Optimal Guaranteed Cost Research Articles

Robust integrated control of autonomous vehicles path following with response performance improvement considering lateral stability

In this paper, a robust integrated control scheme is developed for autonomous vehicles path following considering both yaw stability and roll stability. First, a controller with H∞ and optimal guaranteed cost performances is presented, and the poles of the closed-loop system are configured in a given disk region to improve the state response performance. The controller outputs front and rear wheel angles for path following, as well as an external yaw moment and an external roll moment for lateral stability control. Secondly, the braking forces acted on four wheels are optimally distributed by means of quadratic programing. Besides, the steering angles of the four wheels conform to the Ackermann geometry relation. Finally, the proposed control scheme is verified by CarSim/Simulink co-simulation, the results show that the scheme has better performance on path following accuracy and stability of yaw and roll. Meanwhile, constraining the poles in a given disk region can improve the state response performance of the vehicle during operation.

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.

Fuzzy Optimal Guaranteed Cost Control of a Single Specie Bio-Economic Singular Systems in Algae Environment

Fuzzy Optimal Guaranteed Cost Control of a Single Specie Bio-Economic Singular Systems in Algae Environment

Optimal guaranteed cost control of discrete-time uncertain systems subjected to state saturation nonlinearity

This paper investigates the optimal guaranteed cost (GC) control problem for uncertain discrete-time (DT) systems with state saturation nonlinearities via static-state feedback. The parameter uncertainties in the system state and input matrix are considered to be norm bounded. Utilizing Lyapunov theory and sector-based characterization of saturation nonlinearities, a novel criterion for the existence of GC controllers is proposed. The criterion is expressed in the framework of linear matrix inequalities (LMIs) and is thus computationally tractable. The proposed GC controllers make the closed-loop (CL) system asymptotically stable and ensure an adequate level of performance for all admissible parameter uncertainties. To design an optimum GC controller, a convex optimization problem with LMI constraints is formulated. The effectiveness of the proposed approach is illustrated by examples.

Optimal fault‐tolerant control for Markov jump power systems with asynchronous actuator faults

AbstractCommunication problems in the sensor‐to‐controller and controller‐to‐actuator channels can cause both the controller and actuator to run asynchronously with the original system in different operating modes. This paper investigates an optimal fault‐tolerant control approach for Markov jump power systems (MJPSs) with asynchronous controller and actuator. Firstly, an asynchronous controller is proposed to deal with incomplete information (i.e., system modes) transmission in the sensor‐to‐controller channel. Secondly, a new asynchronous actuator faults model is constructed to simultaneously represent the two partial losses, of modes information in the controller‐to‐actuator channel, and of control effectiveness (LoCE) caused by actuator faults. Under this framework, two related hidden Markov models (HMMs) are formed, which reveal that both the controller and actuator are asynchronous with the controlled system in different modes. By using Lyapunov and optimal approaches, sufficient conditions are derived to ensure that MJPSs are mean square stable with an optimal guaranteed cost. Finally, Monte Carlo simulations are used to verify the effectiveness of the proposed control method.

A Hierarchical Optimal Control of Uncertain and Time-Varying Knowledge Dissemination Model in Complex Network

In this paper, considering the multifactor influence of the knowledge dissemination process, a new ignorant-knower-spreader-forgetter (IKSF) knowledge dissemination model is proposed, which considers internalization mechanism, degradation mechanism, communication, and willingness, as well as time-varying and uncertain parameters. First, we prove that the knowledge loss equilibrium of the model is globally asymptotically stable when the basic reproduction number R 0 < 1 , and knowledge is permanent when R 0 > 1 . Next, improving the willingness of knower individuals and reducing the knowledge degradation function of spreader individuals can make the best effect of propagation; a hierarchical control strategy is designed. At the upper layer, an effective optimal control mechanism of the IKSF knowledge dissemination model is studied to provide optimal control action and minimization costs. At the lower layer, to guarantee robustness control performance and track the control targets, an intervention optimal guaranteed cost control strategy for the IKSF knowledge dissemination system with uncertain parameters is studied. Converting the controller’s design problem into a minimization problem with linear matrix inequalities, not only the impact of uncertain parameters is reduced but also the propagation effect of the knowledge dissemination model is guaranteed. Simulation results confirm our method.

