Time-varying Norm-bounded Uncertainties Research Articles

Multivariable Robust Proportional-Integral-Derivative Control for Linear Quadratic Compensation of a Class of Norm-Bounded Uncertain Systems

AbstractThis paper is concerned with designing multi-input multi-output (MIMO) proportional-integral-derivative (PID) control having filtered derivative terms to achieve optimal linear quadratic performance for a class of linear uncertain MIMO systems with norm-bounded time-varying uncertainties. A necessary and sufficient condition for existence of the PID controller is obtained in terms of rank constrained linear matrix inequalities (LMIs). Using an existing penalty-function-based approximation for matrix rank minimization, an algorithm is proposed to solve these rank constrained LMIs and find PID gains. A suitable numerical example is considered to show the efficacy of the proposed approach in ensuring robust performance as compared to the existing ones. The proposed algorithm is also tested on several benchmark examples and found to be computationally much more efficient than some well-known methods.

Design of Robust Dynamic Output Feedback Event-Triggering Controllers for Nonlinear Uncertain Systems

This paper presents a design of dynamic output feedback event-triggering control for nonlinear uncertain networked control systems. The plant and actuator asynchronously transmit the measurement and control signals over two different communication channels. We address the norm-bounded time-varying parameter uncertainties in a nonlinear plant. First, considering the exogenous disturbances and noises in the control and measurement signals, sufficient conditions for the <i>L</i>₂ stability of the nonlinear networked control systems are given in the presence of the uncertainties. Then, we propose design conditions to choose the dynamic output feedback control and triggering laws in terms of linear matrix inequalities (LMIs). The proposed conditions enable the controller and event-triggering parameters to be jointly optimized to lessen the number of transmissions, guaranteeing a certain level of <i>L</i>₂ gain. Numerical examples demonstrate the effectiveness of the proposed method.

Delay-Dependent and Order-Dependent Guaranteed Cost Control for Uncertain Fractional-Order Delayed Linear Systems

This paper addresses the guaranteed cost control problem of a class of uncertain fractional-order (FO) delayed linear systems with norm-bounded time-varying parametric uncertainty. The study is focused on the design of state feedback controllers with delay such that the resulting closed-loop system is asymptotically stable and an adequate level of performance is also guaranteed. Stemming from the linear matrix inequality (LMI) approach and the FO Razumikhin theorem, a delay- and order-dependent design method is proposed with guaranteed closed-loop stability and cost for admissible uncertainties. Examples illustrate the effectiveness of the proposed method.

Robust Admissibilization for Discrete-Time Singular Systems with Time-Varying Delay

The problems of the admissibility and state feedback stabilization for discrete-time singular systems with interval time-varying delay and norm-bounded uncertainty are studied. The system is equivalently transformed into a new comparison form by decomposition. By taking advantage of the Seuret summation inequality, the reciprocally convex inequality, and some relaxation techniques, a delay-dependent criterion that ensures the admissibility of the concerned systems is established. The result on robust stabilization is also obtained by fixing some parameters. It should be pointed out that the results are less dependent on the parameters so that some conservatism is reduced. A numerical example is included to illustrate the effectiveness and improvement of the proposed methods.

Path following of a surface ship sailing in restricted waters under wind effect using robust H∞ guaranteed cost control

The path following problem of a ship sailing in restricted waters under wind effect is investigated based on Robust H∞ Guaranteed Cost Control (RHGCC). To design the controller, the ship maneuvering motion is modeled as a linear uncertain system with norm-bounded time-varying parametric uncertainty. To counteract the bank and wind effects, the integral of path error is augmented to the original system. Based on the extended linear uncertain system, sufficient conditions for existence of the RHGCC are given. To obtain an optimal robust H∞ guaranteed cost control law, a convex optimization problem with Linear Matrix Inequality (LMI) constraints is formulated, which minimizes the guaranteed cost of the close-loop system and mitigates the effect of external disturbance on the performance output. Numerical simulations have confirmed the effectiveness and robustness of the proposed control strategy for the path following goal of a ship sailing in restricted waters under wind effect.

