Robust state-feedback control design for active suspension system with time-varying input delay and wheelbase preview information

This paper develops a robust state-feedback controller for active suspension system with time-varying input delay and wheelbase preview information in the presence of the parameter uncertainties. By employing system augmentation technique, a multi-objective control optimization model is first established and then this controller design is converted to a static full-state feedback controller design with robust H_∞ and generalized H₂ performance, wherein the model-dependent control gain is evaluated by transforming the related nonlinear matrix inequalities into their corresponding linear matrix inequality forms based on Lyapunov theory, and then LMI (Linear-Matrix-Inequality) technique is applied to solve and obtain the desired controller. A numerical simulation case is finally provided to reveal the effectiveness and advantages of the proposed controller.     

Event-triggered control for active vehicle suspension systems with network-induced delays

This paper presents a novel event-triggered H_∞ static output-feedback control for active vehicle suspension systems with network-induced delays. The proposed control schema introduces an event-triggering mechanism in the suspension system such that the communication resources can be significantly saved. By applying some improved slack inequalities and an augmented Lyapunov–Krasovskii functional (LKF), a new design condition expressed in the form of linear matrix inequalities (LMIs) is developed to derive the desired event-triggered controller. The obtained algorithm is then employed to solve the static output-feedback control gain. Compared with the traditional sampled-data H_∞ control scheme, the proposed controller is able to provide an enhanced disturbance attenuation level while saving the control cost. Finally, comparative simulation results are provided to show the performance of the proposed event-triggered controller.     

H∞ guaranteed cost control for uncertain Markovian jump systems with mode-dependent distributed delays and input delays

This paper investigates the H_∞ guaranteed cost control problem for mode-dependent time-delay jump systems with norm-bounded uncertain parameters. Both distributed delays and input delays appear in the system model. Based on a matrix inequality, a sufficient condition for the existence of robust H_∞ guaranteed cost controller is derived, which stabilizes the considered system and guarantees that both the H_∞ performance level and a cost function have upper bounds for all admissible uncertainties. By the cone complementary linearization approach, the desired state-feedback controller can be constructed. A numerical example is provided to show the effectiveness of the proposed theoretical results.     

Nonlinear H∞ robust control applied to F-16 aircraft with mass uncertainty using control surface inverse algorithm

In this paper, an analytic solution of nonlinear H_∞ robust controller is first proposed and used in a complete six degree-of-freedom nonlinear equations of motion of flight vehicle system with mass and moment inertia uncertainties. A special Lyapunov function with mass and moment inertia uncertainties is considered to solve the associated Hamilton-Jacobi partial differential inequality (HJPDI). The HJPDI is solved analytically, resulting in a nonlinear H_∞ robust controller with simple proportional feedback structure. Next, the control surface inverse algorithm (CSIA) is introduced to determine the angles of control surface deflection from the nonlinear H_∞ control command. The ranges of prefilter and loss ratio that guarantee stability and robustness of nonlinear H_∞ flight control system implemented by CSIA are derived. Real aerodynamic data, engine data and actuator system of F-16 aircraft are carried out in numerical simulations to verify the proposed scheme. The results show that the responses still keep good convergence for large initial perturbation and the robust stability with mass and moment inertia uncertainties in the permissible ranges of the prefilter and loss ratio for which this design guarantees stability give same conclusion.     

Adaptive backstepping trajectory tracking control of robot manipulator

An adaptive backstepping control scheme is proposed for task-space trajectory tracking of robot manipulators in the presence of uncertain parameters and external disturbances. In the case of external disturbance-free, the developed controller guarantees that the desired trajectory is globally asymptotically followed. Moreover, taking disturbances into consideration, the controller is synthesized by using adaptive technique to estimate the system uncertainties. It is shown that L₂ gain of the closed-loop system is allowed to be chosen arbitrarily small so as to achieve any level of L₂ disturbance attenuation. The associated stability proof is constructive and accomplished by the development of a Lyapunov function candidate. Numerical simulation results are included to verify the control performance of the control approach derived.     