Moving Target Landing of a Quadrotor Using Robust Optimal Guaranteed Cost Control

Dear Editor, This letter proposes a robust control strategy for the autonomous landing of a quadrotor on a moving target. Specifically, a force command that consists of a cascade dynamics estimator and an optimal guaranteed cost control law is exploited for the position-loop tracking. Then, an orientation constraint torque command is employed for the attitude-loop tracking such that the quadrotor refrains from flipping during the landing operation. Stability analysis indicates that the overall closed-loop system is asymptotically stable. Finally, flight experiments validate and access the theoretical results.

Guaranteed cost sampled‐data control for high‐speed train systems

AbstractThe optimal guaranteed cost sampled‐data control problem is studied for high‐speed train systems. To keep the relative speed and relative displacement of each high‐speed train stable, and ensure the performance level of high‐speed trains at the same time, sufficient conditions are obtained for the optimal guaranteed cost sampled‐data controller of train systems. By the convex optimization method, the minimum upper bound of high‐speed train systems is obtained. At last, two examples are presented to substantiate the correctness of theoretical results.

Recoil Control of Deepwater-Drilling Riser with Optimal Guaranteed Cost H∞ Control

In deepwater-drilling engineering, it is necessary to disconnect the bottom equipment of the lower marine-riser package from the blowout preventer when encountering multi-hazard environmental factors. In order to reduce the impact of recoil on the drilling platform after the sudden disconnection of the riser, in this paper, an optimal guaranteed cost H∞ recoil control problem is considered for the drilling riser. First, a three-element mass-damper-spring deepwater-drilling riser model subject to fluid discharge and heave motion of offshore platform is given. Then, an optimal guaranteed cost H∞ controller (OGCHC) is designed to suppress the recoil response of the drilling riser, and the sufficient conditions for the asymptotic stability of the closed-loop system are derived. Third, it is found through simulation results that the designed OGCHC can reduce the recoil response effectively. In order to further analyze the advantages of the OGCHC, the performance indices of the riser without active-recoil control and with optimal control (OC) and OGCHC are compared. It is shown that the average response amplitudes of three mass blocks of the riser are almost the same, while the control cost by the OGCHC is less than that by the OC. Further, under the designed recoil control, no riser compression occurs, thereby ensuring the safety of the riser system.

Optimal guaranteed cost intermittent control to the efficient movement of freight trains

Freight train system is under constant pressure to optimize operational efficiency, a factor that has led the sector to spearhead many new technologies. To address this, the optimal guaranteed cost intermittent cruise control of freight train system with time-varying uncertain parameters is investigated. In particular, the guaranteed cost intermittent control approach is proposed, which can achieve both advantages of guaranteed cost control and intermittent control methods. In addition, the acceptable conditions for the guaranteed cost control laws are weakened to insure that the proposed strategy is suitable for the application in freight train systems. Moreover, to promote the optimal control design in the freight train system, the proposed optimal guaranteed cost intermittent control for the nonlinear system subjected to norm bounded parametric uncertainties is addressed. The results of numerical experiments are presented to ascertain the effectiveness of the proposed freight train control methodology and to compare it to prior methods.

Optimal dynamic output feedback control of Lipschitz nonlinear systems under input saturation

In this study, the problem of optimal guaranteed cost control (OGCC) for nonlinear systems under input saturation is investigated. The purpose is to design a dynamic output feedback controller such that the closed-loop system is asymptotically stable and the upper bound of the cost function is minimized. Moreover, the designed controller ensures that the control signals do not exceed their permissible values. This leads to an optimization problem with bilinear matrix inequality (BMI) constraints. The BMI conditions are converted into the linear matrix inequality conditions by using some technical lemmas for straightforward computation of the controller matrices. The simulation results show the effectiveness and advantages of the proposed theoretical results.

