Dynamic Output Feedback Control Problem Research Articles

Dynamic output feedback control for UAVs with limited network bandwidth: A GA-assisted design approach

This paper studies the dynamic output feedback (OF) control problem for unmanned aerial vehicles (UAVs) with limited network bandwidth by a genetic-algorithm-assisted design approach. In order to make full use of the limited network bandwidth, only partial measurement information is transmitted to the controller via the sensor-to-controller network. Round-Robin protocol is introduced to administrate the transmission rule. Sufficient conditions are presented to make sure that the closed-loop UAV system is exponentially stable with the required L2-gain performance. However, due to the nonlinear coupling terms of the dynamic OF controller parameters and some redundant variables in the system modeling, the established conditions are non-convex and difficult to be solved. Fortunately, genetic algorithms (GA) show good performance in solving optimization problem with nonlinear and non-convex constraints. Therefore, this paper skillfully combines GA with linear matrix inequality techniques to solve the established conditions. Finally, all the dynamic OF controller parameters and the minimal L2-gain can be obtained simultaneously. At the end of this paper, an UAV networked control example and a numerical example are performed to verify the effectiveness and superiorities of our method.

Dynamic output-feedback model predictive control for polytopic uncertain systems with amplify-and-forward relays

In this paper, the dynamic output-feedback model predictive control (MPC) problem is investigated for systems with polytopic uncertainties and amplify-and-forward (AF) relays, where the signal transmission with random power is adopted to facilitate the remote transmission with the limited transmission capacity of sensors. With respect to the parameter uncertainties of the system and the randomness of AF relays, a new objective function is constructed, which is defined by the mathematical expectation of the conventional quadratic function over the infinite time horizon. Then, the singular value decomposition technique is applied to handle the inherent couplings of variables to formulate a solvable optimization problem. Furthermore, sufficient conditions are provided to guarantee the recursive feasibility of the proposed MPC algorithm, meanwhile the underlying system can be stabilized in the mean-square sense by the designed controllers. Finally, two simulation examples are used to show the effectiveness of the proposed MPC strategy.

Finite-frequency fixed-order dynamic output-feedback control via a homogeneous polynomially parameter-dependent technique

This paper investigates the problem of fixed-order dynamic output-feedback (DOF) control for linear polytopic systems over finite-frequency ranges. Firstly, based on the generalized Kalman–Yakubovich-Popov lemma, we formulate the necessary and sufficient conditions for the finite-frequency disturbance-attenuation performance as bilinear matrix inequalities (BMIs), which are known to be NP-hard. In light of the homogeneous polynomially parameter-dependent technique, we construct relaxed synthesis conditions by employing higher-order decision variables dependent on the uncertainty parameter. To address the BMI problem, we develop an iterative procedure, under which feasible solutions to the original non-convex programming are achieved by vicariously solving a sequence of tractable convex approximations. Finally, we verify the efficacy of the theoretical results by an active suspension system.

Dynamic output feedback control for networked systems with limited communication based on deadband event-triggered mechanism

In this paper, a deadband event-triggered mechanism is used to reduce the transmission data of the network channel to improve the performance of networked control systems (NCSs) with limited communication. In view of the unmeasurable state signal in the actual network system, the dynamic output feedback control problem for the NCSs is studied. When network-induced delays, time-varying sampling intervals and signal transmission deadbands are considered simultaneously, the model of NCSs under the deadband event-triggered mechanism is constructed, and a sufficient condition for the stability of NCSs is given. Furthermore, the design method of the dynamic output feedback controller of NCSs under deadband event-triggered mechanism is proposed. Two simulation examples are used to show that the proposed approach can obtain the dynamic output feedback controller for NCSs with the deadband event-triggered mechanism, and also illustrate the deadband event-triggered mechanism can reduce the signal transmission in the network channel to obtain better system performance.

