Stability analysis for linear discrete-time systems subject to actuator saturation

In this paper, stability of discrete-time linear systems subject to actuator saturation is analyzed by combining the saturation-dependent Lyapunov function method with Finsler’s lemma. New stability test conditions are proposed in the enlarged space containing both the state and its time difference which allow extra degree of freedom and lead to less conservative estimation of the domain of attraction. Furthermore, based on this result, a useful lemma and an iterative LMI-based optimization algorithm are also developed to maximize an estimation of domain of attraction. A numerical example illustrates the effectiveness of the proposed methods.

STOCHASTIC OPTIMAL CONTROL OF STRONGLY NONLINEAR SYSTEMS UNDER WIDE-BAND RANDOM EXCITATION WITH ACTUATOR SATURATION

A bounded optimal control strategy for strongly non-linear systems under non-white wide-band random excitation with actuator saturation is proposed. First, the stochastic averaging method is introduced for controlled strongly non-linear systems under wide-band random excitation using generalized harmonic functions. Then, the dynamical programming equation for the saturated control problem is formulated from the partially averaged Itō equation based on the dynamical programming principle. The optimal control consisting of the unbounded optimal control and the bounded bang-bang control is determined by solving the dynamical programming equation. Finally, the response of the optimally controlled system is predicted by solving the reduced Fokker-Planck-Kolmogorov （FPK） equation associated with the completed averaged Itō equation. An example is given to illustrate the proposed control strategy. Numerical results show that the proposed control strategy has high control effectiveness and efficiency and the chattering is reduced significantly comparing with the bang-bang control strategy.

Stability analysis for continuous-time systems with actuator saturation

The aim of this paper is to study the determination of the stability regions for continuous-time systems subject to actuator saturation. Using an affine saturation-dependent Lyapunov function, a new method is proposed to obtain the estimation of the domain of attraction of the closed-loop system. A family of linear matrix inequalities （LMIs） that provides sufficient conditions for the existence of this type of Lyapunov function are presented. The results obtained in this paper can reduce the conservativeness compared with the existing ones. Numerical examples are given to illustrate the effectiveness of the proposed results.

PID Control of Planar Nonlinear Uncertain Systems in the Presence of Actuator Saturation

This paper investigates PID control design for a class of planar nonlinear uncertain systems in the presence of actuator saturation.Based on the bounds on the growth rates of the nonlinear uncertain function in the system model,the system is placed in a linear differential inclusion.Each vertex system of the linear differential inclusion is a linear system subject to actuator saturation.By placing the saturated PID control into a convex hull formed by the PID controller and an auxiliary linear feedback law,we establish conditions under which an ellipsoid is contractively invariant and hence is an estimate of the domain of attraction of the equilibrium point of the closed-loop system.The equilibrium point corresponds to the desired set point for the system output.Thus,the location of the equilibrium point and the size of the domain of attraction determine,respectively,the set point that the output can achieve and the range of initial conditions from which this set point can be reached.Based on these conditions,the feasible set points can be determined and the design of the PID control law that stabilizes the nonlinear uncertain system at a feasible set point with a large domain of attraction can then be formulated and solved as a constrained optimization problem with constraints in the form of linear matrix inequalities(LMIs).Application of the proposed design to a magnetic suspension system illustrates the design process and the performance of the resulting PID control law.

Adaptive fault-tolerant control of linear time-invariant systems in the presence of actuator saturation

This paper studies the problem of designing adaptive fault-tolerant controllers for linear tirne-invariant systems with actuator saturation. New methods for designing indirect adaptive fault-tolerant controllers via state feedback are presented for actuator fault compensations. Based on the on-line estimation of eventual faults, the adaptive fault-tolerant controller parameters are updating automatically to compensate the fault effects on systems. The designs are developed in the framework of linear matrix inequality （LMI） approach, which can enlarge the domain of attraction of closed-loop systems in the cases of actuator saturation and actuator failures. Two examples are given to illustrate the effectiveness of the design method.