A robust delay-dependent guaranteed cost PID multivariable output feedback controller design for time-varying delayed systems: An LMI optimization approach

This paper deals with the new formulated problem of designing a robust delay-dependent guaranteed optimal cost proportional-integral-derivative (PID) multivariable output feedback controller for linear uncertain time delay systems with nonlinear parameter perturbations using a linear matrix inequalities (LMI) approach. Several less conservative delay-dependent stability conditions are formulated for the time-delay system under consideration in terms of LMIs. Based on an augmented form of Lyapunov-Krasovskii functionals, the free weighting matrices and Wirtinger inequality techniques are employed to obtain improved performance. An optimal guaranteed cost PID controller which minimizes the upper bound of cost function is provided. The main advantage of the proposed approach is to decouple the input and the output gain matrices allowing to synthesize the controller gain matrices through a strict LMI technique. The synthesis conditions are thus formulated in LMI form which avoids the use of any iterative approach to resolve the feasibility problem. Two numerical examples selected from the literature are presented to illustrate the effectiveness of the developed methodology. The numerical results indicate that the proposed method performs efficiently in comparison to the approaches from the existing literature.

Membership-Function-Dependent Control Design and Stability Analysis of Interval Type-2 Sampled-Data Fuzzy-Model-Based Control System

This article investigates the design and stability analysis of the interval type-2 (IT2) sampled-data (SD) fuzzy-model-based (FMB) control system with the optimal guaranteed cost performance. An IT2 Takagi–Sugeno (T-S) fuzzy model is applied to describe the dynamics of the nonlinear systems where the parameter uncertainties are captured by the lower and upper membership functions. To conduct the stability analysis for the SD FMB control system, a looped-functional approach taking the advantage of the information about the sampling periods is employed. Because of the SD control strategy, the state will be sampled at each sampling instant and the control signal generated by the IT2SD fuzzy controller will be kept by the zero-order holder during the sampling period, which will result in mismatched membership grades between IT2 T-S fuzzy model and IT2SD fuzzy controller that leads to the complexity in carrying out stability analysis. Thanks to the imperfect premise matching concept, which allows the difference on the number of rules and the premise membership functions between model and controller, the design of the IT2SD fuzzy controller can be more flexible. To further relax the stability conditions and minimize the upper bound of the guaranteed cost index, the membership-function-dependent stability analysis approach which can make use of the features of the IT2 membership functions is adopted. The performance of the control system can also be adjusted through the choice of the weighting matrices in the cost function. The stability conditions building on the Lyapunov stability theory and the performance conditions building on the concept of the guaranteed cost control in the shape of linear matrix inequalities are established to assure the system stability and acquire the optimal guaranteed cost performance. The proposed IT2SDFMB control design is tested on the inverted pendulum system and the simulation results verify the effectiveness of the proposed approach.

Design and application of a tire slip energy control scheme based on optimal guaranteed cost theory for four‐in‐wheel drive electric vehicles

AbstractIn this paper, vehicle stability with time‐varying tire cornering stiffness and tire slip energy torque distribution is investigated for four‐in‐wheel motor drive electric vehicles thanks to the control flexibility. On the issue of tire slip energy, a scheme of “semi‐empirical tire slip energy model” is proposed and analyzed. In this scheme, the hierarchical control method is used to reduce tire slip energy and improve vehicle stability. In the outer loop controller, cost control is designed based on optimal guaranteed cost theory, which is compared with the traditional linear quadratic regulator. The integrated control method of active front steering and direct yaw moment control is evaluated and studied from the cost perspective by norm‐bounded uncertainty. Finally, the simulation results verify that the control framework considering time‐varying uncertainty has significant advantages under the condition of high‐friction coefficient single‐lane change and low‐friction coefficient slalom change. Compared with the linear quadratic regulator and the minimization of tire slip energy control, the control framework with optimal guaranteed cost can achieve smaller sideslip angle; meanwhile, it can save more tire slip energy.

Decentralized coordinated optimal guaranteed cost control for a roll-to-roll web machine

This article investigates a coordinated optimal guaranteed cost control (DCOGCC) for a multi-motor roll-to-roll web machine with time-varying and uncertain parameters. The state–space oriented DCOGCC law is designed to ensure that each subsystem of the web machine is stable and the upper bound of performance index is minimum. Linear matrix inequality (LMI) conditions to guarantee the stability of the systems with DCOGCC are derived. A decentralized model is adopted by regarding the entire machine as a synthetic system, then the original decentralized model is transformed into an equivalent one. By choosing appropriate information of consecutive subsystems as coordination variables, the DCOGCC scheme may attenuate the interaction effects between subsystems. The results of some simulations and experiments are given to verify the feasibility and effectiveness of the DCOGCC.

