Dynamic Output Feedback Control of Discrete-Time Systems with Actuator Nonlinearities

Abstract This paper considers the problem of stabilization of discrete-time systems with actuator nonlinearities. Specifically, dynamic, output feedback control design for discrete-time systems with time-varying, sectorbounded, input nonlinearities is addressed. The proposed framework is based on a linear matrix inequality approach and directly accounts for robust stability and robust performance over the class of actuator nonlinearities. F'urthermore, it is directly applicable to actuator saturation control and provides dynamic, output feedback controllers with guaranteed domains of attraction. The effectiveness of the approach is illustrated by a numerical example

Recent advances on filtering and control for nonlinear stochastic complex systems with incomplete information: A survey

This Article is provided by the Brunel Open Access Publishing Fund - Copyright @ 2012 Hindawi PublishingSome recent advances on the filtering and control problems for nonlinear stochastic complex systems with incomplete information are surveyed. The incomplete information under consideration mainly includes missing measurements, randomly varying sensor delays, signal quantization, sensor saturations, and signal sampling. With such incomplete information, the developments on various filtering and control issues are reviewed in great detail. In particular, the addressed nonlinear stochastic complex systems are so comprehensive that they include conventional nonlinear stochastic systems, different kinds of complex networks, and a large class of sensor networks. The corresponding filtering and control technologies for such nonlinear stochastic complex systems are then discussed. Subsequently, some latest results on the filtering and control problems for the complex systems with incomplete information are given. Finally, conclusions are drawn and several possible future research directions are pointed out.This work was supported in part by the National Natural Science Foundation of China under Grant nos. 61134009, 61104125, 61028008, 61174136, 60974030, and 61074129, the Qing Lan Project of Jiangsu Province of China, the Project sponsored by SRF for ROCS of SEM of China, the Engineering and Physical Sciences Research Council EPSRC of the UK under Grant GR/S27658/01, the Royal Society of the UK, and the Alexander von Humboldt Foundation of Germany

Observer-based anti-windup compensator design for saturated control systems using an LMI approach

AbstractIn practical control systems, actuator saturation usually induces a windup phenomenon and potentially results in system instability. Accordingly, this paper develops an observer-based auxiliary anti-windup compensation scheme to mitigate the effects of actuator limitations on the performance and stability of the controlled system. In the proposed approach, the controller output signal passing through the saturation element is treated as an external disturbance imported to the designed controller and an auxiliary controller is designed to minimize the difference between the controller output signal and the system input signal. The conditions required to maintain the system performance in the presence of actuator saturation are formulated as an LMI criterion. The L2-stability criterion of the anti-windup compensator design is also formulated as an LMI condition. It is shown that by integrating the two LMI conditions and solving the resulting optimization problem, the resulting anti-windup controller both minimizes the performance attenuation of the saturated control system and guarantees its L2-stability

Application of Lyapunov matrix inequality based unsymmetrical saturated control to a multi-vectored propeller airship

The problem of the design of a controller for a multi-vectored propeller airship is addressed. The controller includes anti-windup that takes into account unsymmetrical actuator constraints. First, a linear transformation is applied to transform the unsymmetrical constraints into symmetric constraints with an amplitude-bounded exogenous disturbance. Then, a stability condition based on a quadratic Lyapunov function for the saturated closed-loop system is proposed. The condition considers both amplitude-bounded and energy-bounded exogenous disturbances. Thus, the controller design problem is transformed into a convex optimization problem expressed in a bilinear matrix inequality form. Two controller design methods were applied: one-step controller and traditional anti-windup controller. The one-step method obtains the controller and the anti-windup compensator in one step while the anti-windup controller method separates this process into the linear controller design and the compensator design. Simulation results showed that both controllers enlarge the stability zone of the saturation system and have good tracking performance. It is shown that the anti-windup controller design method not only has a larger region of stability, but the demanded actuator output exceeds the constraints less and has a smaller anti-windup coefficient matrix compared to the one-step method

Application of Lyapunov matrix inequality based unsymmetrical saturated control to a multi-vectored propeller airship

The problem of the design of a controller for a multi-vectored propeller airship is addressed. The controller includes anti-windup that takes into account unsymmetrical actuator constraints. First, a linear transformation is applied to transform the unsymmetrical constraints into symmetric constraints with an amplitude-bounded exogenous disturbance. Then, a stability condition based on a quadratic Lyapunov function for the saturated closed-loop system is proposed. The condition considers both amplitude-bounded and energy-bounded exogenous disturbances. Thus, the controller design problem is transformed into a convex optimization problem expressed in a bilinear matrix inequality form. Two controller design methods were applied: one-step controller and traditional anti-windup controller. The one-step method obtains the controller and the anti-windup compensator in one step while the anti-windup controller method separates this process into the linear controller design and the compensator design. Simulation results showed that both controllers enlarge the stability zone of the saturation system and have good tracking performance. It is shown that the anti-windup controller design method not only has a larger region of stability, but the demanded actuator output exceeds the constraints less and has a smaller anti-windup coefficient matrix compared to the one-step method

A review of convex approaches for control, observation and safety of linear parameter varying and Takagi-Sugeno systems

This paper provides a review about the concept of convex systems based on Takagi-Sugeno, linear parameter varying (LPV) and quasi-LPV modeling. These paradigms are capable of hiding the nonlinearities by means of an equivalent description which uses a set of linear models interpolated by appropriately defined weighing functions. Convex systems have become very popular since they allow applying extended linear techniques based on linear matrix inequalities (LMIs) to complex nonlinear systems. This survey aims at providing the reader with a significant overview of the existing LMI-based techniques for convex systems in the fields of control, observation and safety. Firstly, a detailed review of stability, feedback, tracking and model predictive control (MPC) convex controllers is considered. Secondly, the problem of state estimation is addressed through the design of proportional, proportional-integral, unknown input and descriptor observers. Finally, safety of convex systems is discussed by describing popular techniques for fault diagnosis and fault tolerant control (FTC).Peer ReviewedPostprint (published version

