Guaranteed Cost Control Research Articles

IT2‐Fuzzy‐Model‐Based Guaranteed Cost Control for Continuous‐Time MJSs With Non‐Consecutive Transmission and Quantization

ABSTRACTThis article addresses the asynchronous guaranteed cost control (GCC) problems for interval type‐2 (IT2) fuzzy continuous‐time Markov jump systems (C‐TMJSs) with quantization and non‐consecutive transmission. A dynamic event‐triggered mechanism (ETM) for IT2 fuzzy C‐TMJSs is designed to address the limited bandwidth and communication burden, which incorporates mode‐dependent thresholds and weighting matrices. An asynchronous IT2 fuzzy guaranteed cost controller possessing unmatched premise variable information is developed to stabilize the considered system, achieving desired GCC performance. The relationship between system mode and controller mode is described by the hidden Markov model (HMM). A quantizer is employed to quantize the signal prior to transmission to the next node, modeled as a stochastic quantization utilizing the HMM. Furthermore, an improved mode‐dependent and fuzzy‐dependent Lyapunov function is constructed for stability analysis, and the conditions of optimal GCC performance are derived. Finally, two examples are performed to validate the effectiveness of the proposed algorithms.

A High Performance Nonlinear Longitudinal Controller for Fixed-Wing UAVs Based on Fuzzy-Guaranteed Cost Control

Unmanned aerial vehicles (UAVs) have garnered more attention across various industries in recent years, leading to significant development in their design and application globally. Due to the high coupling between UAV states, model uncertainties, and various disturbances, precise longitudinal control of UAVs remains a significant research challenge. Oriented for the speed and altitude control of an electrical-powered fixed-wing UAV, this paper introduces a new control strategy based on the fuzzy guaranteed cost control (F-GCC) technique, which results in a nonlinear longitudinal state feedback control law with strict stability criterion, effectively addressing the issue of state coupling. Moreover, the strategy also includes a thrust estimation model of the electrical propulsion system to significantly reduce the nonlinearity, simplifying the controller design while effectively preserving tracking control performance. Through numerical validation, the UAV longitudinal nonlinear controller designed using the F-GCC technique offers better transient response and stronger robustness than the traditional linear and ADRC controllers.

Event-triggered finite-time guaranteed cost control of uncertain active suspension vehicle system

The event-triggered finite-time guaranteed cost control problem is important for an uncertain active suspension vehicle system. Existing works on the design of finite-time controllers for active suspension systems have not been extended to the event-triggered finite-time guaranteed cost control problem for uncertain active suspension systems. In this paper, we investigate the problem of designing an event-triggered finite-time guaranteed cost controller for an uncertain active suspension system. A new event-triggered controller and a cost function are first defined. Then, some new sufficient conditions for designing an event-triggered state feedback controller are derived based on linear matrix inequalities to stabilise the closed-loop systems while guaranteeing an adequate cost level of performance. Finally, numerical results and simulations are given to illustrate the effectiveness of the proposed method.

Event-triggered explorized IRL-based decentralized fault-tolerant guaranteed cost control for interconnected systems against actuator failures

This paper presents a novel data-based decentralized guaranteed cost (DGC) fault tolerant control (FTC) scheme for the large-scale systems subject to actuator faults and mismatched interconnection. First, the FTC issues of interconnected systems are converted into a series of near optimal event-triggered control (ETC) methods for isolated subsystems via constructing a modified performance index function of each subsystem. By means of adaptive dynamic programming (ADP) algorithm, the upper bound of performance index function of large-scale systems can be obtained by solving the Hamilton–Jacobi-Bellman (HJB) equation of each auxiliary subsystem. Second, according to the proposed ADP-based decentralized approach and utilizing the event-based synchronous integral reinforcement learning (IRL) algorithm, a model-free guaranteed cost (GC) FTC approach is developed for interconnected large-scale system which can relax the restriction on the condition that system functions must be known. Further, the ultimate uniformly bounded (UUB) stability of auxiliary subsystems can be proved according to the Lyapunov principle. Finally, the effectiveness of the proposed control method is verified by presenting the simulation results.