Analysis and design of output feedback control systems with actuator saturation

A dynamic output feedback controller design approach based on cone complementary linearisation procedure is proposed for linear time-invariant （LTI） systems with actuator saturation. First, the estimation of the domain of attraction is given. Then, a design method to find a larger estimation of the domain of attraction is presented. In the process of design, nonconvex conditions are obtained, so a cone complementary linearisation procedure is exploited to solve the nonconvex feasibility problem. Two examples are given to illustrate the efficiency of the design method.

Robust stabilization of switched discrete-time systems with actuator saturation

This paper studies the robust stabilization problem of switched discrete-time linear systems subject to actuator saturation. New switched saturation-dependent Lyapunov functions are exploited to design a robust stabilizing state feedback controller that maximizes an estimation of the domain of attraction. The design problem of controller （coefficient matrices） is then reduced to an optimization problem with linear matrix inequality （LMI） constraints. A numerical example is given to show the effectiveness of the proposed method.

Distributed Model Predictive Control with Actuator Saturation for Markovian Jump Linear System

This paper is concerned with the distributed model predictive control(MPC) problem for a class of discrete-time Markovian jump linear systems(MJLSs) subject to actuator saturation and polytopic uncertainty in system matrices. The global system is decomposed into several subsystems which coordinate with each other. A set of distributed controllers is designed by solving a min-max optimization problem in terms of the solutions of linear matrix inequalities(LMIs). An iterative algorithm is developed to achieve the online computation. Finally,a simulation example is employed to show the effectiveness of the proposed algorithm.

Adaptive fault-tolerant control of linear systems with actuator saturation and L_2-disturbances

This paper studies the problem of designing adaptive fault-tolerant H-infinity controllers for linear timeinvariant systems with actuator saturation. The disturbance tolerance ability of the closed-loop system is measured by an optimal index. The notion of an adaptive H-infinity performance index is proposed to describe the disturbance attenuation performances of closed-loop systems. New methods for designing indirect adaptive fault-tolerant controllers via state feedback are presented for actuator fault compensations. Based on the on-line estimation of eventual faults, the adaptive fault-tolerant controller parameters are updated automatically to compensate for the fault effects on systems. The designs are developed in the framework of the linear matrix inequality （LMI） approach, which can guarantee the disturbance tolerance ability and adaptive H-infinity performances of closed-loop systems in the cases of actuator saturation and actuator failures. An example is given to illustrate the efficiency of the design method.

A Delay-Dependent Anti-Windup Compensator for Wide-Area Power Systems With Time-Varying Delays and Actuator Saturation

In this paper, a delay-dependent anti-windup compensator is designed for wide-area power systems to enhance the damping of inter-area low-frequency oscillations in the presence of time-varying delays and actuator saturation using an indirect approach. In this approach, first, a conventional wide-area damping controller is designed by using output feedback with regional pole placement approach without considering time-varying delays and actuator saturation. Then to mitigate the effect of both time-varying delays and actuator saturation, an add-on delay-dependent anti-windup compensator is designed. Based on generalized sector conditions, less conservative delay-dependent sufficient conditions are derived in the form of a linear matrix inequality(LMI) to guarantee the asymptotic stability of the closedloop system in the presence of time-varying delays and actuator saturation by using Lyapunov-Krasovskii functional and Jensen integral inequality. Based on sufficient conditions, the LMI-based optimization problem is formulated and solved to obtain the compensator gain which maximizes the estimation of the region of attraction and minimizes the upper bound of-gain. Nonlinear simulations are performed first using MATLAB/Simulink on a two-area four-machine power system to evaluate the performance of the proposed controller for two operating conditions, e.g.,3-phase to ground fault and generator 1 terminal voltage variation. Then the proposed controller is implemented in real-time on an OPAL-RT digital simulator. From the results obtained it is verified that the proposed controller provides sufficient damping to the inter-area oscillations in the presence of time-varying delays and actuator saturation and maximizes the estimation of the region of attraction.

