Finite L2-gain Research Articles

Improving ℒ2 Gain Performance of Linear Systems by Reset Control

In this paper, new Lyapunov-based reset rules are constructed to improve ℒ2 gain performance of linear-time-invariant (LTI) systems. By using the hybrid system framework, sufficient conditions for exponential and finite gain ℒ2 stability are presented. It is shown that the ℒ2 gain of the closed loop system with resets can be improved compared with the base system. Numerical example supports our results.

Control of plant-wide systems using dynamic supply rates

This paper presents a framework for analysis of plant-wide processes from a network perspective. Using the concept of dissipativity, the conditions for plant-wide input–output stability and performance are developed, based on the dissipativity of individual subsystems and the topology of the network of the plant-wide process. Dynamic supply rates, expressed as quadratic differential forms, are proposed not only to render dissipativity based analysis less conservative but also allow the dynamic plant-wide performance criteria to be specified in terms of desired closed loop supply rates. The links between the plant-wide supply rate, finite L2 gain in an extended input–output space and weighted H∞ norm are explored in this paper. These results lay a foundation for a supply rate-centric approach to plant-wide distributed control.

Nonlinear L2 Design for the Generator Hamiltonian System Included Excitation and PSS

In this paper, the generator included typical automatic voltage regulation (AVR) and power system stabilizer (PSS) SCR excitation system is taken as the research object, The Hamiltonian energy function and its general Hamilton control model are analyzed, on the basis of the five order Hamilton system model, positive definite conditions of the damping matrix R(x) was derived, and the system dissipation characteristics was analyzed. Using the Hamilton energy design method, the control strategy of system was designed, under the above control, the system is finite-gain L2 stable when external disturbance occurs.

Finite-gain L p consensus of multi-agent systems

This paper studies consensus problems for multi-agent systems modeled by linear time-invariant systems with external disturbances under a fixed directed communication topology. It is shown that consensus can be achieved if each agent with the same disturbance signals. But the result is different for each agent with different disturbances. In this case, the finite-gain Lp consensus is introduced to describe the effects of the external disturbance on the consensus performance. A necessary and sufficient condition for reaching finite-gain Lp consensus is presented, and analytic estimation of the Lp gain is given. A distributed algorithm is proposed to ensure that the finite-gain L2 consensus can be reached with a desired L2 gain. Numerical examples are given to illustrate the given results.

Hamiltonian Robust Controller Design of Permanent Magnet Wind Generators

In this paper, the dual-input nonlinear controller of permanent magnet wind generators was designed based on energy dissipation theory and Hamiltonian energy approach. Under the action of the Hamiltonian controller, the closed-loop system is asymptotically stable on case of no disturbances and finite-gain L2 stable in the presence of disturbances. The Hamiltonian energy approach provides us a physical insight and a new way to the controller design of nonlinear systems. The simulation results show the effectiveness of the proposed robust controller.

Event-triggered output feedback control for networked control systems using passivity: Achieving [formula omitted] stability in the presence of communication delays and signal quantization

When network induced delays are considered in the event-triggered control literature, they are typically delays from the plant to the network controller and a tight bound on the admissible delays is usually imposed based on the analysis of inter-event time to guarantee stability of the event-triggered control systems. In this paper, we introduce a framework for output feedback based event-triggered networked control systems (NCSs). The triggering condition is derived based on passivity theory which allows us to characterize a large class of output feedback stabilizing controllers. The proposed set-up enables us to consider network induced delays both from the plant to the network controller and from the network controller to the plant. We also take quantization of the transmitted signals in the communication network into consideration and we show that finite-gain L2 stability can be achieved in the presence of time-varying (or constant) network induced delays with bounded jitters, without requiring that the network induced delays be upper bounded by the inter-event time.

Performance bounds for nonlinear systems with a nonlinear ℒ2-gain property

Nonlinear ℒ2-gain is a finite gain concept that generalises the notion of conventional (linear) finite ℒ2-gain to admit the application of ℒ2-gain analysis tools of a broader class of nonlinear systems. The computation of tight comparison function bounds for this nonlinear ℒ2-gain property is important in applications such as small gain design. This article presents an approximation framework for these comparison function bounds through the formulation and solution of an optimal control problem. Key to the solution of this problem is the lifting of an ℒ2-norm input constraint, which is facilitated via the introduction of an energy saturation operator. This admits the solution of the optimal control problem of interest via dynamic programming and associated numerical methods, leading to the computation of the proposed bounds. Two examples are presented to demonstrate this approach.