Polynomial chaos-based [formula omitted] output-feedback control of systems with probabilistic parametric uncertainties

H2 static and dynamic output-feedback control problems are investigated for linear time-invariant uncertain systems. The goal is to minimize the averaged H2 performance in the presence of nonlinear dependence on time-invariant probabilistic parametric uncertainties. By applying the polynomial chaos theory, the control synthesis problem is solved using a high-dimensional expanded system which characterizes stochastic state uncertainty propagation. Compared to existing polynomial chaos-based control designs, the proposed approach addresses the simultaneous presence of parametric uncertainties and white noises. The effect of truncation errors due to using finite-degree polynomial chaos expansions is captured by time-varying norm-bounded uncertainties, and is explicitly taken into account by adopting a guaranteed cost control approach. This feature avoids the use of high-degree polynomial chaos expansions to alleviate the destabilizing effect of expansion truncation errors, thus significantly reducing computational complexity. Moreover, rigorous analysis clarifies the condition under which the stability of the high-dimensional expanded system implies the internal mean square stability of the original system under control. Using iterations between synthesis and post-analysis, a bisection algorithm is proposed to find the smallest bounding parameter on the effect of expansion truncation errors such that robust closed-loop stability is guaranteed. A numerical example is used to illustrate the effectiveness of the proposed approach.

Dynamic output feedback control for networked systems subject to communication delays, packet dropouts, and quantization

In this paper, the dynamic output feedback control problem for uncertain network control systems in the presence of constraints on network communication channels is investigated. These limitations include time-varying delays, packet dropouts, and quantization in both communication channels from sensor-to-controller and controller-to-plant. Packet dropouts are modeled by i.i.d Bernoulli processes. Also, logarithmic quantization and time-interval delays are considered in the communication network. To ensure the robust mean square stability and H∞ performance of the closed-loop system under imperfect communication channels, a dynamic output feedback control approach based on H2/H∞ criteria is proposed in the framework of linear matrix inequalities. A numerical example is presented to illustrate the validity of the theoretical analysis, and applicability of the proposed control approach.

Dynamic Output Feedback Control of Discrete-Time Switched Affine Systems

This article deals with the codesign of an output-dependent switching function and a full-order affine filter for discrete-time switched affine systems. More specifically, from the measured output, the switched filter has the role of providing essential information for the switching function, which must assure global practical stability of a desired equilibrium point. The design conditions are based on a general quadratic Lyapunov function and are expressed in terms of linear matrix inequalities. Moreover, whenever the system is quadratically detectable, the solution to the output feedback problem coincides with the one for the state feedback case and the associated filter admits the observer form. To the best of the authors' knowledge, this is the first time that the dynamic output feedback control problem is treated in the context of discrete-time switched affine systems. The results can be used to cope with sampled-data control and have the property of assuring global asymptotic stability when the sampling period tends to zero. A practical application concerning the velocity control of a dc motor driven by a buck-boost converter illustrates the theoretical results.

A Guaranteed Cost Approach to Dynamic Output Feedback Control for Neutral-Type Markovian Jumping Stochastic Systems

This paper is devoted to investigating the dynamic output feedback (DOF) control problem of Markovian jump neutral-type stochastic systems with a guaranteed cost function. Both of the state and measurement equations contain time delays. Mode-dependent DOF controllers are first designed such that the closed-loop system is asymptotically stable in mean-square and an adequate performance level of this system is guaranteed. Then, sufficient conditions for the solvability of this problem are derived in the form of linear matrix inequalities (LMIs). A numerical example is presented to reveal the effectiveness of our findings.

Emulation-Based Dynamic Output-Feedback Control of Saturating Discrete-Time LPV Systems

This letter addresses the problem of emulation-based dynamic output-feedback control for discrete-time linear parameter varying systems under actuator saturation. Sufficient conditions based on linear matrix inequalities (LMI) are derived to design the parameters of two dependent event-triggering rules handling the sensor-to-controller and controller-to-actuator communication and to guarantee the regional asymptotic stability of the closed-loop system. A convex optimization scheme incorporating these conditions is also formulated to reduce the output and control signals' update rate through communication channels. A numerical example illustrates the usefulness of the proposal.

Intelligent event-based output feedback control with Q-learning for unmanned marine vehicle systems

This paper addresses the Dynamic Output Feedback Control (DOFC) problem for the network-based unmanned marine vehicle (UMV) systems, where the controller is located at the land-based console. The output measurements on the system are transmitted to the land-based console via a communication network. A novel event-based transmission mechanism is devised to alleviate the communication burden, where the threshold of the event function is intelligently updated by a Q-learning algorithm. Since the communication delay is inevitably present in the networked controller design, a time-delay system model is established which incorporates both event-based transmission and communication delay. With help of the Lyapunov stability theory and the extended reciprocally convex matrix inequality approach, a sufficient condition is obtained which ensures asymptotic stability of the tracking error system while a prescribed H∞ disturbance attenuation performance is met. Finally, the simulation study on a benchmark system shows that the proposed controller design not only attenuates the Yaw Velocity (YV) error variation and the Yaw Angle (YA) oscillation, but also reduces the communication load effectively. Compared with the existing results in literature, it is shown that the proposed control algorithm can provide a better tracking performance.

