Stabilization Of Control Systems Research Articles

Finite‐time stabilization control of nonlinear systems with full‐state constraints

AbstractThis paper studies the finite time stabilization control (FTSC) problem of nonlinear systems with unknown functions and full‐state constraints (FSCs). A lemma dealing with unknown functions is put forward so that the assumptions and the “explosion of terms” (EOT) of backstepping are avoided. Compared with approximation algorithms, this algorithm can make the system states converge to the origin in a finite time. On the other hand, a new logarithmic constraint function is utilized to solve the drawback of barrier Lyapunov functions (BLFs). Then, combined with finite time control (FTC), an FTSC algorithm with FSCs is proposed. Finally, simulations of Chua's circuit system are given to verify the effectiveness and superiority of this algorithm. Compared with the approximation algorithm, this algorithm can theoretically make the states of Chua's circuit system to the origin in a finite time.

Stabilization and Synchronization Control of Multi Coupled Hyperbolic-Parabolic Partial Differential Systems Based on Backstepping Method

Stabilization and Synchronization Control of Multi Coupled Hyperbolic-Parabolic Partial Differential Systems Based on Backstepping Method

Relaxed static output stabilization of polynomial fuzzy control systems by Lagrange membership functions

AbstractThis article is concerned with the stability analysis of the static output‐feedback polynomial fuzzy‐model‐based (SOF PFMB) control systems through designing a novel membership grade integration (MGI) approach. The nonconvex problems of the SOF PFMB control systems are convexificated into the convex conditions by introducing block diagonal positive‐definite Lyapunov matrix and nonsingular transformation matrix. We proposed new approximate membership functions, that is, Lagrange membership functions (LMFs), which can be introduced into the stabilization process to relieve the conservativeness of stability results. The LMFs are general representations of piecewise‐linear membership functions, which makes the number of stability conditions not limited by the number of sample points. In a fixed subdomain, arbitrary sample points can be employed by the LMFs method and achieve higher approximation capability by increasing more sample points so that membership grades can be incorporated into the system analysis. Furthermore, a novel MGI approach, including the information of premise variables and LMFs, is proposed making the stability conditions more relaxed. Finally, two simulation examples show the merits of the developed techniques.

Emulation-based stabilization for networked control systems with stochastic channels

This paper studies the stabilization problem of networked control systems (NCSs) with random packet dropouts caused by stochastic channels. To describe the effects of stochastic channels on the information transmission, the transmission times are assumed to be deterministic, whereas the packet transmission is assumed to be random. We first propose a stochastic scheduling protocol to model random packet dropouts, and address the properties of the proposed stochastic scheduling protocol. The proposed scheduling protocol provides a unified modelling framework for a general class of random packet dropouts due to different stochastic channels. Next, the proposed scheduling protocol is embedded into the closed-loop system, which leads to a stochastic hybrid model for NCSs with random packet dropouts. Based on this stochastic hybrid model, we follow the emulation approach to establish sufficient conditions to guarantee uniform global asymptotical stability in probability. In particular, an upper bound on the maximally allowable transmission interval is derived explicitly for all stochastic protocols satisfying Lyapunov conditions that guarantee uniform global asymptotic stability in probability. Finally, two numerical examples are presented to demonstrate the derived results.

Decentralized Predictor Stabilization for Interconnected Networked Control Systems with Large Uncertain Delays and Event-Triggered Input

In this article, we propose a control scheme with predictors in a decentralized manner for coupled networked control systems (NCSs) under uncertain, large time-delays and event-triggered inputs. The network-induced delays are handled via the prediction; thus, the delay value is allowed to be large, and the burden of the network is relieved by the event-triggered input. Two methods are employed to deal with the large delay issue: the state and output feedback. When the state of each subsystem is measurable, full-state feedback is used, whereas when the plant state cannot be measured, output feedback is employed with the help of an observer, which is more common in practice. Instead of treating the interactive plants like a global system, the exponential stability of the coupled systems, under decentralized predictors with asynchronous sampled-data feedback, is analyzed in a decentralized way. Finally, the proposed methods are verified via an example of three interconnected cart–pendulum systems, while such systems would not be stabilizable by the traditional approach when the network-induced delays are relatively large.

Genetic algorithm for stabilization of complex control systems

Genetic algorithm for stabilization of complex control systems

Prescribed-time stabilization and inverse optimal control of stochastic high-order nonlinear systems

Prescribed-time stabilization and inverse optimal control of stochastic high-order nonlinear systems

Sampled-data stabilization for networked control systems under deception attack and the transmission delay

For the stability analysis and stabilization synthesis problems, this paper considers networked control systems (NCSs) with the transmission delay and the deception attack under aperiodic samplings, where the deception attack and its activation function are represented as a sector bound function and a random variable with Bernoulli distribution, respectively. This paper proposes the stability and stabilization criteria for the NCSs by constructing Lyapunov–Krasovskii (L–K) functionals with continuous functionals and looped-functionals. Compared with the literature, the proposed continuous functionals take into account the mixed delay including the transmission delay and the maximum allowable sampling interval, as well as the augmented vector and integral terms. Also, the proposed looped-functionals construct two augmented vectors with integral vectors that are zeros at t=tk and t=tk+1, respectively. By utilizing these two augmented vectors, the looped-functionals fully utilize the sampling patterns compared with the literature. Based on the proposed L–K functionals, this paper derives not only the stability criterion for the NCSs with the transmission delay, but also the stabilization criterion for the NCSs with the transmission delay and the deception attack in terms of linear matrix inequalities (LMIs), respectively. Numerical example demonstrates the validity of the proposed approach.