Consensus and its ℒ2-gain performance of multi-agent systems with intermittent information transmissions

This article addresses the consensus problem for cooperative multiple agents with nonlinear dynamics on a fixed directed information network, where each agent can only communicate with its neighbours intermittently. A class of control algorithms is first introduced, using only intermittent relative local information. By combining tools from switching systems and Lyapunov stability theory, some sufficient conditions are established for consensus of multi-agent systems without any external disturbances under a fixed strongly connected topology. Theoretical analyses are further provided for consensus of multi-agent systems in the presence of external disturbances. It is shown that a finite ℒ2-gain performance index for the closed-loop multi-agent systems can be guaranteed if the coupling strength of the network is larger than a threshold value determined by the average communication rate and the generalised algebraic connectivity of the strongly connected topology. The results are then extended to consensus with prescribed ℒ2-gain performance with a virtual leader where the underlying topology is not necessarily strong connected or contain a directed spanning tree. Numerical simulations are finally provided to verify and visualise the theoretical analysis.

Nonlinear [formula omitted]-gain verification for nonlinear systems

The conventional (linear) notion of finite L2-gain has been extensively studied and applied in the analysis and control of both linear and nonlinear dynamical systems over the last few decades. The connection between this finite gain property and dissipation is well-known, and is fundamental to providing a verification mechanism for the property via solution of a related Hamilton–Jacobi–Bellman equation. Motivated by an interest in broadening the applicability of finite L2-gain in the analysis and control of nonlinear systems, this paper presents a generalized verification mechanism that permits nonlinear gain functions to be incorporated in the notion of finite L2-gain.

L2 stability, H∞ control of switched homogeneous nonlinear systems and their semi‐tensor product of matrices representation

SUMMARYThis paper investigates the problems of L2 stability and H∞ control of switched homogeneous nonlinear systems. This paper gives that if a switched homogeneous nonlinear system with disturbance is internally homogeneously asymptotically stable, then it has a finite L2 gain, and if a switched homogeneous nonlinear system with disturbance and controls is homogeneously stabilizable under the zero disturbance condition, its H∞ control problem is solvable under some mild conditions, and a homogeneous solution is given. Then, via the semi‐tensor product of matrices method, the aforementioned obtained results are transformed to linear‐like forms, and the aforementioned obtained Hamilton–Jacobi–Isaacs inequality is transformed to a linear‐like matrix inequality, which makes it feasible to compute the solutions by computer. Copyright © 2012 John Wiley & Sons, Ltd.

Finite-gain L2 Stability of PID Set Position Control with Anti-windup Compensation for Euler-Lagrange Systems with Actuator Saturation

Finite-gain L2 stabilization is achieved locally for a system using a PID set position controller and a newly proposed static anti-windup compensation for Euler-Lagrange systems with actuator saturation and external disturbances. In a closed-loop nonlinear system with feedback and input saturation, L2 stability of the Euler-Lagrange systems is guaranteed based on the passivity of anti-windup compensation. The control performance to counter an external disturbance added for the purpose of input saturation is verified by numerical simulations and experiments using a two-link robot arm.

Modelling and analysis of distributed networked control systems

This study reports the l2 stability problem for a class of distributed heterogeneous systems interconnected via communication channels. First, the model of distributed networked control system (DNCS) is given, taking into account both the heterogeneity of the subsystems and the non-idealisation of the communication network. The sufficient condition for the finite-gain l2 stability is then derived. A numerically solvable condition is further given based on the frequency domain result. Finally, a simulation example is provided to demonstrate the usefulness of the theoretical results obtained.

Asynchronous networked control of linear systems via L 2 -gain-based transformations: analysis and synthesis

This study presents a method to analyse the stability of the feedback interconnection of a class of systems, when the signals associated with the feedback interconnection are sampled asynchronously. A transformation based on L2-gain is designed and introduced on both sides of the interconnection. This transformation enlarges the maximum sampling time such that the interconnection remains stable. The transformation is designed in such a way that both systems have finite L2-gain and verifies the small-gain theorem. This design method makes easier the migration of wired continuous-time control loops to unwired asynchronous ones by just adding this transformation to both sides of the interconnection. The analysis is performed by using the concept of maximum sampling time that preserves small gain (MASG), starting from the continuous-time definition of the property. Finally, a synthesis method is included to obtain the transformation, assuming that the minimum sampling time available in the communication channel is given as a constraint. The synthesis method follows an iterative procedure and solves a set of matrix inequalities. We report on real experiments applied to the remote control of the rotor speeds of a quadrotor.