Event-triggered output feedback control for discrete Markov jump systems under deception attack

An event-triggered dynamic output feedback control (DOFC) problem for discrete Markov jump systems is considered, where both measurement and control channel are under the deception attacks. To reduce the data traffic in the channel and the control actions against attack, two event-triggered schemes (ETSs) are implemented on sensor and controller node asynchronously. And two quantizers are installed independently. Sufficient criterions for ensuring asymptotic stability of the networked control systems (NCSs) are obtained by deriving the Lyapunov functional, and the co-design of DOFC with ETSs can be acquired in terms of the linear matrix inequality (LMI). An application on DC motor is utilized to prove the feasibility of this method.

Dynamic output-feedback control of linear semi-Markov jump systems with incomplete semi-Markov kernel

This paper is devoted to the dynamic output-feedback control problem for a class of linear semi-Markov jump systems (SMJSs) in discrete-time domain. A mode-dependent control scheme is employed with an adaptation sense under incomplete semi-Markov kernel, which has been shown to be more practical. By introducing the upper bound of sojourn time for each system mode, numerically testable stabilization criteria are established for discrete-time linear SMJSs via a novel form of Lyapunov function. The adopted Lyapunov matrix depends on the modes and their elapsed time simultaneously. Based on above-mentioned Lyapunov function combined with Projection Lemma, a desired mode-dependent stabilizing controller is designed such that the closed-loop system is mean-square stable. Finally, the theoretical results are applied to a practical example of F-404 aircraft engine system to demonstrate the effectiveness and applicability of the proposed control strategy.

Dynamic output feedback control of systems with event-driven control inputs

In this paper, a dynamic output feedback control problem is investigated for systems with event-driven control inputs. With both continuous and sampled output measurements in the systems, two types of dynamic output feedback controllers are designed based on a predefined event-driven scheduler for the control signals, respectively. With the proposed event-driven control scheme, the Zeno behavior can be avoided, and the states of closed-loop systems are also guaranteed to be globally uniformly ultimately bounded. Detailed parameters of the event-driven controllers are constructed under the stabilizable conditions of the closed-loop systems. Finally, both the effectiveness and merits of the proposed design techniques are verified by the numerical examples.

Abel lemma‐based finite‐sum inequality approach to stabilization for 2‐D time‐varying delay systems

AbstractThe problem of delay‐dependent stability is concerned for two‐dimensional discrete‐time systems with interval time‐varying delays in this paper. Choosing a Lyapunov functional with the upper bound and lower bound of delays, considering all terms in the difference and using two‐dimensional Abel lemma‐based finite‐sum inequalities, a new delay‐dependent stability criterion in terms of linear matrix inequality is derived for two‐dimensional discrete‐time systems. Then, based on the delay‐dependent stability criteria, a state feedback control problem and a dynamic output feedback control problem are considered to realize the stability control for the two‐dimensional discrete‐time system. Finally, it is shown through four numerical examples that the stability criterion can provide a larger admissible maximum upper bound with less decision variables than the stability criterion using two‐dimensional Jensen inequalities approach.

Finite-time dynamic output-feedback dissipative control for singular uncertainty T–S fuzzy systems with actuator saturation and output constraints

This paper studies the problem of finite-time dynamic output-feedback control for singular uncertainty T–S time-varying delay fuzzy systems with actuator saturation and output constraints. Through a dynamic parallel distributed compensator, the (U,V,R)−α− dissipative output-feedback fuzzy controller is designed. Furthermore, by employing reciprocally convex approach and a new lemma, the sufficient conditions are obtained to guarantee that the systems are finite-time bounded subject to (U,V,R)−α− dissipative performance level. Then, the desired fuzzy state-feedback controller and dynamic output feedback controller are derived by solving the linear matrix inequalities (LMIs). Finally, the feasibility and effectiveness of the proposed method can be validated by some simulations.