Non-fragile exponential synchronization of delayed complex dynamical networks with transmission delay via sampled-data control

This paper is devoted to the non-fragile exponential synchronization problem of complex dynamical networks with time-varying coupling delays via sampled-data static output-feedback controller involving a constant signal transmission delay. The dynamics of the nodes contain s quadratically restricted nonlinearities, and the feedback gain is allowed to have norm-bounded time-varying uncertainty. The control design is based on a Lyapunov–Krasovskii functional, which consists of the sum of terms assigned to the individual nodes, i.e., it is constructed without merging the complex dynamical network’s nodes into a single large-scale system. In this way, the proposed design method has substantially reduced computational complexity and improved conservativeness, and guaranties non-fragile exponential stability of the error system. The sufficient stability condition is expressed in terms of linear matrix inequalities that are solvable by standard tools. The efficiency of the proposed method is illustrated by numerical examples.

A Fuzzy Lyapunov–Krasovskii Functional Approach to Sampled-Data Output-Feedback Stabilization of Polynomial Fuzzy Systems

This paper presents an output-feedback exponential stabilization condition of sampled-data polynomial fuzzy control systems under variable sampling rates. Compared with previous work, the proposed method is less conservative because of the newly developed time-dependent fuzzy Lyapunov–Krasovskii functional that is based on the conventional fuzzy Lyapunov function. Moreover, the controller is allowed to contain polynomial gain matrices, thereby improving the control performance and design flexibility. This is realized by assuming the difference between the continuous- and discrete-time state vectors as time-varying norm-bounded uncertainties, which are manipulated using a robust control technique. A new sufficient condition is introduced to cast the stability condition containing the integral term as the sum-of-square conditions. Finally, the effectiveness of the proposed method is validated by simulations.

Observer-based output feedback control of networked control systems with non-uniform sampling and time-varying delay

ABSTRACTThis paper investigates the problem of observer-based output feedback control for networked control systems with non-uniform sampling and time-varying transmission delay. The sampling intervals are assumed to vary within a given interval. The transmission delay belongs to a known interval. A discrete-time model is first established, which contains time-varying delay and norm-bounded uncertainties coming from non-uniform sampling intervals. It is then converted to an interconnection of two subsystems in which the forward channel is delay-free. The scaled small gain theorem is used to derive the stability condition for the closed-loop system. Moreover, the observer-based output feedback controller design method is proposed by utilising a modified cone complementary linearisation algorithm. Finally, numerical examples illustrate the validity and superiority of the proposed method.

Robust H1 control for a class of switched nonlinear systems

This article is concerned with the robust H1 control problem of a class of switched nonlinear systems with norm-bounded time-varying uncertainties. The system considered in this class is composed of two parts: a uncertain linear switched part and a nonlinear part, which is also switched systems. Under the circumstances, that the H1 control problem of all subsystems are not all solvable, the switched feedback control law and the switching law are designed using the average dwell-time method. The corresponding closed-loop switched system is exponentially stable and achieves a weighted L2-gain.

Observer-based robust stabilization for a class of uncertain polynomial systems

This paper focuses on the observer-based robust stabilization problem for a class of polynomial systems with norm-bounded time-varying uncertainties. The structural features of such systems guarantee the fulfilment of the separation principle between the reduced-order observer and the state feedback. The existence conditions of the observer-based robust stabilization controller are obtained by using Lyapunov stability theory. Furthermore, based on the polynomial sum of squares (SOS) theory, the above conditions are transformed into the corresponding SOS convex optimization constraints, for the avoidance of computing difficulties that exist widely in the control of non-linear systems. Finally, two numerical examples are given to illustrate the feasibility and effectiveness of the proposed approach.

