Multirate sampled‐data stabilization for a class of low‐order lower‐triangular nonlinear systems

This paper investigates the problem of sampled‐data controller design for a class of lower‐triangular systems in the p‐normal form (0<p<1). A multirate digital feedback control scheme is proposed to achieve the global strong stabilization of the sampled‐data closed‐loop system under some assumptions. In the design of the controller, the input‐Lyapunov matching strategy and multirate control approach are combined to obtain better stabilizing performance. Unlike the design method based on the approximate discrete‐time model, our controller is obtained from the exact discrete‐time equivalent model, which does not need to be computed completely. The approximate multirate digital controllers are proved to be effective in the practical implementation. It is shown that, compared with the emulated control scheme, our controller may provide faster decrease of Lyapunov function for each subsystem. This will lead to allow large sampling periods. An illustrative example is provided to verify the effectiveness of the proposed control scheme.     

An augmented system approach to static output‐feedback stabilization with ℋ︁∞ performance for continuous‐time plants

This paper revisits the static output‐feedback stabilization problem of continuous‐time linear systems from a novel perspective. The closed‐loop system is represented in an augmented form, which facilitates the parametrization of the controller matrix. Then, new equivalent characterizations on stability and ??_∞ performance of the closed‐loop system are established in terms of matrix inequalities. On the basis of these characterizations, a necessary and sufficient condition with slack matrices for output‐feedback stabilizability is proposed, and an iteration algorithm is given to solve the condition. An extension to output‐feedback ??_∞ control is provided as well. The effectiveness and merits of the proposed approach are shown through several examples. Copyright © 2008 John Wiley & Sons, Ltd.     

Model‐free adaptive formation control for unknown multiinput‐multioutput nonlinear heterogeneous discrete‐time multiagent systems with bounded disturbance

Based on the model‐free adaptive control, the distributed formation control problem is investigated for a class of unknown heterogeneous nonlinear discrete‐time multiagent systems with bounded disturbance. Two equivalent data models to the unknown multiagent systems are established through the dynamic linearization technique considering the circumstances with measurable and unmeasurable disturbances. Based on the obtained data models, two distributed controllers are designed with only using the input/output and disturbance data of the neighbor agents system. The tracking error of the closed‐loop system driven by the proposed controllers is shown to be bounded by the contraction mapping principle and inductive methods. An example illustrates the effectiveness of the proposed two distributed controllers.     

A novel symmetrical Wilkinson power divider for dual‐band application

A symmetrical two‐way Wilkinson power divider with shifted output ports, much wide bandwidth and large frequency‐ratio is proposed for dual‐band application. The corresponding transcendental design equations are derived by using the even‐ and odd‐mode analysis. Moreover, the closed‐form scattering parameter expressions are derived. Transcendental design equations are solved and accurate numerical design parameters along with different frequency ratios are obtained. Finally, the proposed structure and design method are validated by simulated and experimental results of typical microstrip planar power dividers, the performance is clearly observed for the input and output matching, isolation and transmission characteristic very well at the two band frequencies. More specifically, the measured transmission characteristics of the divider are 3.11 dB/3.58 dB at the 1.0 GHz/3.5 GHz, respectively. © 2013 Wiley Periodicals, Inc. Int J RF and Microwave CAE 24:102–108, 2014.     

Active Disturbance Rejection in Affine Nonlinear Systems Based on Equivalent‐Input‐Disturbance Approach

This paper presents a disturbance rejection method for an affine nonlinear system. The control system is constructed based on the equivalent‐input‐disturbance (EID) approach. An affine nonlinear state observer is used to reconstruct the state of the affine nonlinear system and to estimate an EID. The well‐known differential mean value theorem enables us to describe the closed‐loop system in the state space as a linear‐parameter‐varying system. This makes it easy to derive sufficient conditions of global uniform ultimate boundedness in term of linear matrix inequalities (LMIs) by using a Lyapunov function and convexity theory. Controllers are designed based on the LMIs. A numerical example is used to illustrate the design of the control system. And a comparison between the EID‐based control and the sliding‐mode control demonstrates the effectiveness and advantages of the EID‐based control method.     

