State Feedback Control Problem Research Articles

Decentralised adaptive control of switched interconnected high-order nonlinear systems with unknown control direction and time-delay

ABSTRACTThis paper studies the dynamic state feedback control problem for a class of interconnected large-scale switched high-order nonlinear systems with unknown control direction and time-varying time-delay. The adaptive laws are designed to estimate the bounds of switched parameters under arbitrary switching for subsystems. The Nussbaum function is used to deal with the unknown control direction problem. By combining the backstepping and homogeneous domination technique, the decentralised adaptive control strategies are developed and the resulting closed-loop system is asymptotically stable. Finally, a simulation example is given and the results show the effectiveness of the proposed control design method.

A combined NN and dynamic gain-based approach to further stabilize nonlinear time-delay systems

This paper focuses on the state-feedback control problem for a class of high-order nonlinear systems with unknown time delay and control coefficients. Based on a novel dynamic gain-based backstepping technique and radial basis function neural network (RBF NN) approximation approach, the restrictions on high-order and nonlinearities are removed or further relaxed. Under these weaker conditions, a smooth state-feedback controller is skillfully constructed with only one adaptive parameter. In addition, the knowledge of time delay, NN nodes and weights is not necessary to be known a priori. It is proven that the designed controller can render the closed-loop system be semi-globally uniformly ultimately bounded. Finally, both practical and numerical examples are shown to demonstrate the effectiveness of the proposed scheme.

Adaptive Fuzzy Control of Nonlinear Systems With Unmodeled Dynamics and Input Saturation Using Small-Gain Approach

This paper investigates the problem of adaptive fuzzy state-feedback control for a category of single-input and single-output nonlinear systems in nonstrict-feedback form. Unmodeled dynamics and input constraint are considered in the system. Fuzzy logic systems are employed to identify unknown nonlinear characteristics existing in systems. An appropriate Lyapunov function is chosen to ensure unmodeled dynamics to be input-to-state practically stable. A smooth function is introduced to tackle input saturation. In order to overcome the difficulty of controller design for nonstrict-feedback system in backstepping design process, a variables separation method is introduced. Moreover, based on small-gain technique, an adaptive fuzzy controller is designed to guarantee all the signals of the resulting closed-loop system to be bounded. Finally, two illustrative examples are given to validate the effectiveness of the new design techniques.

Application of facial reduction to H∞ state feedback control problem

ABSTRACTOne often encounters numerical difficulties in solving linear matrix inequality (LMI) problems obtained from H∞ control problems. For semidefinite programming (SDP) relaxations for combinatorial problems, it is known that when either an SDP relaxation problem or its dual is not strongly feasible, one may encounter such numerical difficulties. We discuss necessary and sufficient conditions to be not strongly feasible for an LMI problem obtained from H∞ state feedback control problems and its dual. Moreover, we interpret the conditions in terms of control theory. In this analysis, facial reduction, which was proposed by Borwein and Wolkowicz, plays an important role. We show that the dual of the LMI problem is not strongly feasible if and only if there exist invariant zeros in the closed left-half plane in the system, and present a remedy to remove the numerical difficulty with the null vectors associated with invariant zeros in the closed left-half plane. Numerical results show that the numerical stability is improved by applying it.

Observer-Based Controllers for Max-Plus Linear Systems

Max-plus algebra is a suitable algebraic setting to model discrete event systems involving synchronization and delay phenomena which are often found in transportation networks, communications systems, and manufacturing systems. One way of controlling this kind of systems consists in choosing the dates of input events in order to achieve the desired performances, e.g., to obtain output events in order to respect given dates. This kind of control is optimal, according to a just-in-time criterion, if the input-event dates are delayed as much as possible while ensuring the output events to occur before a desired reference date. This paper presents the observer-based controller for max-plus linear systems where only estimations of system states are available for the controller. As in the classical sense, this is a state-feedback control problem, which is solved in two steps: first, an observer computes an estimation of the state by using the input and the output measurements, then, this estimated state is used to compute the state-feedback control action. As a main result, it is shown that the optimal solution of this observer-based control problem leads to a greater control input than the one obtained with the output feedback strategy. A high throughput screening example in drug discovery illustrates this main result by showing that the scheduling obtained from the observer-based controller is better than the scheduling obtained from the output feedback controller.

