Decentralized adaptive backstepping stabilization of interconnected systems with dynamic input and output interactions

So far there is still no result available for backstepping based decentralized adaptive stabilization of unknown systems with interactions directly depending on subsystem inputs, even though such interactions commonly exist in practice. In this paper, we provide a solution to this problem by considering both input and output dynamic interactions. To clearly illustrate our approaches, we will start with linear systems and then extend the results to nonlinear systems. Each local controller, designed simply based on the model of each subsystem by using the standard adaptive backstepping technique without any modification, only employs local information to generate control signals. It is shown that the designed decentralized adaptive backstepping controllers can globally stabilize the overall interconnected system asymptotically. The L₂ and L_∞ norms of the system outputs are also established as functions of design parameters. This implies that the transient system performance can be adjusted by choosing suitable design parameters.     

Decentralized adaptive stabilization in the presence of unknown backlash-like hysteresis

Due to the difficulty of handling both hysteresis and interactions between subsystems, there is still no result available on decentralized stabilization of unknown interconnected systems with hysteresis, even though the problem is practical and important. In this paper, we provide solutions to this challenging problem by proposing two new schemes to design decentralized output feedback adaptive controllers using backstepping approach. For each subsystem, a general transfer function with arbitrary relative degree is considered. The interactions between subsystems are allowed to satisfy a nonlinear bound with certain structural conditions. In the first scheme, no knowledge is assumed on the bounds of unknown system parameters. In case that the uncertain parameters are inside known compact sets, we propose an alternative scheme where a projection operation is employed in the adaptive laws. In both schemes, the effects of the hysteresis and the effects due to interactions are taken into consideration in devising local control laws. It is shown that the designed local adaptive controllers can ensure all the signals in the closed-loop system bounded. A root mean square type of bound is obtained for the system states as a function of design parameters. This implies that the transient system performance can be adjusted by choosing suitable design parameters. With Scheme II, the proposed control laws allow arbitrarily strong interactions provided their upper bounds are available. In the absence of hysteresis, perfect stabilization is ensured and the L₂ norm of the system states is also shown to be bounded by a function of design parameters when the second scheme is applied.     

Decentralized global disturbance attenuation for a class of large-scale uncertain nonlinear systems

This paper studies the problem of global robust disturbance attenuation via decentralized state feedback for a class of large-scale nonlinear systems with parameter and interconnection uncertainties. The parameter uncertainty is from a compact set and the uncertain interconnections are bounded by higher-order polynomials of state variables. The problem that we address is to design a robust decentralized controller such that the closed-loop large-scale nonlinear system is input-to-state stable and the L₂ gain from the disturbance input to the controlled output is below a prescribed value for all admissible uncertain parameters and interconnections. A Lyapunov-based recursive design approach is developed to construct the decentralized controller explicitly. As a special case, the problem of almost disturbance decoupling via decentralized state feedback is also solved.     

Design of decentralized robust controller for voltage regulation and stabilization of multimachine power systems

This paper presents a decentralized state-feedback controller design based on robust control theory to ensure system stability and voltage regulation in multimachine power systems. The power system is decomposed in n subsystems each represented by a state-space model with bounded parameter uncertainties and unknown input disturbances of class L _∞ which model couplings with the generators of the others subsystems. The proposed controller designed according to a Riccati-based approach is robust with respect to uncertain network parameters and counteracts the effects of the disturbances. A stability analysis in presence of L _∞ disturbances is also given. The control law is straightforward and cost effective because it is function of constant gains and of local measurable machine variables. Numerical simulations give evidence of the achievements in terms of system transient stability as well as voltage regulation, also in comparison with another design technique.     

Robust decentralized direct adaptive output feedback fuzzy control for a class of large-sale nonaffine nonlinear systems

In the previous work of Huang et al., a decentralized direct adaptive fuzzy H_∞ tracking controller of large-scale nonaffine nonlinear systems is obtained predicated upon the assumption that the mismatching error dynamics stay squared integrable. In this note, we focus in the absence of the conservative assumption upon developing a robust decentralized direct adaptive output feedback fuzzy controller. By combination of a state observer, a fuzzy inference system and robust control technique, the previous controller design is modified and no a priori knowledge of bounds on lumped uncertainties is required. All the signals of the closed-loop large-scale system are proved to be uniformly ultimately bounded. The effectiveness of the developed scheme is demonstrated through the simulation results of interconnected inverted pendulums.     