Selective catalytic reduction of NOx with NH3: opportunities and challenges of Cu-based small-pore zeolites

Zeolites, as efficient and stable catalysts, are widely used in the environmental catalysis field. Typically, Cu-SSZ-13 with small-pore structure shows excellent catalytic activity for selective catalytic reduction of NO_x with ammonia (NH₃-SCR) as well as high hydrothermal stability. This review summarizes major advances in Cu-SSZ-13 applied to the NH₃-SCR reaction, including the state of copper species, standard and fast SCR reaction mechanism, hydrothermal deactivation mechanism, poisoning resistance and synthetic methodology. The review gives a valuable summary of new insights into the matching between SCR catalyst design principles and the characteristics of Cu²⁺-exchanged zeolitic catalysts, highlighting the significant opportunity presented by zeolite-based catalysts. Principles for designing zeolites with excellent NH₃-SCR performance and hydrothermal stability are proposed. On the basis of these principles, more hydrothermally stable Cu-AEI and Cu-LTA zeolites are elaborated as well as other alternative zeolites applied to NH₃-SCR. Finally, we call attention to the challenges facing Cu-based small-pore zeolites that still need to be addressed.     

Design and comparison of LQG/LTR and H∞ controllers for a VSTOL flight control system

In this paper two robust controllers for a multivariable vertical short take-off and landing (VSTOL) aircraft system are designed and compared. The aim of these controllers is to achieve robust stability margins and good performance in step response of the system. LQG/LTR method is a systematic design approach based on shaping and recovering open-loop singular values while mixed-sensitivity H_∞ method is established by defining appropriate weighting functions to achieve good performance and robustness. Comparison of the two controllers show that LQG method requires rate feedback to increase damping of closed-loop system, while H_∞ controller by only proper choose the weighting functions, meets the same performance for step response. Output robustness of both controllers is good but H_∞ controller has poor input stability margin. The net controller order of H_∞ is higher than the LQG/LTR method and the control effort of them is in the acceptable range.     

Strong γc-γcl H∞ stabilization for networked control systems under denial of service attacks

This paper is concerned with the strong γ_c-γ_cl H_∞ stabilization problem for networked control systems (NCSs) subject to denial of service (DoS) attacks, which are common attack behaviors that affect the packet transmission of measurement or control signals. The purpose of the problem under consideration is to design a stable dynamic output feedback (DOF) controller (strong stabilizing controller) with the prescribed H_∞ performance norm bound γ_c to tolerate multiple packet dropouts caused by DoS attacks, such that, the closed-loop system is mean-square stable and captures the H_∞ disturbance attenuation norm bound γ_cl. Based on the Lyapunov functional and the stochastic control approach, some sufficient conditions with the form of matrix inequalities for the existence of the desired stable DOF controller are established. Then, by an orthogonal complement space technique, the controller gain is parameterized. Next, an iterative linear matrix inequality (LMI) algorithm is developed to obtain the controller gain. Finally, the usefulness of the proposed method is indicated by a numerical simulation example.     

Interval fuzzy robust non-fragile finite frequency control for active suspension of in-wheel motor driven electric vehicles with time delay

This paper proposes a fuzzy non-fragile finite frequency H_∞ control algorithm for the active suspension system (ASS) of the electric vehicles driven by in-wheel motors with an advanced dynamic vibration absorber (DVA). Firstly, an interval type-2 Takagi-Sugeno (T-S) fuzzy model is established to formulate the nonlinear time-delay ASS with the uncertainties of sprung mass, unsprung mass, suspension stiffness, and tire stiffness. Secondly, a differential evolution (DE) algorithm is adopted to optimize the parameters of vehicle suspension and DVA. Thirdly, a non-fragile finite frequency H_∞ control controller is developed under the consideration of controller perturbation and input delay to improve the comprehensive performance of the chassis under the finite frequency external disturbances. Finally, simulation tests are carried out to verify the effectiveness of the proposed controller.     

Finite-horizon H∞ consensus control for multi-agent systems under energy constraint

In this paper, a finite-horizon H_∞ consensus control problem is studied for multi-agent systems under the limited energy constraint. Due to the limited energy, only a part of agents can use high energy to transmit information infallibly, and the remaining agents are randomly allocated low energy with several levels, which may lead to packet loss in some sense. Different levels result in different packet dropout probability. The purpose of this paper is to design a probability-dependent controller such that, for all probabilistic energy allocation and packet dropout, the H_∞ consensus performance can be guaranteed for multi-agent systems over a finite horizon. To this end, a stochastic and high-availability energy allocation method is first presented via stratified multi-objective optimization methods and stochastic analysis methods. Based on this novel allocation, a H_∞ consensus controller depending on the varying energy allocation is established. Furthermore, in terms of the probability information of both energy allocation and packet dropout, important results are obtained to guarantee the desired performance of the designed probability-dependent controller, and the controller are explicitly parameterized by means of the solutions to a set of linear matrix inequalities. Finally, a simulation example is utilized to illustrate the usefulness of the proposed controller design method.     

