Robustness Analysis of Discrete-time Indirect Model Reference Adaptive Control with Normalized Adaptive Laws

For a class of discrete-time systems with unmodeled dynamics and bounded disturbance, the design and analysis of robust indirect model reference adaptive control （MRAC） with normalized adaptive law are investigated. The main work includes three parts. Firstly, it is shown that the constructed parameter estimation algorithm not only possesses the same properties as those of traditional estimation algorithms, but also avoids the possibility of division by zero. Secondly, by establishing a relationship between the plant parameter estimate and the controller parameter estimate, some similar properties of the latter are also established. Thirdly, by using the relationship between the normalizing signal and all the signals of the closed-loop system, and some important mathematical tools on discrete-time systems, as in the continuous-time case, a systematic stability and robustness analysis approach to the discrete indirect robust MRAC scheme is developed rigorously.

Optimal Guaranteed Cost Control via Static Output Fedback for Uncertain Discrete-Time Systems

目的研究在状态空间模型中的状态及控制矩阵中含有范数有界参数不确定线性离散系统的最优保价静态输出反馈控制问题．方法给出了系统二次代价指标的一个上界，并利用拉格朗日乘子法优化了该界．结果与结论给出了保证闭环系统二次稳定且使得二次代价指标界达到最小的静态输出反馈控制器存在的充分条件．并提供了一个求解输出反馈增益的数值算法．

Delay-dependent robust H_∞ control for uncertain discrete time-delay fuzzy systems

The robust H∞ control problem of norm bounded uncertain discrete Takagi-Sugeno （T-S） fuzzy systems with state delay is addressed. First, by constructing an appropriate basis-dependent Lyapunov-Krasovskii function, a new delay-dependent sufficient condition on robust H∞-disturbance attenuation is presented, in which both robust stability and prescribed H∞ performance are guaranteed to be achieved. Then based on the condition, a delay-dependent robust Hoo controller design scheme is developed in term of a convex algorithm. Finally, examples are given to illustrate the effectiveness of the proposed method.

LMI-based robust control of uncertain discrete-time piecewise affine systems

The main contribution of this paper is to present stability synthesis results for discrete-time piecewise affine （PWA） systems with polytopic time-varying uncertainties and for discrete-time PWA systems with norm-bounded uncertainties respectively.The basic idea of the proposed approaches is to construct piecewise-quadratic （PWQ） Lyapunov functions to guarantee the stability of the closed-loop systems.The partition information of the PWA systems is taken into account and each polytopic operating region is outer approximated by an ellipsoid,then sufficient conditions for the robust stabilization are derived and expressed as a set of linear matrix inequalities （LMIs）.Two examples are given to illustrate the proposed theoretical results.

Book Announcement of L. Celentano, Robust Tracking Controllers Design with Generic References for Continuous and Discrete Uncertain Linear SISO Systems, LAP LAMBERT Academic Publishing, 2012

In this book new results on controller design techniques for the tracking of generic reference inputs are presented. They allow the design of a controller for an uncertain process, either continuous or discrete-time, without zeros, and with measurable state. The controller guarantees that the control system is Type 1 and has the desired constant gain and poles or that the control system tracks, with a specified maximum error and with a specified maximum time constant, a generic reference with bounded derivative (variation in the discrete-time case), also in the presence of a generic disturbance with bounded derivative (variation). In addition, it is considered the case in which the reference is known a priori. The utility and the efficiency of the proposed methods are illustrated with attractive and significant examples of motion control and temperature control. This book is useful for the design of control systems, especially for manufacturing systems, that are versatile, fast, precise and robust.

Mixed Gl2／GH2 multi-channel multi-objective control synthesis for discrete time systems

This paper proposes a new approach for multi-objective robust control. The approach extends the standard generalized l2 (Gl2) and generalized H2(GHz) conditions to a set of new linear matrix inequality (LMI) constraints based on a new stability condition. A technique for variable parameterization is introduced to the multi-objective control problem to preserve the linearity of the synthesis variables. Consequently, the multi-channel multi-objective mixed Gl2/GH2 control problem can be solved less conservatively using computationally tractable algorithms developed in the paper.