Adaptive control of linear time-varying systems

Single-input single-output uncertain linear time-varying systems are considered, which are affected by unknown bounded additive disturbances; the uncertain time-varying parameters are required to be smooth and bounded but are neither required to be sufficiently slow nor to have known bounds. The output, which is the only measured variable, is required to track a given smooth bounded reference trajectory. The undisturbed system is assumed to be minimum-phase and to have known and constant relative degree, known sign of the ‘high frequency gain’, known upper bound on the system order. An adaptive output feedback control algorithm is designed which assures: (i) boundedness of all closed-loop signals; (ii) arbitrarily improved transient performance of the tracking error; (iii) asymptotically vanishing tracking error when parameter time derivatives are L₁ signals and disturbances are L₂ signals.     

Decentralized stabilization of Markovian jump interconnected systems with unknown interconnections and measurement errors

This paper investigates the decentralized output feedback control problem for Markovian jump interconnected systems with unknown interconnections and measurement errors. Different from some existing results, the global operation modes of all subsystems are not required to be completely accessible for the decentralized control system. A decentralized dynamic output feedback controller is constructed using neighboring mode information and local outputs, where the measurement errors between actual and measured outputs are considered. Subsequently, a new design method is developed such that the resultant closed‐loop system is stochastically stable and satisfying an L_∞‐norm constraint. Sufficient conditions are formulated by linear matrix inequalities, and the controller gains are characterized in terms of the solution of a convex optimization problem. Finally, an example is given to illustrate the effectiveness of the proposed theoretical results.     

Almost disturbance decoupling of MIMO nonlinear systems and application to chemical processes

The problem of almost disturbance decoupling is considered for a class of nonlinear systems with unmeasurable time-varying disturbances. A structure, called nested lower triangular form, is introduced, which contains lower triangular form as a special case. The backstepping design technique is applied to construct an H_∞ feedback controller which achieves internal stability of the closed-loop system and renders a bounded L₂ gain from the disturbance input to the output. The application of the developed design method is illustrated through a two continuous stirred tank reactor example, which can be put into the nested lower triangular form.     

L 2-gain analysis and anti-windup design of discrete-time switched systems with actuator saturation

This paper investigates L2-gain analysis and anti-windup compensation gains design for a class of discrete-time switched systems with saturating actuators and L2 bounded disturbances by using the switched Lyapunov function approach.For a given set of anti-windup compensation gains,we firstly give a sufficient condition on tolerable disturbances under which the state trajectory starting from the origin will remain inside a bounded set for the corresponding closed-loop switched system subject to L2 bounded disturbances.Then,the upper bound on the restricted L2-gain is obtained over the set of tolerable disturbances.Furthermore,the antiwindup compensation gains aiming to determine the largest disturbance tolerance level and the smallest upper bound of the restricted L2-gain are presented by solving a convex optimization problem with linear matrix inequality(LMI) constraints.A numerical example is given to illustrate the effectiveness of the proposed design method.     

Decentralized robust H<Subscript>∞</Subscript> output feedback control for value bounded uncertain large-scale interconnected systems

In this paper, decentralized robust H_∞ output feedback control problem for large-scale interconnected system with value bounded uncertainties in the state, control input and interconnection matrices is investigated. A new bounded real lemma for the large-scale interconnected systems is derived by Lyapunov stability theory and linear matrix inequality method. Based on the new bounded real lemma, a sufficient condition expressed as matrix inequalities for the existence of a decentralized robust H_∞ output feedback controller is obtained. The controller which enables the closed-loop large-scale system robust stable and satisfies the given H_∞ performance is designed through a homotopy iterative method. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.     

Decentralized control and communication

In this paper, the past and current issues involved in the design of decentralized networked control systems are reviewed. The basic models of interconnected systems described as continuous-time linear time-invariant systems in the time domain serve as a framework for the inclusion of communication channels in the decentralized feedback loop. The I/O-oriented models and the interaction oriented models with disjoint subsystems and interactions are distinguished. The overview is focused on packet dropouts, transmission delays, and quantization effects which are included in the time-driven design of feedback loop components. Single- and multiple-packet transmissions are considered in this contents. The design of decentralized state feedback gain matrices with delayed feedback uses the methodology of sampled-data feedback design for continuous-time systems, while the decentralized H_∞ quantizer design is based on the static output controller. The Liapunov stability approach results in computationally efficient decentralized control design strategies described by using linear matrix inequalities.     