Untangling the contributions of meteorological conditions and human mobility to tropospheric NO2 in Chinese mainland during the COVID-19 pandemic in early 2020

In early 2020, unprecedented lockdowns and travel bans were implemented in Chinese mainland to fight COVID-19, which led to a large reduction in anthropogenic emissions. This provided a unique opportunity to isolate the effects from emission and meteorology on tropospheric nitrogen dioxide (NO₂). Comparing the atmospheric NO₂ in 2020 with that in 2017, we found the changes of emission have led to a 49.3 ± 23.5% reduction, which was ∼12% more than satellite-observed reduction of 37.8 ± 16.3%. The discrepancy was mainly a result of changes of meteorology, which have contributed to an 8.1 ± 14.2% increase of NO₂. We also revealed that the emission-induced reduction of NO₂ has significantly negative correlations to human mobility, particularly that inside the city. The intra-city migration index derived from Baidu Location-Based-Service can explain 40.4% ± 17.7% variance of the emission-induced reduction of NO₂ in 29 megacities, each of which has a population of over 8 million in Chinese mainland.     

Mixed H∞ and passivity control for a class of stochastic nonlinear sampled-data systems

In this paper, we consider the problem of mixed H_∞ and passivity control for a class of stochastic nonlinear systems with aperiodic sampling. The system states are unavailable and the measurement is corrupted by noise. We introduce an impulsive observer-based controller, which makes the closed-loop system a stochastic hybrid system that consists of a stochastic nonlinear system and a stochastic impulsive differential system. A time-varying Lyapunov function approach is presented to determine the asymptotic stability of the corresponding closed-loop system in mean-square sense, and simultaneously guarantee a prescribed mixed H_∞ and passivity performance. Further, by using matrix transformation techniques, we show that the desired controller parameters can be obtained by solving a convex optimization problem involving linear matrix inequalities (LMIs). Finally, the effectiveness and applicability of the proposed method in practical systems are demonstrated by the simulation studies of a Chua’s circuit and a single-link flexible joint robot.     

Robust gain-scheduled output feedback yaw stability control for in-wheel-motor-driven electric vehicles with external yaw-moment

This paper presents a robust gain-scheduled output feedback yaw stability H_∞ controller design to improve vehicle yaw stability and handling performance for in-wheel-motor-driven electric vehicles. The main control objective is to track the desired yaw references by managing the external yaw moment. Since vehicle lateral states are difficult to obtain, the state feedback controller normally requires vehicle full-state feedback is a critical challenge for vehicle lateral dynamics control. To deal with the challenge, the robust gain-scheduled output feedback controller design only uses measurements from standard sensors in modern cars as feedback signals. Meanwhile, parameter uncertainties in vehicle lateral dynamics such as tire cornering stiffness and vehicle inertial parameters are considered and handled via the norm-bounded uncertainty, and linear parameter-varying polytope vehicle model with finite vertices is established through reducing conservative. The resulting robust gain-scheduled output feedback yaw stability controller is finally designed, and solved in term of a set of linear matrix inequalities. Simulations for single lane and double lane change maneuvers are implemented to verify the effectiveness of developed approach with a high-fidelity, CarSim^®, full-vehicle model. It is confirmed from the results that the proposed controller can effectively preserve vehicle yaw stability and lateral handling performance.     

Robust mixed H2/H∞ model predictive control for Markov jump systems with partially uncertain transition probabilities

This paper addresses the control problem for a class of discrete-time Markov jump linear systems with partially unknown transition probabilities using model predictive controller subject to external disturbances and input constraints. Our focus is on the design of a model predictive controller to stabilize the system with a given mixed H₂/H_∞ performance index. Sufficient conditions are derived in terms of a set of linear matrix inequalities. Examples are presented to demonstrate the effectiveness of the proposed controller design method.     

