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Journal ArticleDOI

Stabilization of Uncertain Discrete-Time Linear System With Limited Communication

TL;DR: It is shown that the robust control law with aperiodic information ensures input-to-state stability of the original system in the presence of mismatched uncertainty, and derived the event-triggering condition for a discrete-time uncertain system.
Abstract: This technical note proposes a procedure to control an uncertain discrete-time networked system using an aperiodic stabilizing input information. The system is primarily affected by the time-varying, norm bounded, mismatched parametric uncertainty. Aperiodic exchange of information is done due to bandwidth constraint of the communication network. An event-triggered based robust control strategy is adopted to reduce the effects of system uncertainty in such bandwidth constrained networks. In event-triggered control, the control input is computed and actuated at the system end only when a pre-specified event condition is violated. The robust control input is derived to stabilize the uncertain system by solving an optimal control problem based on a virtual nominal dynamics and a modified cost-functional. It is shown that the robust control law with aperiodic information ensures input-to-state stability (ISS) of the original system in the presence of mismatched uncertainty. Deriving the event-triggering condition for a discrete-time uncertain system and ensuring the stability of such system analytically are the key contributions of this technical note. A numerical example is given to prove the efficacy of the proposed event-based control algorithm over the conventional periodic one.
Citations
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01 Jan 2002
TL;DR: In this article, it is shown that Lebesgue sampling gives better performance for some simple systems than traditional Riemann sampling, which is an analog of integration theory and is called event-based sampling.
Abstract: The normal approach to digital control is to sample periodically in time. Using an analog of integration theory we can call this Riemann sampling. Lebesgue sampling or event based sampling is an alternative to Riemann sampling. It means that signals are sampled only when measurements pass certain limits. In this paper it is shown that Lebesgue sampling gives better performance for some simple systems.

77 citations

Journal ArticleDOI
TL;DR: This article considers global exponential synchronization almost surely (GES a.s.) for a class of switched discrete-time neural networks (DTNNs) and finds that the TP matrix plays an important role in achieving the GES a.S., the upper bound of the dwell time (DT) of unsynchronized subsystems can be very large, and the lowerbound of the DT of synchronized subsystems could be very small.
Abstract: This article considers global exponential synchronization almost surely (GES a.s.) for a class of switched discrete-time neural networks (DTNNs). The considered system switches from one mode to another according to transition probability (TP) and evolves with mode-dependent average dwell time (MDADT), i.e., TP-based MDADT switching, which is more practical than classical average dwell time (ADT) switching. The logarithmic quantization technique is utilized to design mode-dependent quantized output controllers (QOCs). Noticing that external perturbations are unavoidable, actuator fault (AF) is also considered. New Lyapunov–Krasovskii functionals and analytical techniques are developed to obtain sufficient conditions to guarantee the GES a.s. It is discovered that the TP matrix plays an important role in achieving the GES a.s., the upper bound of the dwell time (DT) of unsynchronized subsystems can be very large, and the lower bound of the DT of synchronized subsystems can be very small. An algorithm is given to design the control gains, and an optimal algorithm is provided for reducing conservatism of the given results. Numerical examples demonstrate the effectiveness and the merits of the theoretical analysis.

57 citations

Journal ArticleDOI
TL;DR: A model-free solution to the robust stabilization problem of discrete-time linear dynamical systems with bounded and mismatched uncertainty is presented and it is shown that the optimal controller obtained by solving the ARE can robustly stabilize the uncertain system.
Abstract: This paper presents a model-free solution to the robust stabilization problem of discrete-time linear dynamical systems with bounded and mismatched uncertainty. An optimal controller design method is derived to solve the robust control problem, which results in solving an algebraic Riccati equation (ARE). It is shown that the optimal controller obtained by solving the ARE can robustly stabilize the uncertain system. To develop a model-free solution to the translated ARE, off-policy reinforcement learning (RL) is employed to solve the problem in hand without the requirement of system dynamics. In addition, the comparisons between on- and off-policy RL methods are presented regarding the robustness to probing noise and the dependence on system dynamics. Finally, a simulation example is carried out to validate the efficacy of the presented off-policy RL approach.

55 citations


Cites methods from "Stabilization of Uncertain Discrete..."

  • ...Remark 2: In [38], an alternative form of ARE and the optimal feedback gain K ∗ and L∗ are described as P = AT(P−1 + B R1 BT + DR2 DT)−1 A + Q̄ (18) K ∗ = −R−1 1 BT ( P−1 + BT R−1 1 BT + DT R−1 2 DT )−1 A (19) L∗ = −R−1 2 DT ( P−1 + BT R−1 1 BT + DT R−1 2 DT )−1 A....

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  • ...Consider the discrete-time model for the rotating inverted pendulum used in [38]...

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Journal ArticleDOI
TL;DR: In this paper , a model-free λ -policy iteration (λ -PI) for the discrete-time linear quadratic regulation (LQR) problem is presented.
Abstract: This article presents a model-free λ -policy iteration ( λ -PI) for the discrete-time linear quadratic regulation (LQR) problem. To solve the algebraic Riccati equation arising from solving the LQR in an iterative manner, we define two novel matrix operators, named the weighted Bellman operator and the composite Bellman operator. Then, the λ -PI algorithm is first designed as a recursion with the weighted Bellman operator, and its equivalent formulation as a fixed-point iteration with the composite Bellman operator is shown. The contraction and monotonic properties of the composite Bellman operator guarantee the convergence of the λ -PI algorithm. In contrast to the PI algorithm, the λ -PI does not require an admissible initial policy, and the convergence rate outperforms the value iteration (VI) algorithm. Model-free extension of the λ -PI algorithm is developed using the off-policy reinforcement learning technique. It is also shown that the off-policy variants of the λ -PI algorithm are robust against the probing noise. Finally, simulation examples are conducted to validate the efficacy of the λ -PI algorithm.