Robust Dynamic Output Feedback Control for Uncertain Fast Sampling Discrete-Time Singularly Perturbed Systems

This paper considers the dynamic output feedback (DOF) control problems for a class of uncertain discrete-time singularly perturbed systems by using reduced-order subsystems (ROSs). A sufficient condition in terms of a linear matrix inequality (LMI) is provided to guarantee the existence of the DOF controller of the ROSs. The corresponding controller gain matrices can be solved by the proposed LMIs. The results show that the DOF controller that is designed for the ROSs can stabilize the original full-order system (FOS) when the perturbation parameter is sufficiently small, although there are system uncertainties. Thus, the presented DOF controller guarantees that the FOS is robust not only for the singular perturbation parameter but also for the system uncertainties. Furthermore, we also explicitly show that this case fails when using static output feedback. That is, a static output feedback controller can always be found to stabilize the ROSs, but it destabilizes the FOSs. Finally, an experimental example for the nuclear reactor model is employed to illustrate the validity and feasibility of the developed methods.

Finite-region dissipative dynamic output feedback control for 2-D FM systems with missing measurements

This paper focuses on the finite-region dissipative dynamic output feedback control problem for a class of discrete-time two-dimensional (2-D) Fornasini–Marchesini (FM) systems with missing measurements. Firstly, the definitions of finite-region boundedness (FRB) and finite-region (T, S, R)-ϑ-dissipativity are introduced for 2-D FM systems. Secondly, sufficient conditions on the FRB and finite-region (T, S, R)-ϑ-dissipativity of the resultant closed-loop 2-D systems are obtained by the construction of the Lyapunov function and the special recursive formulas. Thirdly, based on the decoupling technique, the desired dynamic output feedback controller design method for the considered 2-D systems is further provided. In the end, an example of the metal rolling process is given to show the effectiveness of the proposed design results.

Dynamic Output-Feedback Control for Chemical Stirred Tank Reactor System with Multiple Time-Delays: A Lyapunov–Krasovskii Functional Approach

This paper addresses the dynamic output feedback control problem for a class of nonlinear multiple time-delays system. First, the system is decomposed into two subsystems based on the input matrix and output matrix. Second, a dynamic compensator is employed for the first subsystem, and then the output feedback controller is designed based on the second subsystem and compensator. With a new Lyapunov–Krasovskii functional, we show that the closed-loop time-delays system is stable and the designed controller make the solutions of the system convergent to an adjustable bounded region. Compared with the previous works, the proposed dynamic output feedback technique is more flexible and the required conditions on the considered systems are less conservative. Finally, the simulations for a discrete-time chemical stirred tank reactor case are performed to verify the effectiveness of the method.

Dynamic Output-Feedback Control for Nonlinear Time-Delay Systems and Applications to Chemical Reactor Systems

The problem of dynamic output-feedback control for nonlinear time-delay systems is studied whose nonlinearities satisfy the homogeneous growth condition. Compared with the existing work, the growth rate here is an unknown constant. We introduce two adaptive gains to handle the unknown growth rate. A homogeneous output-feedback controller is explicitly developed by adding one power integrator method. It is proved that all the signals of the closed-loop system are bounded, meanwhile the system state globally converges to the origin. Finally, we used the proposed method to a two-stage chemical reactor as an application example.

Dynamic output feedback control with output quantizer for nonlinear uncertain T‐S fuzzy systems with multiple time‐varying input delays and unmatched disturbances

AbstractThe dynamic output feedback control problem with output quantizer is investigated for a class of nonlinear uncertain Takagi‐Sugeno (T‐S) fuzzy systems with multiple time‐varying input delays and unmatched disturbances. The T‐S fuzzy model is employed to approximate the nonlinear uncertain system, and the output space is partitioned into operating regions and interpolation regions based on the structural information in the fuzzy rules. The output quantizer is introduced for the controller design, and the dynamic output feedback controller with output quantizer is constructed based on the T‐S fuzzy model. Stability conditions in the form of linear matrix inequalities are derived by introducing the S‐procedure, such that the closed‐loop system is stable and the solutions converge to a ball. The control design conditions are relaxed and design flexibility is enhanced because of the developed controller. By introducing the output‐space partition method and S‐procedure, the unmatched regions between the system plant and the controller caused by the quantization errors can be solved in the control design. Finally, simulations are given to verify the effectiveness of the proposed method.