State feedback design for nonlinear quadratic systems with randomly occurring actuator saturation

This paper is concerned with the problem of state feedback control for nonlinear quadratic systems with randomly occurring actuator saturation. The considered actuator saturation is assumed to occur in a random way, and the randomly occurring rates of the saturation are time-varying with known upper and lower bounds. By using the Lyapunov approach, a sufficient condition is given to guarantee that the closed-loop system is locally asymptotically stable in mean-square sense. The desired controller gain can be obtained in terms of the solutions to certain linear matrix inequalities. Finally, a simulation example is provided to show the effectiveness of the proposed control scheme.

Quantized control for uncertain singular Markovian jump linear systems with general incomplete transition rates

Quantization is indeed a natural way to take into consideration in the control design of the complexity constraints for the controller as well as the communication constraints in the information exchange between the controller and the plant. This paper is devoted to investigating quantized state-feedback control problems for a class of continuous-time uncertain singular Markovian jump linear systems (CUSMJLSs) with generally uncertain transition rates (GUTRs) and input quantization. In this case, each transition rate can be completely unknown or only its estimate value is known. First, input quantization is introduced, then by introducing new matrix inequality conditions, sufficient conditions are formulated for quantized state-feedback control of CSMJLUSs with GUTRs and input quantization. Finally, a numerical example is presented to illustrate the effectiveness and efficiency of the proposed results.

Dissipative stability analysis and control of two-dimensional Fornasini–Marchesini local state-space model

ABSTRACTThis paper is concerned with the problems of dissipative stability analysis and control of the two-dimensional (2-D) Fornasini–Marchesini local state-space (FM LSS) model. Based on the characteristics of the system model, a novel definition of 2-D FM LSS (Q, S, R)-α-dissipativity is given first, and then a sufficient condition in terms of linear matrix inequality (LMI) is proposed to guarantee the asymptotical stability and 2-D (Q, S, R)-α-dissipativity of the systems. As its special cases, 2-D passivity performance and 2-D H∞ performance are also discussed. Furthermore, by use of this dissipative stability condition and projection lemma technique, 2-D (Q, S, R)-α-dissipative state-feedback control problem is solved as well. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.

A novel iterative learning control design for linear discrete time systems based on a 2D Roesser system

This paper is mainly devoted to the iterative learning control (ILC) design for a class of linear discrete time systems. By providing a 2D analysis of the learning process, the ILC design for such systems can be transformed into the problem of state feedback or output feedback control for 2-D systems described by Roesser models. Then, a Lyapunov approach can be used to obtain an ILC law that achieves asymptotical convergence of the tracking error. Sufficient stability conditions are provided in terms of linear matrix inequalities, which can determine learning gains as well. The theoretical results are also verified through simulation tests.DOI: http://dx.doi.org/10.5755/j01.itc.45.4.13391

StochasticH∞Control for Discrete-Time Singular Systems with State and Disturbance Dependent Noise

This paper is concerned with the stochasticH∞state feedback control problem for a class of discrete-time singular systems with state and disturbance dependent noise. Two stochastic bounded real lemmas (SBRLs) are proposed via strict linear matrix inequalities (LMIs). Based on the obtained SBRLs, a state feedbackH∞controller is presented, which not only guarantees the resulting closed-loop system to be mean square admissible but also satisfies a prescribedH∞performance level. A numerical example is finally given to illustrate the effectiveness of the proposed theoretical results.

Adaptive Stabilization of Stochastic Nonlinear Systems Disturbed by Unknown Time Delay and Covariance Noise

This paper considers a more general stochastic nonlinear time-delay system driven by unknown covariance noise and investigates its adaptive state-feedback control problem. As a remarkable feature, the growth assumptions imposed on delay-dependent nonlinear terms are removed. Then, with the help of Lyapunov-Krasovskii functionals and adaptive backstepping technique, an adaptive state-feedback controller is constructed by overcoming the negative effects brought by unknown time delay and covariance noise. Based on the designed controller, the closed-loop system can be guaranteed to be globally asymptotically stable (GAS) in probability. Finally, a simulation example demonstrates the effectiveness of the proposed scheme.

