Stabilization Of Control Systems Research Articles

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.

Zero-Phase FIR Filter Design Algorithm for Repetitive Controllers

Repetitive controllers (RCs) are linear control structures based on the internal model principle. This control strategy is known for its ability to control periodic reference signals, even if these signals have many harmonic components. Despite being a solution that results in a good performance, several parameters of the repetitive controller need to be correctly tuned to guarantee its stability. Among these parameters, one that has high impact on the system performance and stability is the finite impulse response (FIR) filter, which is usually used to increase the stability domain of RC-based controllers. In this context, this paper presents a complete tutorial for designing the zero-phase FIR filter, which is often used to stabilize control systems that use RC-based controllers. In addition, this paper presents a Matlab® application developed for performing the stability analysis of RC systems and designing its FIR filter. Simulation and experimental results of a shunt active power filter are used to validate the algorithm and the Matlab® application.

Event‐triggered adaptive stabilization control of stochastic nonlinear systems with unmodeled dynamics

AbstractIn this paper, we present a novel controller design method for stochastic nonlinear systems with unmodeled dynamics, uncertain parameters, and unknown covariance noise. In order to deal with these uncertainties, a new event‐based small gain controller is designed. The event‐triggered scheme can reduce the computational burden caused by disturbance and noise. By combining the technique of changing supply rate with small gain condition, a stochastic input‐to‐state practically stability Lyapunov function is obtained for the subsystem. Simultaneously, the changing supply function is used to treat with unmodeled dynamics. Based on backstepping process and adaptive control approach, the influence of unknown covariance noise is overcome. It is proved that the designed state‐feedback controller can ensure the overall system is stochastic input‐to‐state practically stability.

Output Feedback Stabilization of Nonlinear Strict-feedback Networked Control Systems

Design of output feedback semiglobally practically input-to-state (SPIS) stabilizing controllers for nonlinear strict-feedback networked systems is considered. We first design continuous-time state feedback globally asymptotically (GA) stabilizing controllers and discrete-time reduced-order observers and combine the emulation of state feedback controllers and the designed observers to construct discrete-time output feedback controllers. Then we show that the designed controllers SPIS stabilize nonlinear strict-feedback networked control systems when transmission intervals are sufficiently small and communication networks satisfy suitable assumptions. A numerical example is also given to illustrate the efficiency of proposed design of controllers.

Accurate Peer-to-Peer Hierarchical Control Method for Hybrid DC Microgrid Clusters

Hybrid DC microgrid clusters contain various types of converters such as BOOST, BUCK, and bidirectional DC/DC converters, making the control strategy complex and difficult to achieve plug-and-play. The common master–slave hierarchical control strategy makes it difficult to achieve accurate and stable system control. This paper proposes an accurate peer-to-peer hierarchical control method for the hybrid DC microgrid cluster, and the working principle of this hierarchical control method is analyzed in detail. The microgrid cluster consists of three sub-microgrids, where sub-microgrid A consists of three BUCK converters, sub-microgrid B consists of three BOOST converters, and sub-microgrid C consists of two bidirectional DC/DC converters. According to all possible operations of various sub-microgrids in the microgrid cluster, the top-, mid-, and bottom-level controls are designed to solve the coordination control problem among different types of sub-microgrids. In this paper, a hybrid microgrid cluster simulation model is built in the PLECS simulation environment, and an experimental hardware platform is designed. The simulation and experiment results verified the accuracy of the proposed control strategy and its fast plug-and-play regulation ability for the system.

Lyapunov-based fixed-time stabilization control of quantum systems

In this paper, we consider the fixed-time stabilization control problem of quantum systems modeled by Schrödinger equations. Firstly, the Lyapunov-based fixed-time stability criterion is extended to finite-dimensional closed quantum systems in the form of coherence vectors. Then for a two-level quantum system with single control input, a non-smooth fractional-order control law is designed using the relative state distance. By integrating the fixed-time Lyapunov control technique and the bi-limit homogeneity theory, the quantum system is proved to be stabilized to an eigenstate of the inherent Hamiltonian in a fixed time. Comparing with existing methods in quantum system control, the proposed approach can guarantee stabilization in a fixed time without depending on the initial states.

Stabilization of uncertain networked control systems with actuator saturation and probabilistic cyberattacks

AbstractThis paper investigates the stabilization of uncertain networked control systems (NCSs) with actuator saturation and cyberattacks. The cyberattacks are governed by a set of independent random variables satisfying Bernoulli distribution. To relieve the network bandwidth load effectively, an event‐triggered communication strategy is proposed. By employing Lyapunov stability theory and stochastic analysis techniques, a stability criterion is obtained for the system with actuator saturation and cyberattacks. Moreover, the desired controller gain is derived by solving some matrix inequalities. Finally, the validity and applicability of the criteria are verified through numerical examples.

An exponential stabilization of random impulsive control systems and its application to chaotic systems

This paper addresses the problem of pth moment exponential stability and stabilization for random impulsive control systems. Some novel pth moment exponential stability and synchronization approaches are established based on the method of maximum and minimum eigenvalues by using the Lyapunov functions and Razumukhin technique. Finally, we show that the stability and synchronization behavior of random impulses are faster than the fixed time impulses. Some physical examples are given to verify the validity and usefulness of the results obtained.