Guaranteed Cost Control of Impulsive Nonlinear Stochastic Systems With Mixed Time Delays

ABSTRACTThis article mainly addresses the guaranteed cost control (GCC) problem for a class of impulsive nonlinear stochastic systems with mixed time delays, where both distributed time delay as well as discrete time delay are considered. Utilizing the Hamilton–Jacobi inequalities technique, Lyapunov–Krasovskii functional (LKF) and stochastic control theory, a new delay‐dependent sufficient condition is acquired to ensure the asymptotic stability in probability (ASP) of the closed‐loop system (CLS). Moreover, the guaranteed cost controller is designed and the upper bound of cost function is given. At the same time, three corollaries are presented for the special circumstance without impulse, distributed time delays or time‐varying time delay, respectively. Finally, the feasibility of the theoretical results is verified by an example.

Event-triggered finite-time guaranteed cost control of asynchronous switched systems under the round-robin protocol via an AED-ADT method

Event-triggered finite-time guaranteed cost control of asynchronous switched systems under the round-robin protocol via an AED-ADT method

Neural Network-Based Robust Guaranteed Cost Control for Image-Based Visual Servoing of Quadrotor.

In this article, a neural network (NN)-based robust guaranteed cost control design is proposed for image-based visual servoing (IBVS) control of quadrotors. According to the dynamics of three subsystems (yaw, height, and lateral subsystems) derived from the quadrotor IBVS dynamic model, the main control design is to solve the robust control problem for the time-varying lateral subsystem with angle constraints and uncertain disturbances. Considering the system dynamics, a two-loop structure is conducted. The outer loop uses the linear quadratic regulator to solve the Riccati equation for the lateral image feature system, and the inner loop adopts the optimal robust guaranteed cost control to solve the lateral velocity system. For the lateral velocity system, the optimal robust control problem is transformed to solve the modified Hamilton-Jacobi-Bellman equation of the corresponding optimal control problem utilizing adaptive dynamic programming. The implementation is accomplished with the time-varying NN and the designed estimated weight update law. In addition, the stability and effectiveness are proved by the theoretic proof and simulations.

Observer-Based Quantized Guaranteed Cost Control of Fuzzy Networked Control Systems With Unreliable Links and Its Applications

Observer-Based Quantized Guaranteed Cost Control of Fuzzy Networked Control Systems With Unreliable Links and Its Applications

Protocol-based secure guaranteed cost control of sampled-data T-S fuzzy system with denial-of-service attack and input saturation

This paper proposes a protocol-based secure guaranteed cost sampled-data controller design problem of Takagi-Sugeno (T-S) fuzzy system under denial-of-service (DoS) attack and input saturation. First, in the absence of an effective description for the characteristics of received signals on controller, a novel scheduling protocol is proposed according to the characteristics of the round-robin protocol and DoS attack, which can guarantee the specific sequence characteristic for control updates. Then, via introducing input delay approach and switched system modeling method, a time-delay switched system with fixed switching sequence is introduced to describe the considered system with DoS phenomenon. Moreover, some novel control criteria are presented to ensure the resulting closed-loop system reaches a required cost level under the obtained control law. And an optimization problem is proposed to compute the optimal upper of the specified cost level. Finally, a simulation example is presented to demonstrate the effectiveness of the algorithm.

Guaranteed cost control for a class of composite hybrid aerial/terrestrial precise manipulator with stochastic switching payloads

AbstractThis article investigates the modeling and attitude control of a class of composite hybrid aerial/terrestrial precise manipulator (Chat‐PM) with stochastic switching payloads when attaching to a vertical surface. The dynamics of the Chat‐PM for aerial locomotion are modeled by transferring the force and moment of the end‐effector to the body based on the recursive Newton–Euler equations. Furthermore, the attitude dynamics of the Chat‐PM under the wall‐attachment condition is obtained by limiting the attitude angle/angular velocity and introducing the friction torque acting on the passive wheels for the first time. Taking into consideration the complexity of the task and the stochastic nature of environmental changes, the payload attached to the end‐effector is modeled as a continuous‐time Markov process with mode‐dependent fixed sojourn time in this study. The proposed guaranteed cost controller results in the Chat‐PM capable of stably attaching to a wall under random switching loads, while guaranteeing the quadratic performance cost with an attainable upper bound. Additionally, a convex‐optimization‐based guaranteed cost controller is proposed to optimize the performance cost in the random switching part. Finally, the effectiveness of the proposed guaranteed cost controllers is demonstrated by illustrative examples.

