Continuous-time State Feedback Controller Research Articles

Optimal Output Consensus of Heterogeneous Linear Multiagent Systems Over Weight-Unbalanced Directed Networks.

This article investigates the distributed optimal output consensus problem of heterogeneous linear multiagent systems over weight-unbalanced directed networks. A novel distributed continuous-time state feedback controller is proposed to steer the outputs of all the agents to converge to the optimal solution of the global cost function. Under the standard condition that the unbalanced digraph is strongly connected and the local cost functions are strongly convex with global Lipschitz gradients, the exponential convergence of the closed-loop multiagent system is established. Then, the proposed state feedback control law is extended to an observer-based output feedback setting. Two examples are finally provided to illustrate the effectiveness of the proposed control schemes.

Robustness of polynomial stability with respect to sampling

We provide a partially affirmative answer to the following question on robustness of polynomial stability with respect to sampling: “Suppose that a continuous-time state-feedback controller achieves the polynomial stability of the infinite-dimensional linear system. We apply an idealized sampler and a zero-order hold to a feedback loop around the controller. Then, is the sampled-data system strongly stable for all sufficiently small sampling periods? Furthermore, is the polynomial decay of the continuous-time system transferred to the sampled-data system under sufficiently fast sampling?” The generator of the open-loop system is assumed to be a Riesz-spectral operator whose eigenvalues are not on the imaginary axis but may approach it asymptotically. We provide conditions for strong stability to be preserved under fast sampling. Moreover, we estimate the decay rate of the state of the sampled-data system with a smooth initial state and a sufficiently small sampling period.

A framework for distributed control via dynamic periodic event-triggering mechanisms

Dynamic event-triggered mechanisms (ETMs) have shown potential in further reducing the number of events in comparison to their static counterparts while delivering similar system performance. In this paper, we provide a framework to design dynamic periodic event-triggered controllers for multi-agent systems (MASs) with nonlinear dynamics. A preliminary version of this work on single-agent systems was studied in Dhullipalla et al. (2020). The design methodology adopts an emulation-based technique that assumes the existence of a continuous-time state feedback controller that stabilizes the MAS. The dynamic ETMs are constructed based on an agent’s ability or inability to sense states (or relative states) of fellow agents in the network. To illustrate the design methodologies, two case studies on nonlinear MASs (with Lipschitz and one-sided Lipschitz dynamics), interacting over undirected and directed communication networks, are presented. Finally, the results of the case studies are demonstrated via numerical examples.

Dynamic periodic event-triggered control for nonlinear plants with state feedback

In this work, we propose two methods to design a dynamic periodic event-triggered controller that stabilizes nonlinear plants using static state feedback. The design methodology begins by assuming the knowledge of a continuous-time state-feedback controller that stabilizes the nonlinear plant. Considering an event-driven controller updation, the resultant closed-loop plant is modelled as a hybrid system. Two approaches are proposed for the event-triggering mechanism (ETM) depending on continuous availability of states. Each method provides an ETM and an upper bound on the sampling period that ensures closed-loop stability. We provide some remarks comparing the two approaches and substantiate them through an illustrative example.

Sampled-data control of pan-tilt platform using discrete-time high gain observer

In this paper we have presented the design of sampled-data control algorithm for Pan-tilt platform using Discrete-time High Gain Observer (DHGO). The Pan-Tilt platform is a 2-axis serial robotic manipulator having a nonlinear dynamic model. The design of the control algorithm is carried out in 2 steps. In 1st steps, a continuous time state feedback control law based on feedback linearization is designed which is subsequently discretized. In the second stage, the states of the system are estimated using DHGO. To evaluate the performance of the suggested algorithm extensive simulations are carried out in Matlab Simulink.

Inducing sustained oscillations in feedback-linearizable single-input nonlinear systems

The present paper concerns the induction of stable sustained oscillation in feedback-linearizable single-input affine nonlinear dynamical systems via continuous-time state feedback control. The proposed application-oriented control approach is based on the conception of a state feedback controller that ensures the tracking of a limit cycle characterized in terms of the feedback-linearized system. Boundedness and convergence of the closed-loop trajectories are established following the Lyapunov theoretical framework and applying LaSalle׳s stability principle. The proposed approach is demonstrated with computer-simulated control experiments, showing that it ensures the convergence of the state trajectories of the controlled system to a designed limit cycle and that the methodology can, in principle, be applied to any single input feedback linearizable system.