A Closed‐Form Solution to Single Scattering for General Phase Functions and Light Distributions

Due to the intricate nature of the equation governing light transport in participating media, accurately and efficiently simulating radiative energy transfer remains very challenging in spite of its broad range of applications. As an alternative to traditional numerical estimation methods such as ray‐marching and volume‐slicing, a few analytical approaches to solving single scattering have been proposed but current techniques are limited to the assumption of isotropy, rely on simplifying approximations and/or require substantial numerical precomputation and storage. In this paper, we present the very first closed‐form solution to the air‐light integral in homogeneous media for general 1‐D anisotropic phase functions and punctual light sources. By addressing an open problem in the overall light transport literature, this novel theoretical result enables the analytical computation of exact solutions to complex scattering phenomena while achieving semi‐interactive performance on graphics hardware for several common scattering modes.     

Observer‐based decentralized adaptive control for large‐scale pure‐feedback systems with unknown time‐delayed nonlinear interactions

This paper presents an approximation design for a decentralized adaptive output‐feedback control of large‐scale pure‐feedback nonlinear systems with unknown time‐varying delayed interconnections. The interaction terms are bounded by unknown nonlinear bounding functions including unmeasurable state variables of subsystems. These bounding functions together with the algebraic loop problem of virtual and actual control inputs in the pure‐feedback form make the output‐feedback controller design difficult and challenging. To overcome the design difficulties, the observer‐based dynamic surface memoryless local controller for each subsystem is designed using appropriate Lyapunov‐Krasovskii functionals, the function approximation technique based on neural networks, and the additional first‐order low‐pass filter for the actual control input. It is shown that all signals in the total controlled closed‐loop system are semiglobally uniformly bounded and control errors converge to an adjustable neighborhood of the origin. Finally, simulation examples are provided to illustrate the effectiveness of the proposed decentralized control scheme. Copyright © 2013 John Wiley & Sons, Ltd.     

Complete parasitic‐capacitance‐shell extraction of high‐frequency switch‐HEMT equivalent‐circuit model

This paper presents a new solution to a particular problem of high electron‐mobility transistor (HEMT) equivalent‐circuit modeling, that is, complete parasitic‐capacitance‐shell extraction of high‐frequency single‐gate and dual‐gate switch‐based HEMTs, which is very important to the accuracy of high‐frequency HEMT switch models, but not important in the conventional common‐source HEMT modeling for amplifier‐applications. A full‐wave electromagnetic (EM) analysis based method is proposed to analytically extract the complete parasitic‐capacitance‐shell of single‐gate and dual‐gate switch‐based HEMTs. All the 6 parasitic capacitances of the single‐gate switch‐based HEMT and all the 10 parasitic capacitances of the dual‐gate switch‐based HEMT are extracted by linear equations. No resistance parameter is needed to calculate the capacitance‐to‐ground and the interelectrode‐capacitance, and for the first time, all the 10 parasitic capacitances of the dual‐gate switch‐based HEMT are completely considered and analytically extracted. Then, a consistent and systematic modeling procedure of single‐gate and dual‐gate switch‐based HEMT is verified. With the complete parasitic‐capacitance‐shells extracted, the accurate intrinsic model of the single‐gate HEMT can be directly embedded into the parasitic‐shell of the dual‐gate HEMT. The predicted scattering parameters of the single‐gate and dual‐gate series switches fit well with the measurements up to 40 GHz, and accurate linear scalability are also found.     

Synthesis of broadband dispersive delay structures formed by commensurate C‐ and D‐sections

We propose an exact closed‐form synthesis method for the design of broadband dispersive delay structures (DDSs) formed by the series connection of commensurate all‐pass C‐ and D‐sections. In this method, the transfer function synthesis problem is converted into a Hurwitz polynomial generation problem, where the real roots correspond to C‐sections and the complex roots correspond to D‐sections. Several design examples are provided to illustrate the proposed synthesis method. A prototype is implemented in strip‐line configuration and fabricated in LTCC technology, and the measured response is in good agreement with the prescribed and full‐wave responses. © 2013 Wiley Periodicals, Inc. Int J RF and Microwave CAE 24:322–331, 2014.     

Stabilization of state‐constrained switched nonlinear systems in p‐normal form

This paper is concerned with the stabilization problem for a class of state‐constrained switched nonlinear system in p‐normal form in a domain. A key point in the backstepping design procedure is to find a common stabilizing function at each step. A barrier Lyapunov function, which grows to infinity when its arguments approach some limits, is introduced to ensure that the state constraint is not violated at any time. Bounded state feedback controllers of individual subsystems and a common Lyapunov function are explicitly constructed to asymptotically stabilize the closed‐loop system under arbitrary switchings. An example is given to show the effectiveness of the proposed method. Copyright © 2013 John Wiley & Sons, Ltd.     