Quantized based dynamic-output-feedback guaranteed-cost control of interval-type-2 Takagi-Sugeno fuzzy systems under DoS attacks

This article investigates the issue of quantized guaranteed-cost dynamic-output-feedback control for uncertain-nonlinear NCSs with DoS attacks. Firstly, the interval-type-2 Takagi-Sugeno fuzzy model is built to deal with the nonlinear NCSs. Secondly, to reduce the burden on communication resources, the dynamic quantization is introduced from measurement-output and control-input. Considering the existence of DoS attacks in network channel, the DoS attacks model is constructed by binary-Markov-chain. This paper aims to obtain the controller and quantizers with DoS attacks. Some sufficient conditions of uncertain-nonlinear NCSs are received to ensure the stochastic stability and guaranteed-cost performance. Finally, an example is simulated to prove the advantage of proposed method.

Non‐fragile reliable guaranteed cost control and L2‐gain analysis for saturated switched nonlinear systems

AbstractFor the nonlinear continuous‐time saturated switched system, this article investigates the problem of non‐fragile reliable guaranteed cost control of the system. Due to the simultaneous occurrence of controller perturbation, actuator saturation and actuator failure, when designing the cost function, this article considers three scenarios affecting the system performance, controller perturbation, actuator saturation and actuator failure, simultaneously in the cost function, which has not been investigated in the existing literature. For nonlinear switched systems, we derive some sufficient conditions to satisfy simultaneously the stabilization of non‐fragile reliable guaranteed cost control and the performance index. In order to ensure the exponential stabilization of the nonlinear switched systems and minimize the upper bound of cost function, a switching law and the non‐fragile reliable guaranteed cost state feedback controllers are designed by using the minimum dwell‐time method. Furthermore, by solving optimization problems with linear matrix inequality constraints, the minimum upper bound of the cost function and the performance of the system are determined. At the end of the article, we give a numerical example to verify the effectiveness of the proposed approach.

Finite-time master–slave synchronization for implicit hybrid neural networks under event-triggered guaranteed cost control and random deception attacks

This paper researches the finite-time master–slave synchronization for implicit hybrid neural networks under event-triggered guaranteed cost control and random deception attacks. By developing Lyapunov–Krasovskii functional and exploiting singular value decomposition technique, the finite-time boundedness of synchronization error closed-loop system is achieved under deception attacks and event-triggered scheme, then the finite-time master–slave synchronization of implicit Markovian jump neural networks is realized. The desired gains of state feedback synchronization guaranteed cost controller are designed by solving a set of linear matrix inequalities. The availability of the given approach is confirmed by an artificial neural network and a numerical example.

Finite-time annular domain robust guaranteed cost control of interval positive linear systems

The issue of finite-time annular domain robust guaranteed cost control of positive linear systems with interval uncertainties is investigated in this paper. First, by using the linear copositive Lyapunov function, a sufficient condition for the existence of state feedback controller is given to ensure the positivity and finite-time annular domain robust stability of the closed-loop system, and guarantee the cost function is no more than a given upper bound. The corresponding controller design method is derived based on linear programming technique. Then, an optimisation algorithm is further developed to obtain the optimal guaranteed cost controller, which is convenient to be computed. Finally, a numerical example and an application example are given to demonstrate the effectiveness of theoretical results.

Pareto-based guaranteed cost control of discrete-time uncertain stochastic systems

The Pareto-based guaranteed cost control (GCC) of discrete-time uncertain stochastic systems in the infinite horizon is studied. Firstly, the convexity of the weighted sum objective function is proved. Based on this convexity, we demonstrate the relationship between Pareto optimality and minimization of the weighted sum objective function. This relationship confirms that the Pareto-based GCC strategy can be obtained by optimizing the weighted sum objective function. Secondly, to address the Pareto-based GCC issue for discrete-time uncertain stochastic systems, we derive the generalized algebraic Riccati inequality (GARI) specific to these systems. Thirdly, the necessary condition for a Pareto-based guaranteed cost controller is derived using the Karush–Kuhn–Tucker (KKT) condition. Lastly, we introduce a method based on linear matrix inequality (LMI) to determine the Pareto-based GCC strategy. This method reduces computational complexity and establishes the sufficient conditions for a Pareto-based guaranteed cost controller. To validate our findings, we provide a example implemented in MATLAB, confirming the accuracy of the proposed approach.