Nonlinear control of feedforward systems with bounded signals

Published versio

Design of state-feedback controllers for linear parameter varying systems subject to time-varying input saturation

All real-world systems are affected by the saturation phenomenon due to inherent physical limitations of actuators. These limitations should be taken into account in the controller’s design to prevent a possibly severe deterioration of the system’s performance, and may even lead to instability of the closed-loop system. Contrarily to most of the control strategies, which assume that the saturation limits are constant in time, this paper considers the problem of designing a state-feedback controller for a system affected by time-varying saturation limits with the objective to improve the performance. In order to tie variations of the saturation function to changes in the performance of the closed-loop system, the shifting paradigm is used, that is, some parameters scheduled by the time-varying saturations are introduced to schedule the performance criterion, which is considered to be the instantaneous guaranteed decay rate. The design conditions are obtained within the framework of linear parameter varying (LPV) systems using quadratic Lyapunov functions with constant Lyapunov matrices and they consist in a linear matrix inequality (LMI)-based feasibility problem, which can be solved efficiently using available solvers. Simulation results obtained using an illustrative example demonstrate the validity and the main characteristics of the proposed approach.Peer ReviewedPostprint (published version

Event-triggered control for rational and Lur’e type nonlinear systems

In the present work, the design of event-triggered controllers for two classes of nonlinear systems is addressed: rational systems and Lur’e type systems. Lyapunov theory techniques are used in both cases to derive asymptotic stability conditions in the form of linear matrix inequalities that are then used in convex optimization problems as means of computing the control system parameters aiming at a reduction of the number of events generated. In the context of rational systems, state-feedback control is considered and differentialalgebraic representations are used as means to obtain tractable stability conditions. An event-triggering strategy which uses weighting matrices to strive for less events is proposed and then it is proven that this strategy does not lead to Zeno behavior. In the case of Lur’e systems, observer-based state-feedback is addressed with event generators that have access only to the system output and observed state, but it imposes the need of a dwell-time, i.e. a time interval after each event where the trigger condition is not evaluated, to cope with Zeno behavior. Two distinct approaches, exact time-discretization and looped-functional techniques, are considered to ensure asymptotic stability in the presence of the dwell-time. For both system classes, emulation design and co-design are addressed. In the emulation design context, the control law (and the observer gains, when appropriate) are given and the task is to compute the event generator parameters. In the co-design context, the event generator and the control law or the observer can be simultaneously designed. Numerical examples are presented to illustrate the application of the proposed methods.Neste trabalho é abordado o projeto de controladores baseados em eventos para duas classes de sistemas não lineares: sistemas racionais e sistemas tipo Lur’e. Técnicas da teoria de Lyapunov são usadas em ambos os casos para derivar condições de estabilidade assintótica na forma de inequações matriciais lineares. Tais condições são então utilizadas em problemas de otimização convexa como meio de calcular os parâmetros do sistema de controle, visando uma redução no número de eventos gerados. No contexto de sistemas racionais, realimentação de estados é considerada e representações algébrico-diferenciais são usadas como meio de obter condições de estabilidade tratáveis computacionalmente. Uma estratégia de disparo de eventos que usa uma medida de erro ponderado através de matrizes definidas positivas é proposta e é demonstrado que tal estratégia não gera comportamento de Zenão. No caso de sistemas tipo Lur’e, considera-se o caso de controladores com restrições de informações, a saber, com acesso apenas às saídas do sistema. Um observador de estados é então utilizado para recuperar a informação faltante. Neste contexto, é necessária a introdução de um tempo de espera (dwell time, em inglês) para garantir a inexistência de comportamento de Zenão. Todavia, a introdução do tempo de espera apresenta um desafio adicional na garantia de estabilidade que é tratado neste trabalho considerando duas técnicas possíveis: a discretização exata do sistema e o uso de looped-functionals (funcionais em laço, em uma tradução livre). Para ambas classes de sistemas, são tratados os problemas de projeto por emulação e co-design (projeto simultâneo, em uma tradução livre). No projeto por emulação, a lei de controle (e os ganhos do observador, quando apropriado) são dados a priori e a tarefa é projetar os parâmetros do gerador de eventos. No caso do co-design, o gerador de eventos e a lei de controle ou o observador são projetados simultaneamente. Exemplos numéricos são usados para ilustrar a aplicação dos métodos propostos

A state feedback input constrained control design for a 4-semi-active damper suspension system: a quasi-LPV approach

International audienceThis paper addresses a semi-active suspension control of the full vehicle equipped with 4 controlled semi-active dampers by using a full 7 degree of freedom (DOF) vertical model. First, the dissipativity conditions of the semi-active dampers are recast as saturation conditions on the control inputs. Then, the suspension controller is derived by solving a state feedback control design problem for a class of linear parameter-varying (LPV) system in the presence of actuator saturation. To this aim, a generalized sector condition for LPV system is applied to treat the nonlinearity, caused by the input saturation and to relax the stability condition. The proposed control law ensures the disturbance attenuation by reducing the L 2 gain from the disturbance to the controlled output. This controller, derived in the LPV/H ∞ framework, is based on the LMI solution for polytopic systems. Some realistic simulation results are presented in order to illustrate the effectiveness of the proposed approach