A CLOSED‐LOOP SUBSPACE IDENTIFICATION METHOD FOR CONTINUOUS‐TIME SYSTEMS BASED ON δ‐OPERATOR MODEL

This paper is concerned with a subspace identification of a continuous‐time plant operating in closed‐loop in the framework of the joint input‐output approach. The main procedure consists of two steps. Firstly, the dual‐Youla parametrization of the plant is used for obtaining an equivalent open‐loop problem to the original closed‐loop identification problem. Then, a δ‐operator based IV‐MOESP type subspace identification algorithm is developed to estimate the state space model for the joint input‐output process, whereby a higher‐order state space model of the plant is obtained by an algebraic operation. Subsequently, a model reduction procedure is employed to derive a lower‐order plant model removing irrelevant modes from the higher order model. Simulation results by using numerical and chemical plant models demonstrate the feasibility of the proposed method.     

Stabilization of Single‐Input LTI Systems by Proportional‐Derivative Feedback

This article presents an efficient solution to the stabilization pole placement problem for single‐input linear time‐invariant (LTI) systems by proportional‐derivative (PD) feedback. For a controllable system, any arbitrary closed‐loop poles can be placed in order to achieve the desired closed‐loop system performance. Its derivation is based on the transformation of linear system into Hessenberg form by a special coordinate transformation before solving the pole placement problem. The available degrees of freedom offered by PD feedback are utilized to obtain closed‐loop systems with small gains. So, the minimization problem for a suitably chosen cost function is formulated. Simulation results are included to show the effectiveness of the proposed approach.     

Sampled‐data control of a class of uncertain switched nonlinear systems in nonstrict‐feedback form

This paper investigates the stabilization problem of sampled‐data output feedback for a class of uncertain switched nonlinear systems in nonstrict‐feedback form. An observer is designed to estimate the unmeasured states, and a sampled‐data controller is obtained by discretizing the virtual controller that is constructed via the dynamic surface control method. It is proved that the designed sampled‐data controller can render all states of the resulting closed‐loop system to converge to a neighborhood of the origin for the arbitrary switching signal, and an allowable sampling period is also given. Finally, 2 examples are presented to illustrate the effectiveness of the proposed method.     

On‐line real‐time physics‐based predictive motion control with balance recovery

In this paper, we present an on‐line real‐time physics‐based approach to motion control with contact repositioning based on a low‐dimensional dynamics model using example motion data. Our approach first generates a reference motion in run time according to an on‐line user request by transforming an example motion extracted from a motion library. Guided by the reference motion, it repeatedly generates an optimal control policy for a small time window one at a time for a sequence of partially overlapping windows, each covering a couple of footsteps of the reference motion, which supports an on‐line performance. On top of this, our system dynamics and problem formulation allow to derive closed‐form derivative functions by exploiting the low‐dimensional dynamics model together with example motion data. These derivative functions and their sparse structures facilitate a real‐time performance. Our approach also allows contact foot repositioning so as to robustly respond to an external perturbation or an environmental change as well as to perform locomotion tasks such as stepping on stones effectively.     

A new microflake model with microscopic self‐shadowing for accurate volume downsampling

Naïve linear methods for downsampling high‐resolution microflake volumes often produce inaccurate appearance, especially when input voxels are very opaque. Preserving correct appearance at all resolutions requires taking into account maskingshadowing effects that occur between and inside dense input voxels. We introduce a new microflake model whose additional parameters characterize self‐shadowing effects at a microscopic scale. We provide an anisotropic self‐shadowing function and microflake distributions for which the scattering coefficients and the phase functions of our model have closed‐form expressions. We use this model in a new downsampling approach in which scattering parameters are computed from local estimations of self‐shadowing probabilities in the input volume. Unlike previous work, our method handles datasets with spatially varying scattering parameters, semi‐transparent volumes and datasets with intricate silhouettes. We show that our method generates LoDs with correct transparency and consistent appearance through scales for a wide range of challenging datasets, allowing for huge memory savings and efficient distant rendering without loss of quality.     

