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
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
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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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
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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TL;DR: This is the post-print version of this Article is the official published version can be accessed from the link below.
Abstract: This is the post-print version of this Article. The official published version can be accessed from the link below - Copyright @ 2012 John Wiley & Sons
44 citations
Proceedings Article•
06 Jul 2003
TL;DR: An optimal control approach to robust control design is proposed for rigid robotic systems under the unknown load and the other uncertainties and the robust control performance of robotic systems by the proposed algorithm is remarkable.
Abstract: An optimal control approach to robust control design is proposed in this study for rigid robotic systems under the unknown load and the other uncertainties. The uncertainties are quadratically bounded for some positive definite matrix. Iterative method to find the matrix is shown. Simulations are made for a weight-lifting operation of a two-link manipulator and the robust control performance of robotic systems by the proposed algorithm is remarkable.
40 citations
Book•
15 Aug 2014
TL;DR: This chapter discusses model-Based Control Systems with Intermittent Feedback, which combines time-Varying and Stochastic Feedback Updates, and Multirate Model-Based systems, which combine Output Feedback and Delays.
Abstract: 1. Introduction.- PART I 2. Model-Based Control Systems: Stability.- 3. Model-Based Control Systems: Output Feedback and Delays.- 4. Model-Based Control Systems with Intermittent Feedback.- 5. Time-Varying and Stochastic Feedback Updates.- 6. Event-Triggered Feedback Updates.- 7. Model-Based Nonlinear Control Systems.- 8. Quantization Analysis and Design.- PART II 9. Optimal Control of Model-Based Event-Triggered Systems.- 10. Performance Analysis using Lifting Techniques.- 11. Reference Input Tracking.- 12. Adaptive Stabilization of Networked Control Systems.- 13. Multirate Model-Based Systems.- 14. Distributed Control Systems.- Appendix.- Index.- References.
38 citations
12 Dec 2005
TL;DR: In this article, Kalman filtering and LQ optimal control of a networked control system (NCS) whose sensors and actuators exchange information with a remote controller over a shared communication medium is discussed.
Abstract: We discuss Kalman filtering and LQ optimal control of a networked control system (NCS) whose sensors and actuators exchange information with a remote controller over a shared communication medium. Access to that medium is governed by a pair of periodic communication sequences. Under the proposed model, the controller and plant handle communication disruptions by "ignoring" sensors and actuators that are not actively communicating. We show that Kalman filtering and LQ optimal control for NCSs can be formulated as a standard LQG problem for an equivalent periodic system. Moreover, under mild conditions, there always exist periodic communication sequences that preserve the detectability and observability of the NCS and thus make it possible to guarantee the existence of a stabilizing LQG controller.
38 citations
17 Jun 2013
TL;DR: The main result is that for the same average communication rate, event-triggered schemes may perform worse than time-trIGgered schemes in terms of the resulting estimation error covariance when the effect of communication network is explicitly considered.
Abstract: This paper considers state estimation for multiple plants across a shared communication network. Each linear time-invariant plant transmits information through the common network according to either a time-triggered or an event-triggered rule. Performance in terms of the communication frequency and the estimation error covariance is analytically characterized. The main result is that for the same average communication rate, event-triggered schemes may perform worse than time-triggered schemes in terms of the resulting estimation error covariance when the effect of communication network is explicitly considered.
26 citations