Output-Feedback Stabilization of Stochastically-Sampled Networked Control Systems Under Packet Dropouts

Output-Feedback Stabilization of Stochastically-Sampled Networked Control Systems Under Packet Dropouts

New results on dynamic output state feedback stabilization of some class of time-varying nonlinear Caputo derivative systems

In modern control theory applications, input–output feedback often arises and plays a crucial role in stabilizing any target control systems. However, in many practical applications, the knowledge of full information on the state of systems may not be available in general due to measurements. In order to control such types of systems, this paper uses a universal concept of real order calculus to stabilize by the method of dynamic output feedback control. Is it possible to design a dynamic output feedback stabilization for time-varying real order control systems? This work develops a new dynamic output feedback control method and proposes linear homogeneous time-varying control law to stabilize incommensurate nonlinear time-varying real order systems under the action of Caputo derivative with an addendum of ultimate random initial-time. We utilize the ideas of the comparison method and establish order-dependent asymptotic results associated with uniform Lipschitz continuous functions that provide stabilization by means of the dynamic output state feedback control method. We provide three examples that include a practical system and show the importance of some theoretical results in the demonstration to stabilize the problems by means of proposed control method.

Anti-windup scheme-based control for fractional-order systems subject to actuator and sensor saturation

This paper addresses the problem of dissipative-based stabilization for fractional-order nonlinear control systems with uncertainties, time-delay, external disturbances, actuator faults, actuator and sensor saturations. Specifically, a non-fragile reliable dynamic output feedback controller is designed for the purpose of stabilization of the addressed system. Due to the effect of saturation phenomena occurring in both the actuator and sensor, the anti-windup loops framed with the help of the observer design are incorporated into the controller design. Some sufficient conditions are formulated in terms of linear matrix inequalities by choosing a suitable Lyapunov function thereby assuring the dissipative-based stabilization. The derived results are thus validated by two numerical examples including the practical model of two-stage chemical reactor.

Exponential stabilization of Riesz-spectral bilinear boundary control systems

Exponential stabilization of Riesz-spectral bilinear boundary control systems

Robustifying event-triggered control to measurement noise

While many event-triggered control strategies are available in the literature, most of them are designed ignoring the presence of measurement noise. As measurement noise is omnipresent in practice and can have detrimental effects, for instance, by inducing Zeno behavior in the closed-loop system and with that the lack of a positive lower bound on the inter-event times, rendering the event-triggered control design practically useless, it is of great importance to address this gap in the literature. To do so, we present a general approach for set stabilization of (distributed) event-triggered control systems affected by additive measurement noise. It is shown that, under general conditions, Zeno-free static as well as dynamic triggering rules can be designed such that the closed-loop system satisfies an input-to-state practical set stability property. We ensure Zeno-freeness by proving the existence of a uniform strictly positive lower-bound on the minimum inter-event time. The general approach is applied to point stabilization and consensus problems as particular cases, where we show that, under similar assumptions as the original work, existing schemes can be redesigned to robustify them to measurement noise. Consequently, using this approach, noise-robust triggering conditions can be designed both from the ground up and by simple redesign of several important existing schemes. Simulation results are provided that illustrate the strengths of this novel approach.

Fuzzy adaptive stabilization control for nonlinear systems with FSCs

This paper proposes a new full-state constraints (FSCs) control scheme for stabilizing nonlinear systems with unknown functions. This scheme solves the “explosion of terms (EOT)” problem of backstepping using a lemma and introduces fuzzy control to approximate the unknown functions. This ensures that all signals are semi-globally uniformly ultimately bounded (SGUUB), and the system state converges to a neighborhood of the origin. In order to get a smaller neighborhood and higher accuracy, a new time-varying constraint function is proposed to solve the FSCs. This method can directly design the constraint functions according to actual needs, and it is easy to implement, thus avoiding the shortcomings of the barrier Lyapunov functions (BLFs) and the mapping constraint functions. And it affects the steady-state performance of the states. Therefore, the constraint functions can be constructed to make the states approach a smaller neighborhood, thus making the steady-state performance error of the states is smaller. Thirdly, the algorithm is applied to Chua's circuit system, which verifies its validity.