具有动态和静态关联项大系统的鲁棒分散自适应镇定

对于一类具有动态和静态关联项的大系统，利用MT-滤波器和反推设计方法设计了一种鲁棒分散自适应输出反馈控制器．在各子系统为最小相位、静态关联项满足Lipschitz条件、动态关联项稳定且严格正则的假设下，证明了闭环系统的所有信号全局一致有界，且除了参数估计外的其他信号皆以指数速率收敛到零，该结果好于其他相关文献中的结果，仿真结果进一步验证了该方法的有效性。     

A receding–horizon approach to the nonlinear H∞ control problem

The receding–horizon (RH) methodology is extended to the design of a robust controller of H_∞ type for nonlinear systems. Using the nonlinear analogue of the Fake H_∞ algebraic Riccati equation, we derive an inverse optimality result for the RH schemes for which increasing the horizon causes a decrease of the optimal cost function. This inverse optimality result shows that the input–output map of the closed-loop system obtained with the RH control law has a bounded L₂-gain. Robustness properties of the nonlinear H_∞ control law in face of dynamic input uncertainty are considered.     

L1 adaptive output regulator design with application to Managed Pressure Drilling

This paper presents a modification to L₁ adaptive control that allows for disturbances entering at the output and application of this control strategy to Managed Pressure Drilling with harmonic disturbances representing the heave motion of a floating drilling rig. By incorporating the disturbance at the output into the closed-loop reference model, it is shown that the L₁ adaptive control structure can be left unchanged while the original transient performance bounds are preserved. It is further shown that rejection of the output disturbance can be taken care of entirely in the filter design step of L₁ adaptive control using the internal model principle. A systematic filter design procedure based on LMIs is provided, that requires only one tuning parameter to be adjusted by the designer. The control design is applied to disturbance attenuation and set-point tracking in the so-called heave problem in oil well drilling. We present experimental results of control system tests in a medium size test facility emulating a 900 m long well.     

Active fault tolerant control for nonlinear systems with simultaneous actuator and sensor faults

The goal of this paper is to describe a novel fault tolerant tracking control (FTTC) strategy based on robust fault estimation and compensation of simultaneous actuator and sensor faults. Within the framework of fault tolerant control (FTC) the challenge is to develop an FTTC design strategy for nonlinear systems to tolerate simultaneous actuator and sensor faults that have bounded first time derivatives. The main contribution of this paper is the proposal of a new architecture based on a combination of actuator and sensor Takagi-Sugeno (T-S) proportional state estimators augmented with proportional and integral feedback (PPI) fault estimators together with a T-S dynamic output feedback control (TSDOFC) capable of time-varying reference tracking. Within this architecture the design freedom for each of the T-S estimators and the control system are available separately with an important consequence on robust L ₂ norm fault estimation and robust L ₂ norm closed-loop tracking performance. The FTTC strategy is illustrated using a nonlinear inverted pendulum example with time-varying tracking of a moving linear position reference.     

Stability and robustness analysis of MIMO MRAC using Kp = L 2 D 2 S 2 factorization

For a class of MIMO systems with input and output unmodeled dynamics, bounded disturbances and any relative degree, using the idea of K_p = L ₂ D ₂ S ₂ factorization, the design and analysis of robust direct model reference adaptive control are further investigated in this article. By establishing the L_p and L _2δ relationship properties between the input and output, multivariable swapping lemmas and relating all the signals in the closed-loop system with the normalizing signal, stability and robustness of adaptive system are analyzed rigorously. Compared with the existing results, the proof procedure is more compact and simple. A simulation example verifies the effectiveness of the control scheme.     

Anti-windup synthesis for linear control systems with input saturation: Achieving regional, nonlinear performance

In this paper, we present LMI-based synthesis tools for regional stability and performance of linear anti-windup compensators for linear control systems. We consider both static and dynamic compensators. Algorithms are developed that minimize the upper bound on the regional L₂ gain for exogenous inputs with L₂ norm bounded by a given value, and that minimize this upper bound with a guaranteed reachable set or domain of attraction. Based on the structure of the optimization problems, it is shown that for systems whose plants have poles in the closed left-half plane, plant-order dynamic anti-windup can achieve semiglobal exponential stability and finite L₂ gain for exogenous inputs with L₂ norm bounded by any finite value. The problems are studied in a general setting where the only requirement on the linear control system is well-posedness and internal stability. The effectiveness of the proposed techniques is illustrated with an example.     

A modified normality condition for decentralized supervisory control of discrete event systems

In this paper, we study nonblocking decentralized supervisory control of discrete event systems. We introduce a modified normality condition defined in terms of a modified natural projection map. The modified normality condition is weaker than the original one and stronger than the co-observability condition. Moreover, it is preserved under union. Given a marked language specification, there exists a nonblocking decentralized supervisor for the supremal sublanguage which satisfies L_m(G)-closure, controllability, and modified normality. Such a decentralized supervisor is more permissive than the one which achieves the supremal L_m(G)-closed, controllable, and normal sublanguage.