Nonlinear modelling and control of a common rail injection system for diesel engines

Modern trends in designing mechatronic systems call for a synergic design of the separated subsystems (mechanic, electronic parts, control modules, etc.) concurring to the overall performance. Following this point of view, this paper presents a control oriented model and a nonlinear control design for a Common Rail injection system. First a model is developed, which is tuned in a virtual simulation environment, representing the injection system in details in a reliable replication of reality. Then a sliding mode control is developed. Both the model of the injection process and of the control law are validated by a virtual detailed simulation environment. The prediction capability of the model and the control efficiency are clearly shown.     

Dynamically similar control systems and a globally minimum gain control technique: IMSC

The concept of dynamically similar control systems is introduced. The necessary and sufficient conditions to minimize a quadratic modal gain measure are given for dynamically similar closed-loop control systems. The globally minimum modal gain is obtained when the independent modal space control (IMSC) is used. Corollaries of the results for the control of infinite-dimensional structural distributed parameter systems (DPS) are given. Based on the results, a modal interaction parameter (MIP) is defined for all control systems. The minimum value of MIP is zero and uniquely corresponds to the IMSC. A nonzero value of MIP corresponds to all other coupled control (CC) designs and implies suboptimality relative to the IMSC design. The relative optimality of the real-space gain matrices of the IMSC and the CC designs depends on the actuator locations for the IMSC. Based on this, a real-space interaction parameter (RIP) is defined. A positive value of RIP renders IMSC optimal in its real-space gain matrix. The MIP and RIP are indications of suboptimality of a particular control technique and can be used to tune-up the control design via actuator locations. Actuator distribution criteria are suggested for both CC and IMSC designs, based on the values of MIP and RIP, respectively.This work was supported by the National Science Foundation, Grant No. MEA-82-04920.     

Model predictive control for switched systems with a novel mixed time/event-triggering mechanism

This paper investigates observer-based model predictive control (MPC) for switched systems with a mixed time/event-triggering mechanism. The problem of predictive control that can achieve receding horizon optimization is considered and solved by minimizing an upper bound of the quadratic cost function. Since the system state may not be fully measured in practice, state observers are employed to estimate. A mixed mechanism including adaptive event-triggering and time-triggering is proposed, which can be switched determined by a threshold describing system performance to better balance system resource utilization and performance requirements. Then, a closed-loop switched system subject to networked-time-delay is modeled. Piecewise Lyapunov function technique and average dwell time approach are utilized to ensure asymptotical stability. Afterwards, MPC controller construction problem is turned into a LMIs feasibility problem. A new solving method of sufficient conditions for co-design of the state observers, feedback controllers and mixed triggering mechanism is derived. Lastly, simulation examples illustrate the correctness and advantages of research content.     

Stabilization and control of distributed systems with time-dependent spatial domains

This paper considers the problem of the stabilization and control of distributed systems with time-dependent spatial domains. The evolution of the spatial domains with time is described by a finite-dimensional system of ordinary differential equations, while the distributed systems are described by first-order or second-order linear evolution equations defined on appropriate Hilbert spaces. First, results pertaining to the existence and uniqueness of solutions of the system equations are presented. Then, various optimal control and stabilization problems are considered. The paper concludes with some examples which illustrate the application of the main results.This work was supported by the Air Force Office of Scientific Research, Grant No. AFOSR 86-0132, by the National Science Foundation, Grant No. 87-18473, and by the Jet Propulsion Laboratory, Pasadena, California.     

Output feedback regulation control for a class of cascade nonlinear systems and its application to fan speed control

The output feedback regulation problem is considered for a class of nonlinear systems with integral input-to-state stable (iISS) inverse dynamics and unknown control direction. The system output together with the complete unmeasured state components appears in the system uncertainties. A systematic output feedback control scheme is presented with the help of a dynamic observer, whose gain comes from an off-line time-varying Riccati matrix differential equation. The proposed scheme can be applied to the analysis of the speed tracking control of a fan. The simulation results demonstrate the validity of the presented algorithm.     