A Novel Coordinated Algorithm for Vehicle Stability Based on Optimal Guaranteed Cost Control Theory

A Novel Coordinated Algorithm for Vehicle Stability Based on Optimal Guaranteed Cost Control Theory

Robust stabilization of nonlinear stochastic 2‐D systems: LaSalle‐type theorem approach

SummaryLaSalle theorem (also known as the LaSalle invariance principle) plays an essential role in the systems and control theory. Recently, it has been extensively studied and developed for various types of one‐dimensional (1‐D) systems including deterministic and stochastic 1‐D systems in discrete‐ and continuous‐time domains. For two‐dimensional (2‐D) systems, such studies have received considerably less attention. In this article, based on discrete martingale theory, a LaSalle‐type theorem is first developed for a class of discrete‐time nonlinear stochastic 2‐D systems described by a Roesser model. The proposed result can be regarded as an extension of stochastic Lyapunov‐like theorem, which guarantees the convergence almost surely of system state trajectories. Extensions to the problem of optimal guaranteed cost control of nonlinear stochastic 2‐D systems are also presented. The proposed schemes are then utilized to derive tractable synthesis conditions of a suboptimal state‐feedback controller for uncertain 2‐D systems with multiplicative stochastic noises. The effectiveness of the obtained results is illustrated by given numerical examples and simulations.

Reliable H∞ guaranteed cost control for uncertain switched fuzzy stochastic systems with multiple time-varying delays and intermittent actuator and sensor faults

In this paper, the issue of delay-dependent passive fault-tolerant control and optimal guaranteed cost control is considered for multiple time-varying delayed switched Takagi–Sugeno (T–S) fuzzy stochastic systems against intermittent actuator and sensor faults, model uncertainties, external disturbances and measurement noise. This is the first attempt to implement H∞ guaranteed cost control for switched T–S fuzzy stochastic systems with intermittent actuator and sensor faults which allows more kinds of faults. Thus, the method has a wider application range. A dynamic output feedback controller is designed. Then, a closed-loop system is constructed. Stability results of reliable H∞ guaranteed cost control are given via piecewise fuzzy Lyapunov function in terms of linear matrix inequalities. Slack matrices are not required at all. The conservatism of this paper is relatively low. At last, the effectiveness of the addressed approach is presented by explanatory examples.

Guaranteed cost spacecraft attitude stabilization under actuator misalignments using linear partial differential equations

In this paper, the guaranteed cost spacecraft attitude stabilization problem is investigated through solving a linear partial differential equation (PDE). It is proved that the guaranteed cost spacecraft attitude controller design problem under actuator misalignments and disturbances can be reformulated into the problem of solving the linear PDE only once. It is also shown that the optimal guaranteed cost controller can be further designed through recursively solving the linear PDE. To alleviate the computational cost and implement the proposed guaranteed cost controller in higher dimensions, a nested sparse grid Chebyshev spectral collocation method is developed. Taking advantage of the designed numerical method, the resultant linear PDE is transformed into an efficiently solvable quadratic programming (QP) problem, and the controller can then be constructed analytically. Simulations show that the proposed controller successfully stabilizes the nonlinear system and also provides an upper bound for the defined performance index.

Guaranteed Cost Finite-Time Control of Uncertain Coupled Neural Networks.

This article investigates a robust guaranteed cost finite-time control for coupled neural networks with parametric uncertainties. The parameter uncertainties are assumed to be time-varying norm bounded, which appears on the system state and input matrices. The robust guaranteed cost control laws presented in this article include both continuous feedback controllers and intermittent feedback controllers, which were rarely found in the literature. The proposed guaranteed cost finite-time control is designed in terms of a set of linear-matrix inequalities (LMIs) to steer the coupled neural networks to achieve finite-time synchronization with an upper bound of a guaranteed cost function. Furthermore, open-loop optimization problems are formulated to minimize the upper bound of the quadratic cost function and convergence time, it can obtain the optimal guaranteed cost periodically intermittent and continuous feedback control parameters. Finally, the proposed guaranteed cost periodically intermittent and continuous feedback control schemes are verified by simulations.