Robust State Feedback Stabilization of Uncertain Discrete-Time Switched Linear Systems Subject to Actuator Saturation

The robust stabilization problem is investigated for a class of discrete-time switched linear systems with time-varying norm-bounded uncertainties and saturating actuators by using the multiple Lyapunov functions method. A switching law and a state feedback law are designed to asymptotically stabilize the system with a large domain of attraction. Based on the multiple Lyapunov functions method, sufficient conditions are obtained for robust stabilization. Furthermore, when some parameters are given in advance, the state feedback controllers and the estimation of domain of attraction are presented by solving a convex optimization problem subject to a set of linear matrix inequalities (LMI) constraints. A numerical example is given to show the effectiveness of the proposed technique.

Robust stabilization for uncertain T–S fuzzy singular system

In this paper, the robust stabilization for uncertain Takagi–Sugeno (T–S) fuzzy singular system with norm-bounded time-varying uncertainties in both the state and input matrices is studied. By using the Lyapunov stability theory, a sufficient condition in the form of the linear matrix inequality for robust stability is given. Moreover, some sufficient conditions of robust stabilization based on the state and output feedback controllers are presented respectively.

Quadratic stabilisability of multi-agent systems under switching topologies

This paper addresses the stabilisability of multi-agent systems (MASs) under switching topologies. Necessary and/or sufficient conditions are presented in terms of graph topology. These conditions explicitly reveal how the intrinsic dynamics of the agents, the communication topology and the external control input affect stabilisability jointly. With the appropriate selection of some agents to which the external inputs are applied and the suitable design of neighbour-interaction rules via a switching topology, an MAS is proved to be stabilisable even if so is not for each of uncertain subsystem. In addition, a method is proposed to constructively design a switching rule for MASs with norm-bounded time-varying uncertainties. The switching rules designed via this method do not rely on uncertainties, and the switched MAS is quadratically stabilisable via decentralised external self-feedback for all uncertainties. With respect to applications of the stabilisability results, the formation control and the cooperative tracking control are addressed. Numerical simulations are presented to demonstrate the effectiveness of the proposed results.

Robust sampled-data control with random missing data scenario

The problem of robust sampled-data control for uncertain dynamic systems in the presence of missing data has been investigated. By using stochastic variables with a Bernoulli distributed white sequence to model missing data, along with time-varying norm-bounded uncertainties, and the input delay approach for sampled-data systems, two models for the considered sampled-data control system are proposed as the consecutive missing data scenario. Moreover, when data are missing, the control signals are held as the last received data. Sufficient conditions for the existence of desired robust sampled-data controllers are presented in the form of a linear matrix inequality. A numerical example is given to illustrate the validity of the proposed methods and to compare the results between the two proposed models of the sampled-data control system.

Robust PI based set-point learning control for batch processes subject to time-varying uncertainties and load disturbance

Based on the proportional-integral (PI) closed-loop control widely used in industrial engineering practice, a robust iterative learning control (ILC) method is proposed for industrial batch processes subject to time-varying uncertainties and load disturbance. An important merit is that the proposed ILC design is independent of the PI tuning which maintains the closed-loop system stability, owing to that the ILC updating law is implemented through adjusting the set-point of the closed-loop system and adding a feedforward control signal to the plant input along the batch-to-batch direction. Using the robust H infinity control objective, a robust discrete-time PI tuning algorithm is given in terms of the plant state-space model description with norm-bounded time-varying uncertainties. For the batch-to-batch direction, a robust ILC updating law is developed based on the two-dimensional (2D) control system theory, which is capable of perfect output tracking against repetitive type load disturbance. An illustrative example from the literature is adopted to demonstrate the effectiveness and merits of the proposed ILC method.