Event-based reference tracking control of discrete-time nonlinear systems via delta operator method

This paper investigates the event-based tracking control for delta-sampling systems with a reference model. Takagi–Sugeno (T–S) fuzzy model is used to approximate the nonlinearity. The delta operator is used to implement the discrete-time system. The event trigger is adopted for saving the network resources and the controller forces, and its detection period is designed with the same period of the delta-sampling period. Since the measurement is delayed from the sensor to the event-trigger, the methodology of time-delay systems, called the scaled small gain theorem, is applied for the system stability analysis. The reference output tracking controller is designed to ensure the stability of the resulting system in H_∞ sense. The optimization conditions of the desired H_∞ event-based tracking controller are synthesized, and the simulation example validates its effectiveness finally.     

A modified PID controller (PIIσβD)

The purpose of this study is to modify the traditional PID controller in order to improve its performance (stability and tracking) by changing the length of integration interval. The performance of the traditional PID controller was improved by changing the length of integration interval to make the most of the returns of the PID and PI_σD controllers. The asymptotic stability domain, in terms of the feedback gains, is derived for systems of second order using the modified controller which will be identified as PII_σ^βD. Comparing this controller with the traditional PID controller and PI_σD controller proposed in [1], it proves that it is more accurate and more stable. For illustration and comparison, two examples have been simulated to evaluate the performance of the modified controller. All simulation results indicate that the modified controller is better than the traditional PID controller and the PI_σD controller from the accuracy and stability point of view.     

Lr-synchronization and adaptive synchronization of a class of chaotic Lurie systems under perturbations

The synchronous control of a class of disturbed chaotic Lurie systems is probed in. The conception of L_r-synchronization of drive-respond systems is presented. Via Lyapunov function analysis and comparison principle, L_r synchronous controller of the drive-respond systems under perturbation is given and its robustness is also discussed. Barbalat lemma is further used to derive the adaptively synchronous controller for the unknown disturbance situation and the globally asymptotical synchronization is realized. All designed controllers are verified by the simulations and the given controllers are linear, which are convenient and can produce rapid convergence speed of the error systems.     

H∞ control of singular time-delay systems via discretized Lyapunov functional

This paper addresses the problem of robust H_∞ control for uncertain continuous time singular systems with state delays. A new singular-type complete quadratic Lyapunov-Krasovskii functional (LKF) is introduced, which combines with the discretization LKF method to synthesis problems. An improved bounded real lemma (BRL) is presented to ensure the system to be regular, impulse free and stable with H_∞ performance condition. Based on the BRL, a memoryless state feedback controller is designed via linear matrix inequalities (LMIs), which greatly reduces the disturbance attenuation level. Numerical examples are given to illustrate improvements over some existing results.     

H∞ reduced-order observer-based controller synthesis approach for T-S fuzzy systems

For continuous-time nonlinear systems represented by Takagi–Sugeno fuzzy models, a new H_∞ reduced-order-observer based controller synthesis structure is investigated in this paper. By the fuzzy reduced-order observer and fuzzy controller, an augmented error system composed of the estimation and control errors is obtained. The fuzzy modeling residual terms are seen as part of the external disturbance, and an extra design matrix is added to facilitate the design process. The robustness and stability conditions are given based on Lyapunov function approach, then the conditions are transformed into convex form to facilitate the numerical solving process. Finally, by the comparison with existing methods in simulation section, the control performance and conservativeness reduction effects of the proposed methods are verified.     

Stability, L1-gain analysis and asynchronous L1-gain control of uncertain discrete-time switched positive linear systems with dwell time

In this paper, the stability, L₁-gain analysis and asynchronous L₁-gain control problems of uncertain discrete-time switched positive linear systems (DSPLSs) with dwell time are investigated. First, several convex and non-convex conditions on dwell time stability of DSPLSs with interval and polytopic uncertainties are presented, and the relation between these conditions is revealed. Then, via a switched dwell-time-dependent co-positive Lyapunov functions (SDTLFs) approach, convex sufficient conditions on L₁-gain analysis and asynchronous L₁-gain control of DSPLSs with interval uncertainties are derived. Meanwhile, via the switched parameter-dwell-time-dependent co-positive Lyapunov functions (SPDTLFs) approach, the L₁-gain analysis and asynchronous L₁-gain controller design problems of DSPLSs with polytopic uncertainties are also solved. The stability and L₁-gain analysis results are given in terms of linear programming (LP). The controller design results are presented in terms of bilinear programming (BP), which can be solved with the help of iterative algorithm. At last, both numerical and practical examples are provided to show the effectiveness of the results.