Lyapunov-based hybrid loops for stability and performance of continuous-time control systems

We construct hybrid loops that augment continuous-time control systems. We consider a continuous-time nonlinear plant in feedback with a (possibly non stabilizing) given nonlinear dynamic continuous-time state feedback controller. The arising hybrid closed loops are guaranteed to follow the underlying continuous-time closed-loop dynamics when flowing and to jump in suitable regions of the closed-loop state space to guarantee that a positive definite function V of the closed-loop state and/or a positive definite function Vp of the plant-only state is non-increasing along the hybrid trajectories. Sufficient conditions for the construction of these hybrid loops are given for the nonlinear case and then specialized for the linear case with the use of quadratic functions. For the linear case we illustrate specific choices of the functions V and Vp which allow for the reduction of the overshoot of a scalar output. The proposed approaches are illustrated on linear and nonlinear examples.

Stability of sampled-data piecewise affine systems: A time-delay approach

This paper addresses the stability analysis of sampled-data piecewise-affine (PWA) systems consisting of a continuous-time plant in feedback connection with a discrete-time emulation of a continuous-time state feedback controller. The sampled-data system is first considered as a continuous-time system with a variable time delay. Conditions under which the trajectories of the sampled-data closed-loop system will converge to an attracting invariant set are then presented. It is also shown that when the sampling period converges to zero, these conditions coincide with sufficient conditions for non-fragility of the stabilizing continuous-time PWA state feedback controller. The results are successfully applied to a helicopter example.

Analysis of Sampled-data High-gain Observers in the Presence of Measurement Noise

This paper studies sampled-data output feedback control of nonlinear systems using high-gain observers in the presence of measurement noise. The observer is designed in continuous time, then discretized. It is shown that the sampled-data output feedback controller recovers the performance of the continuous-time state feedback controller as the observer gain is increased. However, the effect of measurement noise dominates beyond a certain point, and the gap between the performance of the two controllers widens as the observer gain is increased further. The analysis quantifies the relationship between the high-gain observer parameter and the amplitude of the noise.

Stability of sampled-data piecewise-affine systems under state feedback

This paper addresses stability of sampled-data piecewise-affine (PWA) systems consisting of a continuous-time plant and a discrete-time emulation of a continuous-time state feedback controller. The paper presents conditions under which the trajectories of the sampled-data closed-loop system will exponentially converge to a neighborhood of the origin. Moreover, the size of this neighborhood will be related to bounds on perturbation parameters related to the sampling procedure, in particular, related to the sampling period. Finally, it will be shown that when the sampling period converges to zero the performance of the stabilizing continuous-time PWA state feedback controller can be recovered by the emulated controller.

Performance Recovery Under Output Feedback Sampled-Data Stabilization of a Class of Nonlinear Systems

This paper studies sampled-data output feedback control of a class of nonlinear systems. It is shown that the performance of a stabilizing continuous-time state feedback controller can be recovered by a sampled-data output feedback controller when the sampling period is sufficiently small. The output feedback controller uses a deadbeat discrete-time observer to estimate the unmeasured states. Two schemes are proposed to overcome large initial transients when the controller is switched on.

状態フィードバック系のディジタル再設計法とＣＣＶ飛行制御系設計への適用

This paper proposes a new digital redesign method for linear state-feedback control systems with fixed gain matrices. The method is based on the discretization of the closed-loop control input signal, and then the principle of equivalent area is applied to this discretization. In the closed-loop system the proposed method achieves second-order approximation to the underlying continuous-time state-feedback control system. The proposed method is applied to a digital CCV flight control system design based on the decoupling control. Since from a characteristics of the step invariance discrete-time model the discrete-time approach which designs discrete-time controllers for the discrete-time plant model cannot be applied to the decoupling control, the digital redesign approach is used. The simulation results indicate that the proposed method redesigns the continuous-time state-feedback control system more satisfactorily in control performance than other methods.

New Digital Redesign Method in use of N-Delay Control.

A new digital redesign method is proposed for both a continuous time state feedback controller and a dynamic controller. In the proposed method, the N-Delay control is employed, and the lth plant inputs are changed Nl times during one sampling period. The goal of this paper is to develop a new digital controller from the analog controller so that the states of the digitally controlled closed-loop system completely match those of the original continuous time controlled closed-loop system at every sampling period. An illustrative example of position control using DC servo motor is presented.

Digital redesign of a continuous-time controller using the pade and inverse-pade approximation method

This paper presents a mixed method consisting of the Pade approximation method and the inverse-Pade approximation method for digital redesign of a continuous-time state-feedback controller. Using this digitally redesigned controller, the states of digitally controlled sampled-data system closely match those of the original continuous-time controlled system for a relatively longer sampling period. It is shown that the digitally redesigned controller based on the bilinear and inverse-bilinear transform method is a specific class of the proposed controller.