scholarly journals Robust Local Stabilization of Discrete-Time Systems with Time-Varying State Delay and Saturating Actuators

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
J. V. V. Silva ◽  
L. F. P. Silva ◽  
I. Rubio Scola ◽  
V. J. S. Leite
Keyword(s):  
Discrete Time ◽  
Initial Conditions ◽  
State Feedback Control ◽  
Control Law ◽  
Time Varying ◽  
Region Of Attraction ◽  
Synthesis Conditions ◽  
Saturating Actuators ◽  
Discrete Time Systems ◽  
Time Systems

The robust local stabilization of uncertain discrete-time systems with time-varying state delayed and subject to saturating actuators is investigated in this work. A convex optimization method is proposed to compute robust state feedback control law such that the uncertain closed-loop is locally asymptotically stable if the initial condition belongs to an estimate of the region of attraction for the origin. The proposed procedure allows computing estimates of the region of attraction through the intersection of ellipsoidal sets in an augmented space, reducing the conservatism of the estimates found in the literature. Also, the conditions can handle the amount of delay variation between two consecutive samples, which is new in the literature for the discrete-time case. Although the given synthesis conditions are delay dependent, the proposed control law is delay independent, yielding to easier real time implementations. A convex procedure is proposed to maximize the size of the set of safe initial conditions. Numerical examples are provided to illustrate the effectiveness of our approach and also to compare it with other conditions in the literature.

Local stabilization of nonlinear discrete-time systems with time-varying delay in the states and saturating actuators

2020 ◽  
Vol 518 ◽  
pp. 272-285 ◽  
Author(s):  
Luís F.P. Silva ◽  
Valter J.S. Leite ◽  
Eugênio B. Castelan ◽  
Michael Klug ◽  
Kevin Guelton
Keyword(s):  
Discrete Time ◽  
Time Varying ◽  
Time Varying Delay ◽  
Saturating Actuators ◽  
Discrete Time Systems ◽  
Time Systems ◽  
Varying Delay

scholarly journals State Feedback Guaranteed Cost Repetitive Control for Uncertain Discrete-Time Systems

2011 ◽  
Vol 2011 ◽  
pp. 1-16
Author(s):  
Wentao Chen ◽  
Yechun Lin ◽  
Qingping Wu
Keyword(s):  
Discrete Time ◽  
State Feedback ◽  
Cost Control ◽  
Repetitive Control ◽  
Guaranteed Cost Control ◽  
State Feedback Control ◽  
Control Law ◽  
Discrete Time Systems ◽  
Guaranteed Cost ◽  
Time Systems

This paper considers the problem of guaranteed cost repetitive control for uncertain discrete-time systems. The uncertainty in the system is assumed to be norm-bounded and time-varying. The objective is to develop a novel design method so that the closed-loop repetitive control system is quadratically stable and a certain bound of performance index is guaranteed for all admissible uncertainties. The state feedback control technique is used in the paper. While for the case that the states are not measurable, an observer-based control scheme is adopted. Sufficient conditions for the existence of guaranteed cost control law are derived in terms of linear matrix inequality (LMI). The control and observer gains are characterized by the feasible solutions to these LMIs. The optimal guaranteed cost control law is obtained efficiently by solving an optimization problem with LMI constraints using existing convex optimization algorithms. A simulation example is provided to illustrate the validity of the proposed method.

scholarly journals MTN Optimal Tracking Control of SISO Nonlinear Time-Varying Discrete-Time Systems without Mechanism Models

2018 ◽  
Vol 2018 ◽  
pp. 1-19
Author(s):  
Jiao-Jun Zhang ◽  
Hong-Sen Yan
Keyword(s):  
Optimal Control ◽  
Online Learning ◽  
Discrete Time ◽  
Output Signal ◽  
Tracking Control ◽  
Control Law ◽  
Time Varying ◽  
Discrete Time Systems ◽  
Time Systems ◽  
The Given

Nonlinear time-varying systems without mechanism models are common in application. They cannot be controlled directly by the traditional control methods based on precise mathematical models. Intelligent control is unsuitable for real-time control due to its computation complexity. For that sake, a multidimensional Taylor network (MTN) based output tracking control scheme, which consists of two MTNs, one as an identifier and the other as a controller, is proposed for SISO nonlinear time-varying discrete-time systems with no mechanism models. A MTN identifier is constructed to build the offline model of the system, and a set of initial parameters for online learning of the identifier is obtained. Then, an ideal output signal is selected relative to the given reference signal. Based on the system identification model, Pontryagin minimum principle is introduced to obtain the numerical solution of the optimal control law for the system relative to the given ideal output signal, with the corresponding optimal output taken as the desired output signal. A MTN controller is generated automatically to fit the numerical solution of the optimal control law using the conjugate gradient (CG) method, and a set of initial parameters for online learning of the controller is obtained. An adaptive back propagation (BP) algorithm is developed to adjust the parameters of the identifier and controller in real time, and the convergence for the proposed learning algorithm is verified. Simulation results show that the proposed scheme is valid.

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