Event-triggered Control For Semi-global Stabilisation Of Systems With Actuator Saturation

This paper investigates the problem of event-triggered control for semi-global stabilisation of null controllable systems subject to actuator saturation. First, for a continuous-time system, novel event-triggered low-gain control algorithms based on Riccati equations are proposed to achieve semi-global stabilisation. The algebraic Riccati equation with a low-gain parameter is utilised to design both the event-triggering condition and the linear controller; a minimum inter-event time based on the Riccati ordinary differential equation is set a priori to exclude the Zeno behaviour. In addition, the high-low-gain techniques are utilised to extend the semi-global results to event-based global stabilisation. Furthermore, for a discrete-time system, novel low-gain and high–low-gain control algorithms are proposed to achieve event-triggered stabilisation. Numerical examples are provided to illustrate the theoretical results.postprin

Event-based global stabilization of linear systems via a saturated linear controller

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Sparse and Constrained Stochastic Predictive Control for Networked Systems

This article presents a novel class of control policies for networked control of Lyapunov-stable linear systems with bounded inputs. The control channel is assumed to have i.i.d. Bernoulli packet dropouts and the system is assumed to be affected by additive stochastic noise. Our proposed class of policies is affine in the past dropouts and saturated values of the past disturbances. We further consider a regularization term in a quadratic performance index to promote sparsity in control. We demonstrate how to augment the underlying optimization problem with a constant negative drift constraint to ensure mean-square boundedness of the closed-loop states, yielding a convex quadratic program to be solved periodically online. The states of the closed-loop plant under the receding horizon implementation of the proposed class of policies are mean square bounded for any positive bound on the control and any non-zero probability of successful transmission

General Formula for Event-Based Stabilization of Nonlinear Systems with Delays in the State

International audienceIn this chapter, a universal formula is proposed for event-based stabilization of nonlinear systems affine in the control and with delays in the state. The feedback is derived from the seminal law proposed by E. Sontag (1989) and then extended to event-based control of affine nonlinear undelayed systems. Under the assumption of the existence of a control Lyapunov-Krasovskii functional (CLKF), the proposal enables smooth (except at the origin) asymptotic stabilization while ensuring that the sampling intervals do not contract to zero. Global asymptotic stability is obtained under the small control property assumption. Moreover, the control can be proved to be smooth anywhere under certain conditions. Simulation results highlight the ability of the proposed formula. The particular linear case is also discussed

Experimental evaluation of two complementary decentralized event-based control methods

To appear in Control Engineering PracticeInternational audienceEvent-based control aims at the reduction of the feedback communication effort among the sensors, controllers and actuators in control loops. The feedback communication is invoked by some well-defined triggering condition. This paper presents a new method for the decentralized event-based control of physically interconnected systems and shows its experimental evaluation. The novel method is based on two complementary approaches, called the global and the local approach, which jointly ensure the ultimate boundedness of the closed-loop system. The global approach steers the state of each subsystem into a target region, whereas the local approach makes the state remain in this set in spite of exogenous disturbances and the effect of the interconnections to other subsystems. This event-based control method is applied to a continuous flow process to show its practical implementation and to evaluate the analytical results on the basis of experiments

Integral Input-to-State Stability of Nonlinear Time-Delay Systems with Delay-Dependent Impulse Effects

This paper studies integral input-to-state stability (iISS) of nonlinear impulsive systems with time-delay in both the continuous dynamics and the impulses. Several iISS results are established by using the method of Lyapunov-Krasovskii functionals. For impulsive systems with iISS continuous dynamics and destabilizing impulses, we derive two iISS criteria that guarantee the uniform iISS of the whole system provided that the time period between two successive impulse moments is appropriately bounded from below. Then we provide an iISS result for systems with unstable continuous dynamics and stabilizing impulses. For this scenario, it is shown that the iISS properties are guaranteed if the impulses occur frequently enough. For impulsive systems with stabilizing impulses and stable continuous dynamics for zero input, we obtain an iISS result which shows that the entire system is uniformly iISS over arbitrary impulse time sequences. As applications, iISS properties of a class of bilinear systems are studied in details with simulations to demonstrate the presented results

Robust Control

The need to be tolerant to changes in the control systems or in the operational environment of systems subject to unknown disturbances has generated new control methods that are able to deal with the non-parametrized disturbances of systems, without adapting itself to the system uncertainty but rather providing stability in the presence of errors bound in a model. With this approach in mind and with the intention to exemplify robust control applications, this book includes selected chapters that describe models of H-infinity loop, robust stability and uncertainty, among others. Each robust control method and model discussed in this book is illustrated by a relevant example that serves as an overview of the theoretical and practical method in robust control