Design of switched linear systems in the presence of actuator saturation and L-infinity disturbances

This paper considers the problem of disturbance tolerance/rejection of a switched system resulting from a family of linear systems subject to actuator saturation and E-infinity disturbances. For a given set of linear feedback gains, a given switching scheme and a given bound on the E-infinity norm of the disturbances, conditions are established, in terms of linear or bilinear matrix inequalities, under which a set of a certain form is invariant for a given switched linear system in the presence of actuator saturation and E-infinity disturbances, and the closed-loop system possesses a certain level of disturbance rejection capability. With these conditions, the design of feedback gains and switching scheme can be formulated and solved as constrained optimization problems. Disturbance tolerance is measured by the largest bound on the disturbances for which the trajectories starting from a given set remain bounded. Disturbance rejection is measured either by the E-infinity norm of the system output or by the system＇s ability to steer its state into and/or keep it within a small neighborhood of the origin. In the event that all systems in the family are identical, the switched system reduces to a single system under a switching feedback law. Simulation results show that such a single system under a switching feedback law could have stronger disturbance tolerance/rejection capability than a single linear feedback law can.

Simultaneous anti-windup synthesis for linear systems subject to actuator saturation

A synthesis method for global stability and performance of input constrained linear systems, which uses a linear outputfeedback controller and a static anti-windup compensator is investigated. Different from the traditional two-step anti-windup design procedure, the proposed method synthesizes all controller parameters simultaneously. Sufficient conditions for global stability and minimizing the induced L2 gain are formulated and solved as a linear matrix inequalities（LMIs） optimization problem, which also provides an opportunity to search for a better performance tradeoff between the linear controller and the anti-windup compensator.The well-posedness of the close-loop system is also guaranteed.Simulation results show the effectiveness of the proposed method.

STOCHASTIC OPTIMAL VIBRATION CONTROL OF PARTIALLY OBSERVABLE NONLINEAR QUASI HAMILTONIAN SYSTEMS WITH ACTUATOR SATURATION

An optimal vibration control strategy for partially observable nonlinear quasi Hamiltonian systems with actuator saturation is proposed. First,a controlled partially observable non-linear system is converted into a completely observable linear control system of finite dimension based on the theorem due to Charalambous and Elliott. Then the partially averaged It stochastic differential equations and dynamical programming equation associated with the completely observable linear system are derived by using the stochastic averaging method and stochastic dynamical programming principle,respectively. The optimal control law is obtained from solving the final dynamical programming equation. The results show that the proposed control strategy has high control effectiveness and control effciency.

Finite-time control of formation system for multiple flight vehicles subject to actuator saturation

This paper investigates the problem of formation tracking control for multiple flight vehicle(MFV) system considering actuator saturation constraints. First, the formation tracking control model is established. Then, the problem of formation control of the MFV system is converted to the convergence of a dynamical system, which is obtained by using the differential geometry theory.A class of saturation functions is introduced, and on this basis a second-order finite-time formation control protocol is developed.With the help of the homogeneous theory and Lasalle's invariance principle, it is theoretically proved that the designed formation protocol could complete the formation task in finite time, and the control inputs are shown to remain within their available actuating limits. Finally, simulations are performed to verify the effectiveness of the scheme.

Relative Position and Attitude Control for Drag-Free Satellite with Prescribed Performance and Actuator Saturation

An adaptive prescribed performance control scheme is proposed for the drag free satellite in the presence of actuator saturation and external disturbances.The relative translation and rotation dynamics between the test mass and outer satellite are firstly derived.To guarantee prescribed performance bounds on the transient and steady control errors of relative states,a performance constrained control law is formulated with an error transformed function.In addition,the requirements to know the system parameters and the upper bound of the external disturbance in advance have been eliminated by adaptive updating technique.A command filter is concurrently used to overcome the problem of explosion of complexity inherent in the backstepping control design.Subsequently,a novel auxiliary system is constructed to compensate the adverse effects of the actuator saturation constrains.It is proved that all signals in the closed?loop system are ultimately bounded and prescribed performance of relative position and attitude control errors are guaranteed.Finally,numerical simulation results are given to demonstrate the effectiveness of the proposed approach.