Adaptive tracking control for a class of switched uncertain nonlinear systems under a new state-dependent switching law

This paper deals with the problem of adaptive fuzzy tracking control for a class of switched uncertain nonlinear systems. Fuzzy logic systems are utilized to approximate the unknown nonlinear functions, and the adaptive backstepping and dynamic surface control techniques are adopted. First, a new state-dependent switching method is proposed. By introducing convex combination technique and designing a state-dependent switching law, only the solvability of the adaptive tracking control problem for a convex combination of the subsystems is necessary. Second, a new common Lyapunov function with switched adaptive parameters is constructed to reduce the conservatism. Third, to avoid Zeno behavior, a modified state-dependent switching law with dwell time is proposed. It is shown that under the proposed control and switching laws, all the signals of the closed-loop system are bounded and all the state tracking errors can converge to a priori accuracy, even if some subsystems are uncontrollable. Finally, the effectiveness of the proposed method is illustrated through two simulation examples.     

Stabilization problem of stochastic time-varying coupled systems with time delay and feedback control

The stabilization of stochastic coupled systems with time delay and time-varying coupling structure (SCSTT) via feedback control is investigated. We generalize systems with constant coupling structure to the time-varying coupling structure. Combining the graph theory with the Lyapunov method, a systematic method is provided to construct a Lyapunov function for SCSTT, and a Lyapunov-type theorem and a coefficient-type criterion are obtained to guarantee the stabilization in the sense of pth moment exponential stability. Furthermore, theoretical results are applied to analyze the stabilization of stochastic-coupled oscillators with time delay and time-varying coupling structure in order to illustrate the practicability of the results. Finally, two numerical examples are given to illustrate the effectiveness and feasibility of theoretical results.     

An online identification algorithm of unknown time-varying delay and internal multimodel control for discrete non-linear systems

In this paper, an online algorithm is proposed for the identification of unknown time-varying input delay in the case of discrete non-linear systems described by decoupled multimodel. This method relies on the minimization of a performance index based on the error between the real system and the partial internal models outputs. In addition, a decoupled internal multimodel control is proposed for the compensation of discrete non-linear systems with time-varying delay. This control scheme incorporates partial internal model controls. Each partial controller is associated to a specified operating zone of the non-linear system. The switching between these controllers is ensured by a supervisor that contains a set of local predictors. A simulation example is carried out to illustrate the significance of the proposed time-varying delay identification algorithm and the proposed internal multimodel control scheme.     

Exponential synchronization of discontinuous chaotic systems via delayed impulsive control and its application to secure communication

This paper investigates drive-response synchronization of chaotic systems with discontinuous right-hand side. Firstly, a general model is proposed to describe most of known discontinuous chaotic system with or without time-varying delay. An uniform impulsive controller with multiple unknown time-varying delays is designed such that the response system can be globally exponentially synchronized with the drive system. By utilizing a new lemma on impulsive differential inequality and the Lyapunov functional method, several synchronization criteria are obtained through rigorous mathematical proofs. Results of this paper are universal and can be applied to continuous chaotic systems. Moreover, numerical examples including discontinuous chaotic Chen system, memristor-based Chua’s circuit, and neural networks with discontinuous activations are given to verify the effectiveness of the theoretical results. Application of the obtained results to secure communication is also demonstrated in this paper.     

A novel scheme for the design of backstepping control for a class of nonlinear systems

A novel scheme is proposed for the design of backstepping control for a class of state-feedback nonlinear systems. In the design, the unknown nonlinear functions are approximated by the neural networks (NNs) identification models. The Lyapunov function of every subsystem consists of the tracking error and the estimation errors of NN weight parameters. The adaptive gains are dynamically determined in a structural way instead of keeping them constants, which can guarantee system stability and parameter estimation convergence. When the modeling errors are available, the indirect backstepping control is proposed, which can guarantee the functional approximation error will converge to a rather small neighborhood of the minimax functional approximation error. When the modeling errors are not available, the direct backstepping control is proposed, where only the tracking error is necessary. The simulation results show the effectiveness of the proposed schemes.     

Quantized control for networked switched systems under denial-of-service attacks via a barrier event-triggered mechanism

This paper studies the quantized control problem for networked switched systems (NSSs) under denial-of-service (DoS) attacks. The quantized state information, together with the switching signal, is transmitted to the controller through a network. In order to reduce communication consumption and controller update frequency, a barrier event-triggered mechanism is utilized to monitor the state at discrete time. Because of the event-triggered mechanism and the DoS attacks on the network, the mismatch between the system mode and the controller mode is thus frequently encountered, which may lead to quantization saturation and system instability. To solve the problem, an update rule is presented for the dynamic quantizer by switching between zooming in and zooming out of the zooming variable, and a feedback controller is proposed with a jointly designed event-triggered mechanism and a dynamic quantizer. Sufficient conditions on the constraints of DoS frequency and duration are obtained to ensure the exponential stability of the switched system. The effectiveness of the obtained results is illustrated by simulation examples and comparative studies.     