Dynamic output feedback robust [formula omitted] control of networked control systems with time-Varying delays via T-S fuzzy models

This paper addresses the problem of robust stabilization for networked control systems (NCS) where the stochastic behavior of the network does not allow correct and complete transmission of data to both the actuators and the controller. The objective is to model the NCS using Takagi-Sugeno (T-S) fuzzy systems with uncertainties and external disturbances and to design a time-varying delay fuzzy controller such that the closed-loop system is robustly exponentially stable with a prescribed decay rate. Sufficient conditions are derived using the delay-dependent Lyapunov-Krasovskii functional with a robust H∞ controller in terms of linear matrix inequalities (LMIs). Accordingly, desired fuzzy controllers are designed by using feasible solutions to the obtained LMIs. The proposed fuzzy controller can keep the T-S fuzzy system stable in the presence of time-varying delay, uncertainties, and external disturbance. Two numerical examples with different conditions on parameters are provided to illustrate the performance and robustness of the proposed approach.

LESO-Based Nonlinear Continuous Robust Stabilization Control of Underactuated TORA Systems

In this paper, we consider the robust stabilization control problem of underactuated translational oscillator with a rotating actuator (TORA) system in the presence of unknown matched disturbances by employing continuous control inputs. A nonlinear continuous robust control approach is proposed by integrating the techniques of backstepping and linear extended state observer (LESO). Specifically, based on the backstepping design methodology, a hyperbolic tangent virtual control law is designed for the first subsystem of the cascaded TORA model, via which an integral chain error subsystem is subsequently constructed and the well-known LESO technique is easy to implement. Then, an LEO is designed to estimate the lumped matched disturbances in real-time, and the influence of the disturbances is compensated by augmenting the feedback controller with the disturbance estimation. The convergence and stability of the entire control system are rigorously proved by utilizing Lyapunov theory and LaSalle’s invariance principle. Unlike some existing methods, the proposed controller is capable of generating robust and continuous control inputs, which guarantee that both the rotation and translation of TORA systems are stabilized at the origin simultaneously and smoothly, attenuating the influence of disturbances. Comparative simulation results are presented to demonstrate the effectiveness and superior control performance of the proposed method.

Event‐triggered control of quasi‐LPV systems with communication delays

AbstractThis paper addresses the dynamic periodic event‐triggered control for local stabilization of nonlinear networked control systems with communication delays. Based on a polytopic quasi‐linear parameter‐varying (quasi‐LPV) model of the nonlinear plant and the Lyapunov–Krasovskii stability theory, a local stability analysis condition is established. Then a constructive co‐design condition is proposed to jointly design the state‐feedback control law and the trigger rule. The local asymptotic stability of the closed‐loop equilibrium point of interest is ensured with a guaranteed region of attraction where trajectories remain inside even in the presence of communication delays. An optimization procedure is proposed to perform the co‐design considering the objectives of enlarging the guaranteed region of attraction and reducing the number of transmissions. Numerical examples indicate a trade‐off between these two objectives. Also, the examples illustrate the effectiveness of the proposed dynamic event‐triggered control co‐design approach over both its static counterpart and periodic time‐triggering mechanisms.

Exponential stability of sampled-data control systems with enhanced average sampling interval

The stabilisation of the sampled-data control systems is addressed to tolerate large sampling intervals that tend to destroy the system's stability. A new sampling sequence is constructed from two sequences with two different sampling time intervals, where the short one corresponds to a stable system, while the long one produces an unstable system. The decay rate of the state trajectory of the former is utilised to overcome the growth rate of the latter, such that the resulting system with mixed sampling intervals is globally exponentially stable. A sufficient condition for stabilisation is given. It is applicable to the system with a single sampling interval under the missing data scenario. The examples are given to illustrate the proposed results.

Dynamic real-time optimization for nonlinear systems with Lyapunov stabilizing MPC

The present work addresses the problem of stabilizing dynamic real-time optimization and control of nonlinear systems. Dynamic real-time optimization (DRTO) is a framework for computing an optimal operating trajectory for a plant and providing corresponding set-points for an underlying control algorithm to track. This technique can be enhanced by directly modeling the underlying control algorithm (such as an MPC) in a closed-loop DRTO (CL-DRTO). This allows the CL-DRTO to predict both the controller and plant responses to set-point changes, improving performance of the overall system. Certain systems are additionally complicated by the existence of unstable steady states, which make control of the system substantially more difficult. A number of stabilizing MPC techniques have been developed in order to handle this, and a closed-loop DRTO formulation was recently proposed to handle linear systems. This work seeks to bring the improved performance of a CL-DRTO to stabilizing control systems by formulating a CL-DRTO which utilizes and explicitly models an underlying Lyapunov stabilizing MPC to achieve stabilization for nonlinear systems. The proposed formulation is compared to the previously developed formulation to demonstrate the improved closed-loop control and performance.

Stabilization of networked singular control systems under double-channel quantization and DoS attacks

This paper is concerned with the asymptotic stabilization of discrete singular systems over a bandwidth limited digital network, when the state measurements are periodically sampled and encoded using a finite alphabet, and the control input signals are subject to finite-alphabet encoding and Denial-of-Service attacks. It is assumed that the attack signals are uniform for all sampling periods and have been identified. A dynamic controller is designed based on a restricted equivalent model of the controlled plant. Two types of finite-level quantizers are designed for encoding: uniform and logarithmic. For both types of quantizers, dynamic encoding-decoding strategies for the plant state and the control input are proposed, which exploit the controller’s state and the origin, respectively, as the quantization centers. Sufficient conditions for asymptotic stabilizability involving the sampling period, the numbers of the state and input quantization levels, the beginning time and corresponding duration of the attack signals are established by propagating reachable sets during sampling interval. Finally, several numerical examples are given to illustrate the design procedures and the efficacy of the theoretical results.