Circle Criterion Research Articles

Adolescent treatment initiation and engagement in an evidence-based practice initiative

This study examined client and program factors predicting initiation and engagement for 2,191 adolescents at 28 outpatient substance abuse treatment sites implementing evidence-based treatments. Using Washington Circle criteria for treatment initiation and engagement, 76% of the sample initiated, with 59% engaging in treatment. Analyses used a 2-stage Heckman probit regression, accounting for within-site clustering, to identify factors predictive of initiation and engagement. Adolescents treated in a pay-for-performance (P4P) group were more likely to initiate, whereas adolescents in the race/ethnicity category labeled other (Native American, Asian, Pacific Islander, Native Alaskan, Native Hawaiian, mixed race/ethnicity), or who reported high truancy, were less likely to initiate. Race/ethnicity groups other than Latinos were equally likely to engage. Among White adolescents, each additional day from first treatment to next treatment reduced likelihood of engagement. Although relatively high initiation and engagement rates were achieved, the results suggest that attention to program and client factors may further improve compliance with these performance indicators.

A SYNCHRONIZATION CONDITION FOR COUPLED NONLINEAR SYSTEMS WITH TIME-DELAY: A FREQUENCY DOMAIN APPROACH

This paper considers the synchronization problem for nonlinear systems with time-delay couplings. We assume that the error dynamics can be rewritten as a feedback connection of a linear delay system with multiple inputs and outputs and nonlinear elements which are decentralized and satisfy a sector condition. Then, we derive a synchronization condition for time-delay coupled systems by applying the multivariable circle criterion. Unlike the conventional synchronization criteria, the derived criterion is based on a frequency-domain stability condition and avoids the use of the Lyapunov–Krasovskii approach. As a result, the condition based on the circle criterion does not contain the conservativeness caused by the Lyapunov–Krasovskii approach. The effectiveness of the proposed criterion is shown by examples of coupled Chua systems with delay coupling.

Studies on Influence of Tunnel Surrounding Rock Stability Analysis Based on Material Yield Criterions

Numerical simulation is one of main methods for tunnel surrounding rock stability analysis. By now, there hasn’t be unanimous view on that what kind of yield criterion is adopted for different surrounding rock class and different buried depth. Mohr-Coulomb yield criterion is always adopted abroad, Drucker-Prager yield criterion is always adopted in China, moreover, the principles are different when adopting D-P yield criterion at home and abroad. Based on introducing the Mohr-Coulomb yield criterion and D-P yield criterions, this paper uses the M-C exterior angle point of circle criteria, which is popular in the international arena for the D-P yield criterion, and finds parameters of geotechnical material for D-P yield criterions through the parameter transformation. Combining with 3D elastic-plastic finite element simulation of the tunnel construction process, with the tunnel buried by soft and weak surrounding rock (V class) at shallow (15m) and deep (550m), this paper analyzes the impact of the M-C and D-P yield criterions on surrounding rock’s displacement, stress, strain effects, and proposes the appropriate yield criterion for the simulation of shallow and deep soft and weak rock tunnel construction and for tunnel surrounding rock stability analysis.

The Circle Criterion and Input-to-State Stability

This article provides an overview of the circle criterion and its connection with ISS. Classical absolute stability theory and the circle criterion in particular, is concerned with the analysis of a feedback interconnection of Lure type, which consists of a linear system in the forward path and a sector-bounded nonlinearity in the negative feedback path. Classical absolute stability results are revis ited in the context of systems described by differential inclusions and within a framework based on the complex Aizerman conjecture. Contrast with the classical literature that is focused mainly on asymptotic stability of the feedback interconnection, ISS issues are addressed and resolved.