A Measurement‐Based Approach for Designing Fixed‐Order Controllers for Unknown Closed‐Loop Architecture

This paper presents a new technique to design fixed‐structure controllers for linear unknown systems using a set of measurements. In model‐based approaches, the measured data are used to identify a model of the plant for which a suitable controller can be designed. Due to the fact that real processes cannot be described perfectly by mathematical models, designing controllers using such models to guarantee some desired closed‐loop performance is a challenging task. Hence, a possible alternative to model‐based methods is to directly utilize the measured data in the design process. We propose an approach to designing structured controllers using a set of closed‐loop frequency‐domain data. The principle of such an approach is based on computing the parameters of a fixed‐order controller for which the closed‐loop frequency response fits a desired frequency response that describes some desired performance indices. This problem is formulated as an error minimization problem, which can be solved to find suitable values of the controller parameters. The main feature of the proposed control methodology is that it can be applied to stable and unstable plants. Additionally, the design process depends on a pre‐selected controller structure, which allows for the selection of low‐order controllers. An application of the proposed method to a DC servomotor system is presented to experimentally validate and demonstrate its efficacy.     

Sampled‐data control of networked nonlinear systems with variable delays and drops

This paper investigates the stabilization problem of the nonlinear networked control systems (NCSs) with drops and variable delays. The NCS is modeled as a sampled‐data system. For such a sampled‐data NCS, the stability properties are studied for delay that can be both shorter and longer than one sampling period, respectively. The exponential stability conditions are derived in terms of the parameters of the plant and time delay. On the other hand, a model‐based control scheme based on an approximate discrete‐time model of the plant is presented to guarantee the stability of the closed‐loop system subject to variable time delays and packet losses. The performance of the proposed control schemes are examined through numerical simulations of an automated rendezvous and docking of spacecraft system. Moreover, the simulations show that by employing the model‐based controller, a higher closed‐loop control performance can be achieved. Copyright © 2013 John Wiley & Sons, Ltd.     

Stabilization of Uncertain Multi‐Order Fractional Systems Based on the Extended State Observer

The extended state observer (ESO) based controller has been used successfully with integer‐order systems involving large uncertainties. In this paper, the robust control of uncertain multi‐order fractional‐order (FO) systems based on ESO is investigated. First, we transform the multi‐order FO system into an equivalent system in the form of a same‐order state‐space equation. Then, the ESO for the new system is established for estimating both the state and the total disturbance. Sufficient conditions for bounded‐input and bounded‐output stability are derived, and the asymptotic stability of the closed loop system is analyzed, based on whether the states are available or not. Finally, numerical simulations are presented to demonstrate the validity and feasibility of the proposed methodology.     

Robust‐decentralized tracking control for a class of uncertain MIMO nonlinear systems with time‐varying delays

A new control design method based on signal compensation is proposed for a class of uncertain multi‐input multi‐output (MIMO) nonlinear systems in block‐triangular form with nonlinear uncertainties, unknown virtual control coefficients, strongly coupled interconnections, time‐varying delays, and external disturbances. By this method, the controller design is performed in a backstepping manner. At each step of backstepping procedure, a nominal virtual controller is first designed to get desired output tracking for the nominal disturbance‐free subsystem, and then a robust virtual compensator is designed to restrain the effect of the uncertainties, delays involved in the subsystem, and the couplings among the subsystems. The designed controller is linear and time‐invariant, so the explosion of complexity in the control law is avoid. It is proved that robust stability and robust practical tracking property of the closed‐loop system can be ensured, and the tracking errors can be made as small as desired. Copyright © 2013 John Wiley & Sons, Ltd.     

Triangular‐shaped super‐thin microwave network cloak in antenna applications

In this research article, a triangular‐shaped microwave network cloak made out of interconnected patches was designed at the frequency of 2.88 GHz. Its performances in terms of field distributions and radar cross section scattering were compared with the existing structures. The novel triangular‐shaped cloak structure was then applied to cloak a hindering obstacle placed in front of an electromagnetic source. The simulated scattering parameter and radiation pattern of antenna source were then validated through the experimental results. Also, the proposed structure was applied to reduce the mutual interference between two neighboring antennas. The effects of various parameters such as position and size of the cloak, dielectric constant, and substrate thickness on the cloaking effect were also simulated and studied.