Non-fragile feedback control with gain performance of uncertain neutral-type stochastic Markovian jump systems

ABSTRACTThis paper deals with the problem of robust non-fragile observer-based state feedback control for a class of uncertain neutral-type stochastic Markovian jump systems subject to parameter uncertainties and time-delay. The attention is focused on the design of a non-fragile observer and a non-fragile controller that guarantees exponential mean-square stability and gain performance of the closed-loop system. By using Lyapunov functional theory, delay-dependent less conservative sufficient conditions in terms of linear matrix inequalities (LMIs) based on a new bounded lemma are established to check the feasibility of these two properties. Furthermore, the results are extended to nominal systems without state delay in its derivative. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed method.

Feedback control for a class of second order hyperbolic distributed parameter systems

This paper deals with the problem of state feedback control for a class of {the} distributed parameter systems with {the} disturbance term. {And} the considered distributed parameter systems are composed of {the} second order hyperbolic partial differential equations. Two different classes of restrictions on the disturbance term are given, one is that the disturbance term satisfies the linear growth constraint condition to the state variables of the system, and the other is that the disturbance term obeys the bound constraint under the significance of $L_2 $. Based on {a} variable structure method, the state feedback controllers are obtained by means of constructing appropriate Lyapunov functional. The closed-loop systems are globally asymptotically stable on $W^{1,2}(0,1)\times L_2 (0,1)$ space under the effect of the state feedback control laws. Simulation results illustrate the effectiveness of the proposed method.

NN approach to state-feedback control of high-order non-linear time-delay systems with time-varying control coefficient

This paper considers the adaptive state-feedback control problem for a class of high-order non-linear systems with unknown control coefficient and time delays. By applying the neural network approximation method and the Nussbaum function approach, the restrictions on non-linear functions and the conditions on the time-varying control coefficient are largely relaxed. In addition, an adaptive neural network state-feedback controller with only one adaptive parameter is successfully constructed by introducing proper Lyapunov–Krasovskii functionals and using the backstepping technique. The proposed scheme guarantees the closed-loop system to be semi-globally uniformly ultimately bounded. Finally, a simulation example demonstrates the effectiveness of the controller.

Stochastic optimal linear control of wireless networked control systems with delays and packet losses

In this study, the design of the optimal decentralised state-feedback controllers is considered for a wireless sensor and actuator network (WSAN) with stochastic network-induced delays and packet losses. In particular, taking advantage of multiple controllers, the authors model the WSAN as a wireless networked control system with decentralised controllers, and then formulate the stochastic optimal state-feedback control problem as a non-cooperative linear quadratic game. The optimal control law of each controller is obtained that is a function of the current plant state and past control signals. The performance of the proposed algorithm is investigated by an unstable linearised inverted pendulum and an application of the load frequency control system in power grid.

Sampled-Data State Feedback Stabilization of Boolean Control Networks.

In this letter, we investigate the sampled-data state feedback control (SDSFC) problem of Boolean control networks (BCNs). Some necessary and sufficient conditions are obtained for the global stabilization of BCNs by SDSFC. Different from conventional state feedback controls, new phenomena observed the study of SDSFC. Based on the controllability matrix, we derive some necessary and sufficient conditions under which the trajectories of BCNs can be stabilized to a fixed point by piecewise constant control (PCC). It is proved that the global stabilization of BCNs under SDSFC is equivalent to that by PCC. Moreover, algorithms are given to construct the sampled-data state feedback controllers. Numerical examples are given to illustrate the efficiency of the obtained results.