Decentralized backstepping output-feedback control for stochastic interconnected systems with time-varying delays using neural networks

This paper addresses the decentralized adaptive output-feedback control problem for a class of interconnected stochastic strict-feedback uncertain systems described by It$$\hat{\hbox{o}}$$ differential equation using neural networks. Compared with the existing literature, this paper removes the commonly used assumption that the interconnections are bounded by known functions multiplying unknown parameters, and all unknown interconnections are lumped in a suitable function which is compensated by only a neural network in each subsystem. So, the controller is simpler even than that for the strict-feedback systems described by the ordinary differential equation. Moreover, the circle criterion is applied to designing nonlinear observers for the estimates of system states. A simulation example is used to illustrate the effectiveness of control scheme proposed in this paper.

Stability Analysis of a Type of Takagi-Sugeno PI Fuzzy Control Systems Using Circle Criterion

A type of Takagi-Sugeno (T-S) Proportional-Integral (PI) fuzzy controllers is studied. The T-S PI fuzzy controller is formed by a T-S Proportional-Derivative (PD) fuzzy controller connected with an integrator. In this particular structure, the T-S PD fuzzy controller is a weighted sum of some linear PD sub-controllers. The mathematical properties of our T-S PI fuzzy controller are also investigated. Based on these properties, the global asymptotic stability of the fuzzy control systems, in which the T-S PI fuzzy controllers are employed, are analyzed by using the well-known circle criterion. A sufficient condition with an elegant graphical interpretation in the frequency domain is further derived to guarantee the global asymptotic stability of the above fuzzy control systems. Finally, two numerical examples are provided to demonstrate how to deploy this method in analyzing the T-S PI fuzzy control systems in the frequency domain with the aid of some simple graphs.

Graphical [formula omitted] analysis of Takagi–Sugeno control systems in the frequency domain

In this paper, the upper bound of the L2-gain of the continuous-time SISO Takagi–Sugeno (T–S) fuzzy system is first graphically obtained in the frequency domain. Based on this upper bound of the L2-gain, the L2-stability of the above T–S fuzzy control system is next investigated by using the small gain theorem and circle criterion. Two sufficient conditions are derived, which can be employed to graphically investigate the L2-stability of certain kind of T–S fuzzy control system in the frequency domain. One numerical example is presented to illustrate how the L2-stability of the simplified continuous-time T–S fuzzy system can be graphically examined.

Robust Anti-Windup Compensation for Normal Systems with Application to the Reaction-Diffusion Equation

AbstractNormal systems, which are unitarily diagonalizable systems, appear in a wide variety of applications such as in microelectronics, polymer processes, spacecraft, and the discretization of distributed parameter models. An efficient design method for robust anti-windup compensators for normal systems is proposed based on a diagonalized circle criterion derived by exploiting the system structure. The method is illustrated for the reaction-diffusion equation.

Lur’e feedback systems with both unbounded control and observation: Well-posedness and stability using nonlinear semigroups

This paper is a complement of information to Grabowski and Callier (2006) [1]. A SISO Lur’e feedback control system consisting of a linear, infinite-dimensional system of boundary control in factor form and a nonlinear static incremental sector type controller is considered. Well-posedness and a criterion of absolute strong asymptotic stability of the null equilibrium is obtained using a novel nonlinear semigroup approach. A quadratic form Lyapunov functional is considered via a Lur’e type linear operator inequality. A sufficient strict circle criterion of solvability of the latter is found, using the solution of an operator Riccati equation by a novel self contained exposition, via reciprocal systems with bounded generating operators as recently studied and used by R.F. Curtain. The noncoercive case is finally considered using, in a novel way, LaSalle’s invariance principle.