Dynamics and control of a system of two non‐interacting preys with common predator

In this paper, we consider a Holling type model, which describes the interaction between two preys with a common predator. First, we give some sufficient conditions for the globally asymptotic stability and prove that local stability implies global stability. Then, we present a set of sufficient conditions for the existence of a positive periodic solution with strictly positive components. Finally, the optimal control strategy is developed to minimize the number of predator and maximize the number of preys. We also show the existence of an optimal control for the optimal control problem and derive the optimality system. The technical tool used to determine the optimal strategy is the Pontryagin Maximum Principle. Finally, the numerical simulations of global stability and the optimal problem are given as the conclusion of this paper. Copyright © 2011 John Wiley & Sons, Ltd.     

Stabilization for a class of nonlinear networked control systems via polynomial fuzzy model approach

This article is concerned with the stabilization problem for nonlinear networked control systems which are represented by polynomial fuzzy models. Two communication features including signal transmission delays and data missing are taken into account in a network environment. To solve the network‐induced communication problems, a novel sampled‐data fuzzy controller is designed to guarantee that the closed‐loop system is asymptotically stable. The stability and stabilization conditions are presented in terms of sum of squares (SOS), which can be numerically solved via SOSTOOLS. Finally, a simulation example is provided to demonstrate the feasibility of the proposed method. © 2014 Wiley Periodicals, Inc. Complexity 21: 74–81, 2015     

Flow regulation for water quality restoration in a river section: Modeling and control

This work is devoted to the numerical resolution of an optimal control problem that arises in the management of a reservoir for the remediation of a polluted river section. By using mathematical modeling and optimal control techniques we set the mathematical formulation of the problem (as a hyperbolic optimal control problem with control constraints), and obtain a fully discretized problem. Finally, we propose a gradient-free method to solve it, and present realistic numerical results.     

Semigroup approach for the approximation of a control problem with unbounded dynamics

In this paper, we approximate a control problem in an infinite-dimensional Hilbert space by means of a sequence of discrete problems. In the differential equation which describes the dynamics, a Lipschitz perturbation of an unbounded linear operator appears. We prove a convergence result of the approximation value functions to the value function of the original problem.This research was supported by Ministero dell'Università e della Ricerca Scientifica e Technologica and by Consiglio Nazionale delle Ricerche, Rome, Italy.     

Model simplification and digital design of multivariable sampled-data control systems via a dominant-data matching method

A dominant-data matching method is developed for model simplification and design of digital multivariable sampled-data control systems. A mixed method combining dominant-data matching and the dominant-pole technique is also derived for determining a stable reduced-degree multivariable digital controller. A real semiactive terminal homing missile system is used as an illustrative example.     

A new control method and its robustness for a class of nonlinear systems

For a class of time-varying nonlinear systems described by the equation , the precalculating control is not available if the input matrixg(x,t) is not invertible. With Lyapunov's second method, a stabilizing controller which makes the system practically stable is constructed in this paper. It is shown that the implementation of this scheme depends on some so-called posi-invertibility conditions forg(x,t). In case the system is partly stable, the method, named part-calculating control, can simplify the on-line computations. Without the assumption that the nominal system is asymptotically stable, the method is applied to the problems of control for the corresponding uncertain system that satisfies the matching condition. When the matching condition is not satisfied, the mismatching control problem is also studied with Lyapunov's second method.This work was supported by the Science Fund of the Chinese Academy of Science.     

Nonfragile dynamic output-feedback control for positive singular systems under the switched mechanism and Round-Robin protocol

In this paper, the singular positive system with uncertain parameters and switched structure is analyzed. First of all, a nonfragile dynamic output-feedback controller with Round-Robin protocol is constructed so as to decrease the occupancy of the communication channels and overcome the phenomenon of controller gain fluctuations. Then, the regularity, causality, positivity, and robustly exponential stability of the resultant closed-loop system are discussed respectively by utilizing the method of mode dependent minimum dwell time, mode dependent ranged dwell time, and mode dependent constant dwell time. The explicit design mechanisms of the related controller parameters are simultaneously presented. Finally, two simulation examples are provided to show feasibility of the theoretical results obtained.