Non-fragile stabilisation of nonlinear switched systems with actuator saturation

For nonlinear continuous-time switched systems,the problem ofhowto overcome the controller vulnerability is studied when the saturating actuator is considered.The sufficient condition of non-fragile stabilisation of the system is derived by using the method of multiple Lyapunov functions.Then,a switching law and the non-fragile state feedback controllers are designed such that the closed-loop system can be asymptotically stabilised at the origin.Finally,when some scalar parameters of the closed-loop system are given,the design issue of the non-fragile state feedback controllers and the switching law,which aim at enlarging the estimation of domain of attraction for closed-loop system,is transformed into a convex optimisation issue with linear matrix inequalities(LMI)constraints,and a numerical example is given to verify the effectiveness of the proposed method.

On estimation of attraction domain for port-controlled Hamiltonian systems subject to actuator saturation

This paper investigates the estimation of domain of attraction for nonlinear port controlled Hamiltonian （PCH） systems with actuator saturation （AS）. Several conditions are established under which an ellipsoid is contractively invariant, and thus can be employed to find the biggest ellipsoid contained in the domain of attraction. It is shown that the proposed conditions can be expressed in the form of the linear matrix inequalities （LMIs） optimization problem with constraints. Study of an illustrative example shows that the proposed method works very well in estimating the domain of attraction for some classes of nonlinear PCH systems with AS.

Robust H-infinity control for uncertain discrete-time Markovian jump systems with actuator saturation

The design of robust H-infinity controller for uncertain discrete-time Markovianjump systems with actuator saturation is addressed in this paper. The parameter uncertainties are assumed to be norm-bounded. Linear matrix inequality （LMI） conditions are proposed to design a set of controllers in order to satisfy the closed-loop local stability and closed-loop H-infinity performance. Using an LMI approach, a set of state feedback gains is constructed such that the set of admissible initial conditions is enlarged and formulated through solving an optimization problem. A numerical example is given to illustrate the effectiveness of the proposed methods.

Distributed fixed-time attitude coordinated control for multiple spacecraft with actuator saturation

This paper investigates the distributed fixed-time attitude coordinated control problem for multiple spacecraft subject to actuator saturation under the directed topology. First, a distributed fixed-time observer is presented for each follower spacecraft to estimate the leader spacecraft’s states. Compared with the commonly used fixed-time observer, the settling time of the proposed fixed-time observer can be easily adjusted by some free design parameters. Next, a distributed fixed-time control scheme is derived by using the estimates of the leader spacecraft’s states and the adding a power integrator technique. When considering actuator saturation, an auxiliary system is utilized to compensate the saturation. Further, a rigorous theoretical proof is provided to show that the practical fixed-time stability of the closed-loop system is ensured. Finally, simulation results illustrate the benefits and effectiveness of the developed control scheme.

Control and Optimization of Sampled-Data Systems with Quantization and Actuator Saturation

This paper is concerned with control and optimization for a sampled-data system with quantization and actuator saturation. Based quantization and actuator saturation a controller is introduced. The corresponding closed loop system is transformed into a system with input saturation and bounded external disturbance. A new Lyapunov functional is constructed to derive a sample-interval dependent condition on the existence of a state feedback controller such that the closed-loop system is exponentially convergent to an ultimate ellipsoid for the initial condition starting from some initial ellipsoid. Based on the condition, the desired controller is designed. Furthermore, optimization problems about the sample-interval, the ultimate ellipsoid and the initial ellipsoid are formulated. An example is given to illustrate the effectiveness of the proposed method.