On the design and synthesis of limit cycles using switching linear systems

This article deals with the design and synthesis of limit cycles for a class of switched linear systems. This work is motivated by an application in the context of electrical networks, but the methodologies can be applied in other engineering fields as well. Several methods for the design and synthesis of limit cycles are presented. Based on a monodromy matrix associated with a periodically switched system, a design method and two feedback strategies are developed. The first strategy is based on linear feedback design using pole placement. The second strategy is based on the observation that certain state-dependent switching strategies can be implemented by means of a simple nonlinear output feedback controller. Advantages of this latter strategy are not only the ease with which the switching strategy can be implemented, but also the fact that classical techniques may also be used to ascertain the stability of the resulting limit cycle. Our next contribution is the development of a novel frequency domain-based approach to limit cycle design. This approach is based on the observation that the existence of certain limit cycles can be deduced from an infinity of circle criteria generated by a family of periodic systems. By making use of recent results, this observation can be used to develop a one-parameter spectral search to deduce the approximate frequencies of feasible limit cycles. Having selected a frequency of oscillation, one may then make use of the aforementioned nonlinear elements to realise a switching strategy that generates a stable limit cycle with given frequency and amplitude. Examples are given to illustrate the effectiveness of the approaches presented.

Dynamic Anti-Windup Compensator Design Considering Behavior of Controller State

The purpose of this paper is to study the determination of L2 gain performance index in a design method of anti-windup compensator. Since the purpose of the anti-windup compensation is to control the controller state, we introduce a new L2 gain performance index that contains both the plant state and the controller state. Local control design technique which is based on the circle criterion is used for anti-windup compensator synthesis, while global control performance analysis is conducted using Popov criterion. Better response is obtained by tuning the two weighting matrices on the states of the performance index, which is demonstrated by simulation and experiment examples.

Curved Trajectory Tracking for Surface Vessels under Constant External Disturbances

Controlling a vessel in the presence of constant, unknown disturbances requires control methods capable of adjusting to this situation. In this paper we use the multivariable circle criterion, extended to linear time-varying systems, and propose a method for curved trajectory tracking based on conditional integrators. This control method combines the robustness of sliding mode control and integral action, while avoiding their inherent drawbacks like chattering and integrator wind-up. The problem of curved trajectory tracking in the horizontal plane is discussed, showing a separation between the design of the tracking control law and the disturbance rejection control law. Simulation results are provided to illustrate the effectiveness of the proposed method.

Adaptive NN Backstepping Output-Feedback Control for Stochastic Nonlinear Strict-Feedback Systems With Time-Varying Delays

For the first time, this paper addresses the problem of adaptive output-feedback control for a class of uncertain stochastic nonlinear strict-feedback systems with time-varying delays using neural networks (NNs). The circle criterion is applied to designing a nonlinear observer, and no linear growth condition is imposed on nonlinear functions depending on system states. Under the assumption that time-varying delays exist in the system output, only an NN is employed to compensate for all unknown nonlinear terms depending on the delayed output, and thus, the proposed control algorithm is more simple even than the existing NN backstepping control schemes for uncertain systems described by ordinary differential equations. Three examples are given to demonstrate the effectiveness of the control scheme proposed in this paper.

A NonLinear Observer of an Electrical Transformer: A Bond Graph Approach

A bond graph model of an electrical transformer including the nonlinear saturation is presented. A nonlinear observer for the transformer based on multivariable circle criterion in the physical domain is proposed. In order to show the saturation and hysteresis effects on the electrical transformer, simulation results are obtained. Finally, the paper describes that convergence of the estimates to the true states is achieved.

Nonlinear and Filtered Force/Position Mappings in Bilateral Teleoperation With Application to Enhanced Stiffness Discrimination

Motivated by applications involving soft-tissue manipulation such as robotic surgery, the transparency objectives in bilateral teleoperation are redefined to include monotonic nonlinear and linear-time-invariant filter mappings between the master/slave position and force signals. To demonstrate the utility of the new performance measures, a stiffness discrimination telemanipulation task of soft environments is considered. A nonlinear force mapping can enhance stiffness discrimination thresholds as shown through a set of psychophysics experiments. Lyapunov-based adaptive motion/force controllers are presented that can achieve the new transparency objectives in the presence of dynamic uncertainty in the master, slave, user, and environment and in the absence of time delay. Given <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> known bounds on unknown dynamic parameters, a framework for robust stability analysis is proposed that uses an off-axis circle criterion and the Nyquist envelope of interval plant systems. Nonlinear- and linear-filtered mappings are achieved in experiments with a two-axis teleoperation system.