A Neural-Reinforcement-Learning-Based Guaranteed Cost Control for Perturbed Tracking Systems

A Neural-Reinforcement-Learning-Based Guaranteed Cost Control for Perturbed Tracking Systems

Asynchronous event-triggered guaranteed cost control of uncertain 2-D Markov jump Roesser systems with actuator saturation

This paper investigates the asynchronous event-triggered guaranteed cost control problem for two-dimensional Markov jump Roesser systems with parameter uncertainties and actuator saturation. The hidden Markov model is constructed to characterize the asynchronous phenomenon induced by the mode mismatch between the system and the controller, and a hidden Markov model-based event-triggered mechanism is adopted in controller design to save communication resources. The convex hull representation is employed to process saturated inputs. By using the quadratic Lyapunov function methods and linear matrix inequality techniques, some sufficient criteria are developed to guarantee the asymptotic stability of the addressed system with a guaranteed cost under three different boundary conditions. Finally, a convex optimization algorithm with linear matrix inequality constraints is proposed to design the optimal asynchronous event-triggered guaranteed cost controller, and a numerical example is considered to demonstrate its validity.

Computationally efficient guaranteed cost control design for homogeneous clustered networks

We consider a clustered network where connections inside the cluster are dense and between clusters are sparse. This leads us to a classical decoupling into fast (intra-cluster) and slow (inter-cluster) dynamics. Our objective is to provide a computationally efficient method to design control strategies that guarantee a certain bound on the cost for each cluster. Basically, we design a composite synchronizing controller with two terms: one responsible for the intra-cluster synchronization and the other achieving the synchronization between clusters. The first one does not require much computational effort since an analytic expression describes it. The second term is designed through a satisfaction equilibrium approach. In other words, the internal (fast) and external (slow) controllers are independently designed, and they ensure a guaranteed satisfactory cost for each cluster. Moreover, we show that the internal control affects the cluster cost only for a short time period. Finally, numerical simulations illustrate the theoretical results.

Parametrized guaranteed cost method with prescribed performance via critic‐only ADP for uncertain nonlinear systems and disturbances

AbstractIn this paper, a novel parametrized guaranteed cost control (PGCC) method with prescribed performance control (PPC) is proposed for nonlinear systems with unknown bounded uncertainties and external disturbances described by Euler‐Lagrange (EL) equations. The proposed method is capable of ensuring a robust optimal performance in the presence of dynamics constraints without the specific information of nonlinear perturbation. As a consequence, the conditions in the form of disturbances and uncertainties are also relaxed. The augmented model is converted by transforming the uncertainties and disturbances in the original system to a mismatched term using asymmetric PPC. By designing and modifying the novel guaranteed cost function to account for the maximum value of the nonlinear perturbation, an infinite‐horizon PGCC problem is proposed by the unconstrained stationary optimal control problem. The relevant proposed linear parametrized Hamilton‐Jacobian‐Bellman (PHJB) equation is approximated to solve by a critic‐only neural network (NN) with efficient computationally. Uniformly ultimately bounded stability is guaranteed via a Lyapunov‐based stability analysis. Finally, numerical simulation results demonstrate the effectiveness of the proposed control scheme.

Quantized guaranteed cost dynamic output feedback control for uncertain nonlinear networked systems with external disturbance

In this article, the guaranteed cost control problem for a class of nonlinear networked control systems (NCSs) with dynamic quantization, external bounded disturbance, and data dropout is investigated via the dynamic output feedback. The Takagi–Sugeno (T-S) fuzzy model is used to represent the discrete-time nonlinear system discussed in this paper. Under the dynamic quantization strategy, two quantizers with dynamic parameters are used to quantize the measured output and control input, and the data dropout process is described by introducing the Bernoulli stochastic variable. By using the quadratic boundedness technique, the quadratic stability of the quantized NCS with external disturbance is described. Furthermore, the sufficient condition for the global design approach are proposed, that is, not only the dynamic output feedback controller but parameters of the quantizers are designed synchronously with strict linear matrix inequalities. Eventually, a simulation of nonlinear mass-spring-damper mechanical system is carried out to verify the effectiveness of the provided algorithm.