36 citations

Journal ArticleDOI
TL;DR: An improved event-triggered adaptive backstepping control scheme is presented in this study for a class of uncertain NCSs with non-Lipschitz non-linearities under limited resources to satisfy bandwidth limitation and ensure system stability with acceptable transient performance.
Abstract: Over the past few years, networked control systems (NCSs) have shown rapid progress and have indeed been very popular in terms of research as well as industrial applications. The issue of limited resources has been a fundamental problem in the translation of modern control techniques to NCS design. In order to address the aforesaid design challenge, an improved event-triggered adaptive backstepping control scheme is presented in this study for a class of uncertain NCSs with non-Lipschitz non-linearities under limited resources. Rather than a preselected constant threshold assumption, a well-designed and systematic triggering rule is derived based on the Lyapunov approach in order to satisfy bandwidth limitation and ensure system stability with acceptable transient performance. Relative to existing strategies in the literature, the proposed method leads to a substantially reduced number of transmissions with longer inter-event time. Thereby, the proposed algorithm exhibits more efficiency in resource utilisation. Simulation results on a networked control based robotic manipulator system illustrate the efficacy of the proposed adaptive scheme compared to benchmark control algorithms intended for a similar application.

28 citations

References
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Journal ArticleDOI
TL;DR: In this paper, the authors present a new class of event triggering mechanisms for event-triggered control systems characterized by the introduction of an internal dynamic variable, which motivates the proposed name of dynamic event triggering mechanism.
Abstract: In this technical note, we present a new class of event triggering mechanisms for event-triggered control systems. This class is characterized by the introduction of an internal dynamic variable, which motivates the proposed name of dynamic event triggering mechanism. The stability of the resulting closed-loop system is proved and the influence of design parameters on the decay rate of the Lyapunov function is discussed. For linear systems, we establish a lower bound on the inter-execution time as a function of the parameters. The influence of these parameters on a quadratic integral performance index is also studied. Some simulation results are provided for illustration of the theoretical claims.

965 citations

Proceedings ArticleDOI
10 Dec 2002
TL;DR: In this paper, it is shown that Lebesgue sampling gives better performance for some simple systems than traditional Riemann sampling, which is an analog of integration theory and is called event-based sampling.
Abstract: The normal approach to digital control is to sample periodically in time. Using an analog of integration theory we can call this Riemann sampling. Lebesgue sampling or event based sampling is an alternative to Riemann sampling. It means that signals are sampled only when measurements pass certain limits. In this paper it is shown that Lebesgue sampling gives better performance for some simple systems.

961 citations

Journal ArticleDOI
TL;DR: Self-triggered control as mentioned in this paper uses the current state of the plant to decide the next time instant in which the state should be measured, the control law computed, and the actuators updated.
Abstract: Feedback control laws have been traditionally implemented in a periodic fashion on digital hardware. Although periodicity simplifies the analysis of the mismatch between the control design and its digital implementation, it also leads to conservative usage of resources such as CPU utilization in the case of embedded control. We present a novel technique that abandons the periodicity assumption by using the current state of the plant to decide the next time instant in which the state should be measured, the control law computed, and the actuators updated. This technique, termed self-triggered control, is developed for two classes of nonlinear control systems, namely, state-dependent homogeneous systems and polynomial systems. The wide applicability of the proposed results is illustrated in two well known physical examples: a jet engine compressor and the rigid body.

746 citations

Posted Content
TL;DR: This class is characterized by the introduction of an internal dynamic variable, which motivates the proposed name of dynamic event triggering mechanism, and a lower bound on the inter-execution time as a function of the parameters is established.
Abstract: In this paper, we present a new class of event triggering mechanisms for event-triggered control systems. This class is characterized by the introduction of an internal dynamic variable, which motivates the proposed name of dynamic event triggering mechanism. The stability of the resulting closed loop system is proved and the influence of design parameters on the decay rate of the Lyapunov function is discussed. For linear systems, we establish a lower bound on the inter-execution time as a function of the parameters. The influence of these parameters on a quadratic integral performance index is also studied. Some simulation results are provided for illustration of the theoretical claims.

744 citations


"Stabilization of Uncertain Discrete..." refers background in this paper

  • ...A Girad [6] has proposed a new event-triggering mechanism called dynamic eventtriggering to achieve larger inter-event time with respect to the previous approach [4]....

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  • ...2626967 in [4]–[6], to reduce the information requirement for realizing a stable control law....

    [...]

Posted Content
TL;DR: A novel technique is presented that abandons the periodicity assumption by using the current state of the plant to decide the next time instant in which the state should be measured, the control law computed, and the actuators updated.
Abstract: Feedback control laws have been traditionally implemented in a periodic fashion on digital hardware. Although periodicity simplifies the analysis of the mismatch between the control design and its digital implementation, it also leads to conservative usage of resources such as CPU utilization in the case of embedded control. We present a novel technique that abandons the periodicity assumption by using the current state of the plant to decide the next time instant in which the state should be measured, the control law computed, and the actuators updated. This technique, termed self-triggered control, is developed for two classes of nonlinear control systems, namely, state-dependent homogeneous systems and polynomial systems. The wide applicability of the proposed results is illustrated in two well known physical examples: a jet engine compressor and the rigid body.

718 citations


"Stabilization of Uncertain Discrete..." refers methods in this paper

  • ...To avoid continuous or periodic monitoring, selftriggered control technique has been reported in [8], [9] where the next event occurring instant is computed analytically using system’s state at the previous sampling instant....

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