Proportional navigation-based collision avoidance for UAVs

A collision avoidance algorithm for unmanned aerial vehicles (UAVs) based on the conventional proportional navigation (PN) guidance law is investigated. The proportional navigation guidance law being applied to a wide range of missile guidance problems is tailored to the collision avoidance of UAVs. This can be accomplished by guiding the relative velocity vector of the aircraft to a vector connecting the current aircraft position to the safety boundary of the target aircraft. Stability of the proposed algorithm is also studied using the circle criterion. The stability condition can be established by choosing the navigation coefficient within a certain bound. The guidance law is extended to 3-dimensional maneuver problems. Inherent simplicity and robustness of the PN guidance law provides satisfactory collision avoidance performance with different initial conditions.

An Inner-Loop Controller Guaranteeing Robust Transient Performance for Uncertain MIMO Nonlinear Systems

An output-feedback controller has been recently proposed that has the following features: 1) it is an inner-loop controller so that it can be added on the existing closed-loop system working in harmony with a pre-designed (possibly non-robust) outer-loop controller; 2) it robustifies the closed-loop system in a way that the uncertain plant under external disturbance behaves like a disturbance-free nominal plant; and 3) it recovers the trajectory of the nominal closed-loop system in time domain. However, it is restricted to the single-input-single-output nonlinear systems. In this technical note, we extend this result for a class of multi-input-multi-output (MIMO) nonlinear systems having the same number of inputs and outputs. The tools used in this synthesis are the singular perturbation theory and the multi-variable circle criterion. An example shows the effectiveness of the proposed method.

Control for Actuator Arrays

Actuator arrays are planar arrangements of simple actuators that cooperate to translate and orient objects. This paper derives the equations of motion for manipulating an object in stick/slip contact with the actuators. A controller derived from kinematics considerations is presented and its stability analyzed with the multivariable circle criterion. Stability results are verified through simulation and experimental results on a 20 unit macroscopic actuator array.

New absolute stability criteria for time-delay Lur'e systems with sector-bounded nonlinearity

This paper is concerned with the problem of absolute stability of time-delay Lur'e systems with sector-bounded nonlinearity. Several novel criteria are presented by using a Lur'e–Postnikov function. For a general Lur'e system with known time delay, the absolute stability of it is analyzed by solving a set of linear matrix inequalities (LMIs). The maximum upper bound of the allowable time delay for a general Lur'e system is derived by solving a convex optimization problem. The feasibility of the LMIs implies some frequency-domain interpretations which are similar to the frequency-domain inequalities in the circle criterion and the Popov criterion. Copyright © 2009 John Wiley & Sons, Ltd.

Circle Criterion을 이용한 FLC의 안정도에 대한 고찰

Most of FLC received input data from error e and change-of-error e' with no relation with system complexity. Basic scheme follows typical PD and PI or PID Controller and that has been developed through fixed ME In this paper, We studied the relationship between MF and system response and system response through changing Fuzzy variable of consequence MF and propose the simple FLC using this relationship. The response of FLC is changed according to the width of Fuzzy variable of consequence MF. As changing the Fuzzy variable of consequence MF shows various nonlinear characteristic, we studied the relation between response and MF using analytical method. We designed the effective FLC using three-variable MF and nine rules and took simulation for verification. In this study, we propose the method to design system with FLC in stability point which is an impotent characteristic of designing system. The circle criterion which is adapted to analysis the nonlinear system is put to use for proposed method. Since SISO FLC has a time-invariant and odd characteristic we can use the critical point not disk which is generally used to determine the stability in the circle criterion, to determine the stability. Using this, we can get the maximum critical point plot of SISO FLC with changing the consequence fuzzy variables. The predetermined critical point plot of FLC can be used to decide the region of the system to be stable. This method is effectively used to design the SISO FLC.