State Feedback Controller Synthesis to Achieve a Nonlinear L2-gain Property

AbstractThis paper generalizes the framework of nonlinear H∞-control design methodology for state feedback synthesis. Instead of controlling a system to achieve a (linear) finite L2-gain from disturbance input to penalty output, it is aimed at achieving a more general class of nonlinear L2-gain bounds. This generalization is aimed at allowing the application of the L2-gain based control framework to a larger class of nonlinear systems. State feedback controllers achieving such a generalized performance objective are synthesized based on verification results developed for the nonlinear L2-gain property. An example is included to illustrate these results.

Global asymptotic and finite-gain L<SUB align=right>2 stabilisation of port-controlled Hamiltonian systems subject to actuator saturation

The stabilisation problem for a port-controlled Hamiltonian system subject to actuator saturation and input additive external disturbances is studied. Conditions are identified under which a static output feedback law would achieve global asymptotic stabilisation. Under some additional growth conditions on the nonlinear functions involved in the system, the same feedback law would also achieve finite gain L2 stabilisation. In establishing these results, an estimate of the finite gain is also obtained.

Analytical and numerical Lyapunov functions for SISO linear control systems with first‐order reset elements

AbstractIn this paper we provide analytical and numerical Lyapunov functions that prove stability and performance of a First‐order Reset Element (FORE) in feedback interconnection with a SISO linear plant. The Lyapunov functions also allow to establish finite gain ℒ︁2 stability from a disturbance input acting at the input of the plant to the plant output. ℒ︁2 stability is established by giving a bound on the corresponding ℒ︁2 gains. The proof of stability and performance is carried out by showing that the Lyapunov functions constructed here satisfy the sufficient conditions in the main results of Nešić et al. (Automatica 2008; 44(8):2019–2026). In the paper we also point out and illustrate via a counterexample an analysis subtlety overlooked in the preliminary results of Zaccarian et al. (American Control Conference, Portland, OR, U.S.A., 2005). Copyright © 2010 John Wiley & Sons, Ltd.

Adaptive Neural Network L2-Gain Control for Unmodeled Dynamics Nonlinear System

A new control scheme is proposed for the nonlinear system with unmodeled dynamics based on HJI and adaptive neural network L2-gain controller. The aim is to make the closed-loop system a finite gain L2 stable between the disturbance and output of the system. The approach will avoid the limit of precise modelling, only need the unmodeled dynamics to be bounded without the other transcendent information. The simulation results show that the control system designed can satisfy the performance indicators proposed.

L2 Gain Stability of Switched Output Feedback Controllers for a Class of LTI Systems

Our previous work has been devoted to designing asymptotically stabilizing switching controllers for a class of second order LTI plants. Here, we extend the results of our previous work by proving that, when a plant can be asymptotically stabilized using a particular switching architecture, the overall closed-loop interconnection is also finite L2 gain stable. We shall first prove this result for a simplified problem in which a portion of the switching architecture has full access to the state of the plant and shall then extend to the case where the architecture only has access to the plant output by designing an appropriate observer.

Anti-windup compensation for systems with sensor saturation: a study of architecture and structure

This article proposes a linear dynamic anti-windup strategy for the alleviation of performance and stability problems in systems which are linear apart from saturating sensors. Unlike anti-windup compensation for systems subject to actuator saturation, there is no agreed architecture for applying anti-windup to systems with sensor saturation and therefore attention is devoted to the discussion of various candidate configurations which can be interpreted as a particular choice of a static non-linear map. The main results of the article give existence conditions for compensators which yield global exponential stability and finite ℒ2 gain of the overall non-linear closed-loop system. The existence conditions are different to those which have appeared hitherto in the literature.

NLq Theory: A Neural Control Framework with Global Asymptotic Stability Criteria

In this paper a framework for model-based neural control design is presented, consisting of nonlinear state space models and controllers, parametrized by multilayer feedforward neural networks. The models and closed-loop systems are transformed into so-called NLq system form. NLq systems represent a large class of nonlinear dynamical systems consisting of q layers with alternating linear and static nonlinear operators that satisfy a sector condition. For such NLqs sufficient conditions for global asymptotic stability, input/output stability (dissipativity with finite L2-gain) and robust stability and performance are presented. The stability criteria are expressed as linear matrix inequalities. In the analysis problem it is shown how stability of a given controller can be checked. In the synthesis problem two methods for neural control design are discussed. In the first method Narendra's dynamic backpropagation for tracking on a set of specific reference inputs is modified with an NLq stability constraint in order to ensure, e.g., closed-loop stability. In a second method control design is done without tracking on specific reference inputs, but based on the input/output stability criteria itself, within a standard plant framework as this is done, for example, in H∞ control theory and μ theory. © 1997 Elsevier Science Ltd.