Robust reliable H_∞ control for discrete-time Markov jump linear systems with actuator failures

The robust reliable H∞ control problem for discrete-time Markovian jump systems with actuator failures is studied. A more practical model of actuator failures than outage is considered. Based on the state feedback method, the resulting closed-loop systems are reliable in that they remain robust stochastically stable and satisfy a certain level of H∞ disturbance attenuation not only when all actuators are operational, but also in case of some actuator failures, The solvability condition of controllers can be equivalent to a feasibility problem of coupled linear matrix inequalities （LMIs）. A numerical example is also given to illustrate the design procedures and their effectiveness.

Delay-dependent robust control for uncertain discrete singular systems with time-varying delay

The design problem of delay-dependent robust control for uncertain discrete singular systems with time-varying delay is addressed in this paper. The uncertainty is assumed to be norm-bounded. By establishing a finite sum inequality based on quadratic terms, a new delay-dependent robust stability condition is derived and expressed in terms of linear matrix inequalities (LMIs). A suitable robust state feedback control law is presented, which guarantees that the resultant closed-loop system is regular, causal and stable for all admissible uncertainties. Numerical examples are given to demonstrate the applicability of the proposed method.

Improved Results on Robust H_∞ Control of Uncertain Discrete-time Systems with Time-varying Delay

In this paper, the robust H∞ control problem for uncertain discrete-time systems with time-varying state delay is con- sidered. Based on the Lyapunov functional method, and by resorting to the new technique for estimating the upper bound of the difference of the Lyapunov functional, a new less conservative sufficient condition for the existence of a robust H∞ controller is obtained. Moreover, the cone complementary linearisation procedure is employed to solve the nonconvex feasibility problem. Finally, several numerical examples are presented to show the effectiveness and less conservativeness of the proposed method.

Adaptive Sensor-Fault Tolerant Control of Unmanned Underwater Vehicles With Input Saturation

This paper investigates the tracking control problem for unmanned underwater vehicles(UUVs)systems with sensor faults,input saturation,and external disturbance caused by waves and ocean currents.An active sensor fault-tolerant control scheme is proposed.First,the developed method only requires the inertia matrix of the UUV,without other dynamic information,and can handle both additive and multiplicative sensor faults.Subsequently,an adaptive fault-tolerant controller is designed to achieve asymptotic tracking control of the UUV by employing robust integral of the sign of error feedback method.It is shown that the effect of sensor faults is online estimated and compensated by an adaptive estimator.With the proposed controller,the tracking error and estimation error can asymptotically converge to zero.Finally,simulation results are performed to demonstrate the effectiveness of the proposed method.

Robustness analysis and distributed control of a networked system with time-varying delays

This paper is concerned with the robustness analysis and distributed output feedback control of a networked system with uncertain time-varying communication delays.This system consists of a collection of linear time-invariant subsystems that are spatially interconnected via an arbitrary directed network.Using a dissipation inequality that incorporates dynamic hard lQCs(integral quadratic constraints)for the delay uncertainties,we derive some sufficient robustness conditions in the form of coupled linear matrix inequalities,in which the couplld parts reflect the interconnection structure of the system.We then provide a procedure to construct a distributed controller to ensure the robust stability of the closed-loop system and to achieve a prescribed lzgain performance.The effectiveness of the proposed approach is demonstrated by some numerical examples.

Delay-Dependent Robust Passive Control for Uncertain Discrete-Time Systems with Time Delays

This paper considers the problem of robust passive control for uncertain discrete systems with time-varying delays. We pay attention to designing a state feedback controller which guarantees the passivity of the closed-loop system for all admissible uncertainties. In terms of a linear matrix inequality, a sufficient condition for the solvability of this problem is presented and the explicit expression of the desired state feedback controller is given.

Robust Suboptimal Guaranteed Cost Control for 2-D Discrete Systems Described by Fornasini-Marchesini First Model

This paper considers the guaranteed cost control problem for a class of two-dimensional (2-D) uncertain discrete systems described by the Fornasini-Marchesini (FM) first model with norm-bounded uncertainties. New linear matrix inequality (LMI) based characterizations are presented for the existence of static-state feedback guaranteed cost controller which guarantees not only the asymptotic stability of closed loop systems, but also an adequate performance bound over all the admissible parameter uncertainties. Moreover, a convex optimization problem is formulated to select the suboptimal guaranteed cost controller which minimizes the upper bound of the closed-loop cost function.