Robust Moving HorizonH∞Control of Discrete Time-Delayed Systems with Interval Time-Varying Delays

In this study, design of a delay-dependent type moving horizon state-feedback control (MHHC) is considered for a class of linear discrete-time system subject to time-varying state delays, norm-bounded uncertainties, and disturbances with bounded energies. The closed-loop robust stability and robust performance problems are considered to overcome the instability and poor disturbance rejection performance due to the existence of parametric uncertainties and time-delay appeared in the system dynamics. Utilizing a discrete-time Lyapunov-Krasovskii functional, some delay-dependent linear matrix inequality (LMI) based conditions are provided. It is shown that if one can find a feasible solution set for these LMI conditions iteratively at each step of run-time, then we can construct a control law which guarantees the closed-loop asymptotic stability, maximum disturbance rejection performance, and closed-loop dissipativity in view of the actuator limitations. Two numerical examples with simulations on a nominal and uncertain discrete-time, time-delayed systems, are presented at the end, in order to demonstrate the efficiency of the proposed method.

Improve results on delay-dependent robust H&lt;SUB align="right"&gt;&amp;infin; control for uncertain systems with interval time-varying delay

This paper considers the delay-dependent robust H∞ control problem for a class of linear systems with interval time-varying delay and norm-bounded uncertainties. An improved delay-dependent bounded real lemma (BRL) for the systems is established based on a new candidate Lyapunov-Krasovskii (L-K) functional and linear matrix inequality (LMI). Then by applying the BRL, a memoryless state feedback H∞ controller such that the resulting closed-loop system is asymptotically stable and satisfied a prescribed H∞ performance level for all admissible uncertainties is deduced. Finally, numerical examples are provided to demonstrate the effectiveness and benefits of the proposed method.

Robust sampled-data H ∞ output tracking control for a class of nonlinear networked systems with stochastic sampling

In this article, the problem of robust sampled-data H ∞ output tracking control is investigated for a class of nonlinear networked systems with stochastic sampling and time-varying norm-bounded uncertainties. For the sake of technical simplicity, only two different sampling periods are considered, their occurrence probabilities are given constants and satisfy Bernoulli distribution, and can be extended to the case with multiple stochastic sampling periods. By the way of an input delay, the probabilistic system is transformed into a stochastic continuous time-delay system. A new linear matrix inequality-based procedure is proposed for designing state-feedback controllers, which would guarantee that the closed-loop networked system with stochastic sampling tracks the output of a given reference model well in the sense of H ∞. Conservatism is reduced by taking the probability into account. Both network-induced delays and packet dropouts have been considered. Finally, an illustrative example is given to show the usefulness and effectiveness of the proposed H ∞ output tracking design.

Robust probabilistic sampling [formula omitted] output tracking control for a class of nonlinear networked systems with multiplicative noises

In this paper, the problem of robust sampled-data H∞ output tracking control is investigated for a class of nonlinear networked systems with probabilistic sampling, multiplicative noises and time-varying norm-bounded uncertainties. For the sake of technical simplicity, only two different sampling periods are considered, their occurrence probabilities are given constants and satisfy Bernoulli distribution, and can be extended to the case with multiple stochastic sampling periods. By the way of an input delay, the probabilistic system is transformed into a stochastic continuous time-delay system. A new linear matrix inequality (LMI)-based procedure is proposed for designing state-feedback controllers, which would guarantee that the closed-loop networked system with stochastic sampling tracks the output of a given reference model well in the sense of H∞. Conservatism is reduced by taking the probability into account. Both network-induced delays and packet dropouts have been considered. Finally, an illustrative example is given to show the usefulness and effectiveness of the proposed H∞ output tracking design.

Robust Delay-Dependent Stability Criteria for Dynamic Systems with Nonlinear Perturbations and Leakage Delay

This paper studies the global asymptotic stability for uncertain systems with mixed delays. The mixed delays include constant delay in the leakage term (i.e., leakage delay) and time-varying delays. The uncertainties under consideration are nonlinear time-varying parameter perturbations and norm-bounded uncertainties. Based on a appropriate Lyapunov–Krasovskii functional with triple integral terms, some integral inequalities and convex combination technique, a novel delay-dependent stability criterion is derived in terms of linear matrix inequalities (LMIs). Finally, three numerical examples are included to show the superiority of the proposed method.