Prescribed-time stabilization control for p-norm stochastic nonlinear systems based on homogeneous dominant technique

In this article, a prescribed-time state-feedback stabilization design strategy is proposed for a class of p-norm stochastic nonlinear strict feedback systems. In previous work on prescribed-time stabilization of stochastic systems, only stochastic nonlinear systems with fractional power less than or equal to one are considered. To overcome this problem, we improve the existing method and discuss the issue of prescribed-time stabilization of stochastic nonlinear systems with fractional power is arbitrary positive odd rational number. First, a prescribed-time controller is designed by combining the Lyapunov function with adding a power integrator technique. It should be pointed out that the homogeneous domination approach is adopted when dealing with the nonlinear terms of the system. Then, according to the stochastic prescribed-time stability theorem, it is proved that the designed controller can ensure the closed-loop system is prescribed-time mean-square stable. Finally, three simulation examples are given to investigate the validity of the presented method, in which the last one is an electromechanical system example.

Event-triggered [formula omitted] stabilization of networked cascade control systems under periodic DoS attack: A switching approach

This paper deals with the H∞ control design for the networked cascade control systems (NCCSs) subject to periodic denial-of-service (DoS) attack. The controller structure is based on the state-feedback controller for the both control loops. The communication network of the primary loop is equipped with an event-triggered mechanism while the network is under periodic DoS attack. For stability analysis and controller design, the mathematical model of the closed-loop system is formulated based on the switching systems approach. By using the piecewise Lyapunov-functional-based approach and average dwell time techniques, some stability and stabilization criteria are derived and presented in the form of linear matrix inequalities (LMIs). Finally, an steam temperature cascade control system is utilized as a practical example to demonstrate the effectiveness of the proposed method.

Data-driven quadratic stabilization and LQR control of LTI systems

In this paper, we propose a framework to solve the data-driven quadratic stabilization (DDQS) and the data-driven linear quadratic regulator (DDLQR) problems for both continuous and discrete-time systems. Given noisy input/state measurements and a few priors, we aim to find a state feedback controller guaranteed to quadratically stabilize all systems compatible with the a-priori information and the experimental data. In principle, finding such a controller is a non-convex robust optimization problem. Our main result shows that, by exploiting duality, the problem can be recast into a convex, albeit infinite-dimensional, functional Linear Program. To address the computational complexity entailed in solving this problem, we show that a sequence of increasingly tight finite dimensional semi-definite relaxations can be obtained using sum-of-squares and Putinar’s Positivstellensatz arguments. Finally, we show that these arguments can also be used to find controllers that minimize a worst-case (over all plants in the consistency set) closed-loop H2 cost. The effectiveness of the proposed algorithm is illustrated through comparisons against existing data-driven methods that handle ℓ∞ bounded noise.

Global stabilization control for multiple input multiple output nonlinear systems with unknown function vector

AbstractIn this article, a control algorithm is proposed to solve the global stabilization control problem of multiple input multiple output (MIMO) nonlinear systems with unknown function vectors (UFVs). Firstly, a Lemma dealing with UFVs is proposed. Then, combined with the backstepping method, the controller is designed such that all signals of the closed‐loop system are globally stable. Compared with the approximation method, the algorithm in this article solves the global stabilization control problem. Compared with the assumptions of UFVs, the algorithm in this article reduces the conservatism problem. At the same time, the algorithm in this article also solves the “explosion of terms” problem of backstepping. Compared with the methods to solve this problem: dynamic surface control (DSC) and direct fuzzy control, the algorithm in this article can make all signals of the closed‐loop system converge to the origin. Finally, the algorithm is applied to the model of spacecraft with modified Rodrigues parameters, and the simulation results show the effectiveness of this algorithm.

A Looped Functional Method to Design State Feedback Controllers for Lurie Networked Control Systems

Dear Editor, This letter deals with the stabilization of Lurie networked control systems with network-induced delays (NID). By constructing a two-sided looped Lyapunov functional, a sufficient condition is derived to ensure the absolute stability of the resultant closed-loop system under a state feedback controller. Then, based on this condition, a cone complementary linearisation (CCL) iterative algorithm is presented to design state feedback controller. It is shown via a numerical example that the proposed method can deliver less conservative results as well as fewer iterations if compared with existing ones.

Attack-model-independent stabilization of networked control systems under a jump-like TOD scheduling protocol

This paper is concerned with the stabilization of networked control systems (NCSs) under multi-packet transmission and denial of service (DoS) attacks. To deal with node congestions and DoS attacks, a jump-like try-once-discard (TOD) protocol is first proposed to orchestrate the priority of normal nodes and the attacked nodes over the network. Compared with the existing TOD scheduling, the proposed scheduling scheme has the advantage of jumping out the attacked nodes by designing node weighting matrices. To reduce the effects of DoS attacks, an attack-model-independent impulsive closed-loop model is well established, which couples the effects of the proposed protocol and DoS attacks in a unified framework. Then, a sufficient attack-model-independent stabilization criterion is derived. Compared with the existing attack-model-dependent methods, the desired dynamic output feedback performance is well guaranteed under multi-channel time-varying DoS attacks. Finally, an illustrative example is used to verify the effectiveness of proposed method.