Robust sliding mode control for uncertain discrete time systems

A novel variable structure control (VSC) strategy with a dynamic disturbance compensator based on the reaching law for a class of uncertain discrete systems is presented. The robust stability to disturbance and the system dynamics in the vicinity of the switching plane are studied. A measure of the uncertain parameters and external disturbance is obtained through delaying every sampling time. Theoretical analysis and experimental simulation results demonstrate that the dynamic performance and robustness of the closed-loop system are improved effectively.

Robust passive control for discrete-time T-S fuzzy systems with delays

This article deals with the robust stability analysis and passivity of uncertain discrete-time Takagi- Sugeno （T-S） fuzzy systems with time delays. The T-S fuzzy model with parametric uncertainties can approximate nonlinear uncertain systems at any precision. A sufficient condition on the existence of robust passive controller is established based on the Lyapunov stability theory. With the help of linear matrix inequality （LMI） method, robust passive controllers are designed so that the closed-loop system is robust stable and strictly passive. Furthermore, a convex optimization problem with LMI constraints is formulated to design robust passive controllers with the maximum dissipation rate. A numerical example illustrates the validity of the proposed method.

Fractional Order Proportional Integral Derivative Controller Design and Simulation for Bioengineering Systems

This paper deals with the study of fractional order system tuning method based on Factional Order Proportional Integral Derivative( FOPID) controller in allusion to the nonlinear characteristics and fractional order mathematical model of bioengineering systems. The main contents include the design of FOPID controller and the simulation for bioengineering systems. The simulation results show that the tuning method of fractional order system based on the FOPID controller outperforms the fractional order system based on Fractional Order Proportional Integral( FOPI) controller. As it can enhance control character and improve the robustness of the system.

Analytical design of PI controller for AQM with robustness adjustability

Based on a linearized TCP/AQM model,a new proportional integral(PI)controller design approach is proposed.This analytical approach applies H_(∞) optimization and internal model control(IMC)theory to design active queue management(AQM)routers that support transmission control protocol(TCP)flows.The most important feature of the proposed scheme lies in that it can be explicitly tuned with a single parameter for the trade-off between performance and stability of the AQM control system.It is thus flexible and easy to use in design.The proposed method and the designed PI controller are verified and compared with other existing AQM schemes using ns-2 simulator.The results show the advantages of the new PI controller design approach for AQM routers supporting TCP flows.

Robust Fuzzy Tracking Control for Nonlinear Networked Control Systems with Integral Quadratic Constraints

This paper investigates the robust tracking control problcm for a class of nonlinear networked control systems （NCSs） using the Takagi-Sugeno （T-S） fuzzy model approach. Based on a time-varying delay system transformed from the NCSs, an augmented Lyapunov function containing more useful information is constructed. A less conservative sufficient condition is established such that the closed-loop systems stability and time-domain integral quadratic constraints （IQCs） are satisfied while both time-varying network- induced delays and packet losses are taken into account. The fuzzy tracking controllers design scheme is derived in terms of linear matrix inequalities （LMIs） and parallel distributed compensation （PDC）. Furthermore, robust stabilization criterion for nonlinear NCSs is given as an extension of the tracking control result. Finally, numerical simulations are provided to illustrate the effectiveness and merits of the proposed method.

Optimal dispatching method for integrated energy system based on robust economic model predictive control considering source-load power interval prediction

Effective source-load prediction and reasonable dispatching are crucial to realize the economic and reliable operations of integrated energy systems(IESs).They can overcome the challenges introduced by the uncertainties of new energies and various types of loads in the IES.Accordingly,a robust optimal dispatching method for the IES based on a robust economic model predictive control(REMPC)strategy considering source-load power interval prediction is proposed.First,an operation model of the IES is established,and an interval prediction model based on the bidirectional long short-term memory network optimized by beetle antenna search and bootstrap is formulated and applied to predict the photovoltaic power and the cooling,heating,and electrical loads.Then,an optimal dispatching scheme based on REMPC is devised for the IES.The source-load interval prediction results are used to improve the robustness of the REPMC and reduce the influence of source-load uncertainties on dispatching.An actual IES case is selected to conduct simulations;the results show that compared with other prediction techniques,the proposed method has higher prediction interval coverage probability and prediction interval normalized averaged width.Moreover,the operational cost of the IES is decreased by the REMPC strategy.With the devised dispatching scheme,the ability of the IES to handle the dispatching risk caused by prediction errors is enhanced.Improved dispatching robustness and operational economy are also achieved.