Controller Design for Nonlinear Systems using Takagi Sugeno Model: Closed Loop-FOC of IM Motor Application

This note, we investigate the problem of state feedback controllers for a class of Takagi-Sugeno (TS) Lipschitz nonlinear systems. A simple systematic and useful synthesis method is proposed which based on the use of the Differential Mean Value Theorem (DMVT) and convex theory. The proposed design approach is based on the mean value theorem (MVT) to express the nonlinear error dynamics as a convex combination of known matrices with time varying coefficients as LPV systems. Using the Lyapunov theory, stability conditions are obtained and expressed in term of Linear Matrix Inequalities (LMI). The controller gains are then obtained by solving linear matrix inequalities. The effectiveness of the proposed approach for Field Oriented Control of Induction Motor (FOC-IM) drives is demonstrated through an illustrative simulation for the proof of these approaches. Furthermore, an extension for controller design with parameter uncertainties and perturbation performance is discussed.

Analysis, Modeling and Simulation of State Feedback Control for Positive Output Super Lift Luo Converter

This article studies a design and implementation of state-feedback control problem for dc-dc Positive Output Super Lift Luo (POSLL) converter by considering the line and load disturbances for needing desired power source for various portable electronic equipments like battery charger, hard disk drives, medical device, LED TV etc. The POSLL’s dynamic performance becomes non-linear in nature; the designed controller able to get superior dynamic performance given by load estimation is done by using an observer and by combining the state-feedback control with the load estimator, a controller which is explicitly developed with strong robustness using separation principle. An effectual stability analysis is exemplified to prove that by carefully selecting the state feedback control and observer gain matrix, the output voltage of the dc-dc POSLL converter tracks the desired value irrespective of the uncertainties. Extensive simulation is carried out using MATLAB/Simulink model. The result based on time domain analysis is done by using the controllers for various disturbances given to the converter.

Harmonic voltage resonant compensation control of a three-phase inverter for battery energy storage systems applied in isolated microgrid

The aim of this paper is to propose a sinusoidal voltage signals tracking control strategy, adaptive for frequency of a three-phase inverter for a battery energy storage system (BESS) applied to an isolated microgrid. To support the normal operation of distributed renewable energy and feed the critical loads under the isolated mode, the BESS generally works in voltage control mode (VCM). The proposed control strategy, which transforms the tracking control problem into a state feedback control problem, includes two terms, one of which is state feedback control used to stabilize system while another employs multiple resonant controllers applied to achieve harmonics compensation control. The optimal linear-quadratic (LQ) control approach in which the root locus method is used for optimization selection of weight matrix Q is adopted to tune the control parameters of multiple resonant controllers. The proposed control strategy performs outstanding voltage control performance to maintain an excellent voltage level such as zero steady-state error and low total harmonic distortion (THD) under the situation of sudden load changes, back power flow of renewable energy such as photovoltaic and nonlinear load in an isolated microgrid. Finally, the validity of the proposed approach is verified through simulations and a three-phase experiment prototype of BESS with TMS320F28335 DSP.

An LMI approach for the Integral Sliding Mode and H∞ State Feedback Control Problem

This paper deals with the state feedback control problem for linear uncertain systems subject to both matched and unmatched perturbations. The proposed control law is based on an the Integral Sliding Mode Control (ISMC) approach to tackle matched perturbations as well as the H∞ paradigm for robustness against unmatched perturbations. The proposed method also parallels the work presented in [1] which addressed the same problem and proposed a solution involving an Algebraic Riccati Equation (ARE)-based formulation. The contribution of this paper is concerned by the establishment of a Linear Matrix Inequality (LMI)-based solution which offers the possibility to consider other types of constraints such as \U0001d4d3-stability constraints (pole assignment-like constraints). The proposed methodology is applied to a pilot three-tank system and experiment results illustrate the feasibility. Note that only a few real experiments have been rarely considered using SMC in the past. This is due to the high energetic behaviour of the control signal.It is important to outline that the paper does not aim at proposing a LMI formulation of an ARE. This is done since 1971 [2] and further discussed in [3] where the link between AREs and ARIs (algebraic Riccati inequality) is established for the H∞ control problem. The main contribution of this paper is to establish the adequate LMI-based methodology (changes of matrix variables) so that the ARE that corresponds to the particular structure of the mixed ISMC/H∞ structure proposed by [1] can be re-formulated within the LMI paradigm.