, when appropriately augmented with local optimization methods, is shown to have significant potential for improving both the reliability and efficiency of the current industrial flight clearance process

Error Bounded Sensing for Packet-Based Networked Control Systems

An error bounded sensing strategy is proposed within the packet-based control framework for networked control systems (NCSs). This strategy reduces the data transmissions in both the sensor-to-controller and the controller-to-actuator channels by allowing the transmissions of only the sensing and control data packets that satisfy some predetermined transmission rules. By fitting it into the packet-based control framework for NCSs, this strategy can achieve the goal of reducing the use of the communication resources while at the same time maintaining the system performance at an acceptable level. Stabilized controllers are designed within this framework, and the effects on the system stability brought by this approach are also investigated. Numerical and experimental examples illustrate the effectiveness of the proposed approach.

Moving ground target tracking in dense obstacle areas using UAVs

Abstract Tracking moving ground targets using unmanned air vehicles (UAVs) has important applications in several areas. Keeping a close line of sight from a UAV to a target in a densely populated area is a challenging task because of many constraints. An algorithm for several UAVs to track a moving target cooperatively is proposed. From random samples on the ground and obstacles, a cost inversely proportional to chance to keep the target inside the camera field of view is defined. The centre of the flight path and the separation angles between UAVs along the circular flight path is optimally determined to minimise the cost. The efficiency of the algorithm is tested by Monte-Carlo simulations based on random scenario generators.

Stochastic Noise and Synchronisation during Dictyostelium Aggregation Make cAMP Oscillations Robust

Stable and robust oscillations in the concentration of adenosine 3′, 5′-cyclic monophosphate (cAMP) are observed during the aggregation phase of starvation-induced development in Dictyostelium discoideum. In this paper we use mathematical modelling together with ideas from robust control theory to identify two factors which appear to make crucial contributions to ensuring the robustness of these oscillations. Firstly, we show that stochastic fluctuations in the molecular interactions play an important role in preserving stable oscillations in the face of variations in the kinetics of the intracellular network. Secondly, we show that synchronisation of the aggregating cells through the diffusion of extracellular cAMP is a key factor in ensuring robustness of the oscillatory waves of cAMP observed in Dictyostelium cell cultures to cell-to-cell variations. A striking and quite general implication of the results is that the robustness analysis of models of oscillating biomolecular networks (circadian clocks, Ca2+ oscillations, etc.) can only be done reliably by using stochastic simulations, even in the case where molecular concentrations are very high.

Least-squares methods for identifying biochemical regulatory networks from noisy measurements

BackgroundWe consider the problem of identifying the dynamic interactions in biochemical networks from noisy experimental data. Typically, approaches for solving this problem make use of an estimation algorithm such as the well-known linear Least-Squares (LS) estimation technique. We demonstrate that when time-series measurements are corrupted by white noise and/or drift noise, more accurate and reliable identification of network interactions can be achieved by employing an estimation algorithm known as Constrained Total Least Squares (CTLS). The Total Least Squares (TLS) technique is a generalised least squares method to solve an overdetermined set of equations whose coefficients are noisy. The CTLS is a natural extension of TLS to the case where the noise components of the coefficients are correlated, as is usually the case with time-series measurements of concentrations and expression profiles in gene networks.ResultsThe superior performance of the CTLS method in identifying network interactions is demonstrated on three examples: a genetic network containing four genes, a network describing p53 activity and mdm2 messenger RNA interactions, and a recently proposed kinetic model for interleukin (IL)-6 and (IL)-12b messenger RNA expression as a function of ATF3 and NF-κ B promoter binding. For the first example, the CTLS significantly reduces the errors in the estimation of the Jacobian for the gene network. For the second, the CTLS reduces the errors from the measurements that are corrupted by white noise and the effect of neglected kinetics. For the third, it allows the correct identification, from noisy data, of the negative regulation of (IL)-6 and (IL)-12b by ATF3.ConclusionThe significant improvements in performance demonstrated by the CTLS method under the wide range of conditions tested here, including different levels and types of measurement noise and different numbers of data points, suggests that its application will enable more accurate and reliable identification and modelling of biochemical networks.

Nonlinear robust performance analysis using complex-step gradient approximation

In this paper, the complex-step method is applied in the setting of numerical optimisation problems involving dynamical systems modelled as nonlinear differential equations. The main advantage of the complex-step method for gradient approximation is that it entails no subtractive cancellation error, and therefore the truncation error can be made arbitrarily (to machine precision) small. The method is applied to two robust performance analysis problems. The accuracy and convergence rate of the solutions computed using the proposed approach are seen to be significantly better than those achieved using standard gradient approximation methods.

Robustness analysis of linear periodic time-varying systems subject to structured uncertainty

In this paper, we show how Floquet theory may be combined with a technique known as Lifting to cast a linear periodically time-varying system subject to structured linear time invariant uncertainty in the form of a linear fractional transformation. The stability and performance robustness of the resulting system may then be analysed using standard μ-analysis methods. A significant advantage of the proposed approach is that it allows the computation of a worst-case destabilising uncertainty combination which may be used to estimate the conservatism of the computed robustness margin. An example is given to illustrate the application of the proposed approach.

Cooperative radar jamming for groups of unmanned air vehicles

We consider a scenario where a group of unmanned air vehicles flies in a close formation and cooperates in their use of jamming resources to prevent being tracked by surface-to-air missile (SAM) tracking radars. We consider threats posed by a single or multiple SAM and investigate their impact on minimum-risk path planning.